Predicting hospital length of stay using machine learning on a large open health dataset

Raunak Jain, Mrityunjai Singh, A. Ravishankar Rao, Rahul Garg
BMC Health Services Research
Indian Institute of Technology, Delhi, India

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Table of Contents

Overall Summary

Study Background and Main Findings

This research investigates the application of machine learning to predict hospital Length of Stay (LoS), a crucial factor in healthcare cost estimation and resource management. Using a large, publicly available dataset from the New York State Statewide Planning and Research Cooperative System (SPARCS), containing 2.3 million de-identified patient records, the authors develop and evaluate various predictive models. A key aspect of their approach is the emphasis on model interpretability, ensuring that the results are understandable and actionable for healthcare professionals.

The study employs a robust methodology, including data pre-processing, feature engineering, and the development of both classification and regression models. Several machine learning algorithms are explored, including linear regression, random forests, and CatBoost. Performance is evaluated using metrics such as R-squared (R2) for regression and Area Under the Curve (AUC) for classification. The models are trained and tested on separate datasets to assess their generalizability. Feature importance is analyzed using SHAP (SHapley Additive Explanations) values to understand the key drivers of LoS predictions.

The results demonstrate the effectiveness of machine learning in predicting LoS, with R2 scores of 0.82 for newborns using linear regression and 0.43 for non-newborns using CatBoost regression. Focusing on specific conditions, such as cardiovascular disease, further improves the predictive accuracy. Importantly, the study finds no evidence of bias based on demographic features like race, gender, or ethnicity. The authors also highlight the practical utility of interpretable models, such as decision trees, which provide clear, rule-based predictions based on key features like birth weight for newborns and diagnostic-related group classifications for non-newborns.

The study concludes that machine learning offers a valuable tool for predicting LoS and informing healthcare management decisions. The authors advocate for open data and open-source methodologies to promote transparency and reproducibility in healthcare research. They also acknowledge limitations in the available data, such as the lack of detailed physiological information and co-morbidity data, and suggest directions for future research.

Research Impact and Future Directions

This study makes a valuable contribution to healthcare analytics by demonstrating the potential of machine learning for predicting Length of Stay (LoS), a critical factor in cost management and resource allocation. The focus on model interpretability, particularly through the use of decision trees, enhances the practical utility of the findings for healthcare providers and administrators. The authors' commitment to open data and open-source methodology further strengthens the study's impact, promoting transparency and reproducibility in this important area of research.

While the models achieve reasonable predictive accuracy, particularly for newborns, the limitations imposed by the available data (e.g., lack of physiological data, co-morbidity information) are acknowledged. The study's strength lies in its broad scope, analyzing LoS across a wide range of disease categories and a large patient population, providing a high-level system view. This broad perspective, combined with the emphasis on interpretable models, allows for the identification of key drivers of LoS and informs potential areas for targeted interventions or policy changes.

The study's design, using readily available public data, inherently limits the strength of causal claims that can be made. However, it successfully demonstrates the feasibility and potential of machine learning for LoS prediction, paving the way for future research using more granular data and more sophisticated modeling techniques. The authors' advocacy for open data and open-source methods, combined with their clear articulation of the study's limitations and potential future directions, positions this work as a valuable contribution to the growing field of healthcare analytics.

Critical Analysis and Recommendations

Effective Summary of Key Aspects (written-content)
The abstract effectively summarizes the study's key aspects: the problem of LoS prediction, the use of a large dataset, the focus on interpretability, and specific performance metrics. This concise summary is crucial for attracting readers and conveying the study's significance.
Section: Abstract
Quantify "Promising Results" for Impact (written-content)
The abstract could be strengthened by immediately quantifying the "promising results" with the most impressive R2 score (0.82 for newborns) to enhance impact.
Section: Abstract
Strong Contextualization within Transparency and Open Data (written-content)
The introduction effectively contextualizes the research within the broader movement towards transparency in government and healthcare, establishing the relevance of open data initiatives.
Section: Introduction
Specify LoS Prediction Earlier for Focus (written-content)
The introduction could be improved by specifying LoS prediction as the core problem earlier, rather than waiting until the end of paragraph six, to enhance focus.
Section: Introduction
Clear Articulation of System Requirements (written-content)
The method section clearly articulates the requirements for an ideal system (open-source, interpretable models, understanding feature impact), providing a strong ethical and practical foundation.
Section: Method
Clarify Overarching Methodological Goal Upfront (written-content)
The method section could be improved by explicitly stating the overarching goal (LoS prediction) at the very beginning to orient the reader before delving into specific procedures.
Section: Method
Ambiguous Placement of 'User query' in Figure 1 (graphical-figure)
Figure 1 provides a clear visual overview of the system architecture, but the placement of 'User query' is ambiguous and could be clarified.
Section: Method
Comprehensive Multi-Metric Evaluation (written-content)
The results section uses a diverse suite of metrics (R2, p-value, TPR, FNR, F1, Brier score, AUC, Delong test) to thoroughly evaluate model performance, providing a robust assessment.
Section: Results
Improve Narrative Cohesion Between Result Subsections (written-content)
The results section could be improved by enhancing narrative cohesion between the diverse analytical components (descriptive statistics, feature engineering, model results) to aid reader synthesis.
Section: Results
Honest Appraisal of Model Limitations for Specific Conditions (written-content)
The discussion honestly appraises the challenges in modeling LoS for certain conditions (e.g., schizophrenia, mood disorders) and attributes this to data limitations and inherent variability, demonstrating transparency.
Section: Discussion
Explicitly Discuss Interpretability Trade-offs for Practical Guidance (written-content)
The discussion could be strengthened by explicitly linking the best-performing models (e.g., CatBoost) to their interpretability trade-offs compared to simpler models like decision trees, providing more practical guidance.
Section: Discussion
Effective Summary of Main Achievement and Significance (written-content)
The conclusion effectively summarizes the study's main achievement (LoS prediction pipeline), its scale, and its relevance to healthcare costs, reinforcing the key takeaway.
Section: Conclusion
Elaborate on LoS-Cost Implication for Stakeholders (written-content)
The conclusion could be strengthened by briefly elaborating on how the direct relationship between LoS and costs translates into actionable value for healthcare administrators and policymakers, enhancing the impact for these stakeholders.
Section: Conclusion

Section Analysis

Abstract

Key Aspects

Strengths

Suggestions for Improvement

Introduction

Key Aspects

Strengths

Suggestions for Improvement

Method

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

Fig. 1 Shows the system architecture.
Figure/Table Image (Page 5)
Fig. 1 Shows the system architecture.
First Reference in Text
We have designed the overall system architecture as shown in Fig. 1.
Description
  • Data Sourcing: The diagram outlines a multi-stage system for predicting hospital length of stay. It begins with 'Open Healthcare data sources', specifically citing 'NY SPARCS' (New York State Statewide Planning and Research Cooperative System, a database of hospital discharge data) as an example input.
  • Data Preprocessing: The raw data then undergoes 'Data Cleansing/ETL'. ETL stands for Extract, Transform, Load, which is a standard process in data management where data is taken from a source, converted into a usable format, and then loaded into a target system or database. This step prepares the data for analysis.
  • Feature Engineering: Following cleansing, 'Feature Selection/Encoding' occurs. 'Feature selection' is the process of choosing the most relevant data attributes (features) for model building, while 'feature encoding' involves converting categorical data (non-numeric data like 'type of admission') into a numerical format that machine learning algorithms can understand.
  • Predictive Modeling: The core of the system is 'Predictive Modeling with Open-Source tools'. This stage takes 'Input features' (the selected and encoded data) and potentially a 'User query' to train and utilize various machine learning models. The specific models shown are 'Linear Regression' (a statistical method to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation), 'Random Forest' (an ensemble learning method that operates by constructing multiple decision trees during training and outputting the class that is the mode of the classes or mean prediction of the individual trees), and 'CART' (Classification and Regression Trees, a type of decision tree algorithm). The output of this stage is 'Trained models'.
  • Output Generation: Finally, the 'Trained models' are used to generate the 'Predicted Variable (Length of Stay)', which is the ultimate output of the system.
  • Underlying Technology Stack: The figure caption also notes that the system is implemented using 'Python-based open-source tools such as Pandas and Scikit-Learn'. Python is a versatile programming language; Pandas is a popular Python library for data manipulation and analysis; and Scikit-Learn is a comprehensive Python library for machine learning, providing tools for various tasks including classification, regression, and clustering.
Scientific Validity
  • ✅ Logical and standard workflow: The depicted architecture follows a standard and logical workflow for a machine learning project, starting from data acquisition and preprocessing, through feature engineering, to model training and prediction. This is an appropriate high-level design for the stated goal of predicting hospital length of stay.
  • ✅ Use of open-source tools: The explicit mention of open-source tools (Python, Pandas, Scikit-Learn in caption; Linear Regression, Random Forest, CART in diagram) suggests a commitment to reproducible and accessible methods, which is a strength in scientific research.
  • 💡 High-level overview requiring further textual detail: The diagram provides a high-level overview. For full methodological assessment, details on the specifics of each stage (e.g., specific cleansing techniques, feature selection algorithms, encoding methods, hyperparameter tuning for models) would be necessary in the methods text. The diagram itself is not intended to convey this level of detail but serves as a good conceptual map.
  • ✅ Indication of multiple model exploration: The inclusion of multiple model types (Linear Regression, Random Forest, CART) indicates an intention to explore or compare different approaches, which is good practice for finding the best performing model.
  • ✅ Appropriate separation of preprocessing stages: The separation of 'Data Cleansing/ETL' and 'Feature Selection/Encoding' into distinct steps is appropriate, as these are crucial and often complex phases in building effective predictive models from real-world healthcare data like SPARCS.
  • ✅ Supports claims in reference text: The diagram strongly supports the reference text's claim of having designed an overall system architecture. It visually represents the components and flow described.
Communication
  • ✅ Clear visual flow and logical structure: The diagram effectively uses a top-down flow structure with clear boxes and arrows, making the overall process easy to follow. The use of distinct stages (Data Cleansing, Feature Selection, Predictive Modeling) is logical.
  • ✅ Informative labels for components: The labels within the boxes are generally clear and concise. The inclusion of specific model types (Linear Regression, Random Forest, CART) within the 'Predictive Modeling' stage is informative.
  • 💡 Integrate specific tools mentioned in caption into the diagram: While the caption mentions Python, Pandas, and Scikit-Learn, these are not explicitly shown within the diagram itself. Integrating these specific tools into the relevant stages (e.g., 'Predictive Modeling with Open-Source tools [Python, Scikit-Learn]') could enhance clarity and make the diagram more self-contained.
  • 💡 Ambiguity of 'User query' placement: The term 'User query' is slightly ambiguous in its placement. Clarify if it's an input for model selection, feature selection, or a trigger for the entire prediction process. Perhaps position it more clearly as an initial input to the system or to a specific part of the modeling pipeline.
  • 💡 Input arrows to 'Predictive Modeling' could be more specific: The arrows clearly indicate the direction of data flow, which is a good practice. However, the arrow from 'User query' and 'Input features' points to the general 'Predictive Modeling' box, not directly to the models. It might be clearer if these inputs were shown to feed into the process that uses the models, or directly to the models if they are parameterized by these inputs.
  • ✅ Simplicity and lack of clutter: The diagram is relatively simple and avoids clutter, which aids in understanding the high-level architecture.
Fig. 2 Shows the processing stages in our analytics pipeline
Figure/Table Image (Page 6)
Fig. 2 Shows the processing stages in our analytics pipeline
First Reference in Text
In Fig. 2, we provide a detailed overview of the necessary processing stages.
Description
  • Initial Data Input: The diagram illustrates an analytics pipeline starting with 'Data in SQL database'. An SQL database is a structured system for storing and retrieving data.
  • Data Loading: The data is then 'Read into Pandas Dataframe'. Pandas is a software library used for data manipulation and analysis, particularly in the Python programming language. A DataFrame is a two-dimensional, size-mutable, and potentially heterogeneous tabular data structure with labeled axes (rows and columns), similar to a spreadsheet.
  • Data Cleansing: Next is 'Data cleansing', which involves identifying and correcting or removing errors, inconsistencies, and inaccuracies from the dataset to improve its quality.
  • Data Splitting: The cleansed data is then 'Split into train/test sets'. This is a standard machine learning practice where the dataset is divided into two subsets: a 'Training Set' used to build the predictive model, and a 'Test Set' used to evaluate the model's performance on unseen data.
  • Test Set Processing: For the 'Test Set', 'Numerical variables' are processed directly, while 'Categorical variables' (non-numeric data like gender or diagnosis codes) are converted 'to numbers'. Both lead to a 'Numeric representation' of the test data. This conversion is necessary because most machine learning algorithms require numerical input.
  • Training Set Processing and Encoding: For the 'Training Set', 'Numerical variables' are also processed. 'Categorical variables' undergo 'Target encoding' and 'Label encoding'. 'Target encoding' is a technique where each category is replaced by a statistical measure (like the mean) of the target variable (e.g., length of stay) for that category. 'Label encoding' assigns a unique integer to each category. These encoded variables are then 'Mapping to numbers', resulting in a 'Numeric representation' of the training data.
  • Feature Selection and Explainability: The 'Numeric representation' from the Training Set proceeds to 'Feature Selection & Explainability'. 'Feature selection' is the process of identifying and selecting the most relevant input variables (features) for the model. 'Explainability' refers to techniques that help understand how a model arrives at its predictions.
  • Model Training: This is followed by 'Train relevant models', where machine learning algorithms are applied to the selected features from the training data to learn patterns and create predictive models.
  • Prediction Output: The pipeline then leads to 'Prediction (Length of stay)', which is the output generated by the trained models, presumably when applied to new data (like the test set).
  • Model Evaluation and Interpretation: Finally, the process includes 'Model Evaluation', where the performance of the trained models is assessed (typically using the test set), and 'Model interpretation', which involves understanding the behavior and decisions of the developed models.
Scientific Validity
  • ✅ Standard and sound machine learning workflow: The pipeline depicts a standard and methodologically sound approach to a supervised machine learning task, including crucial steps like data cleansing, train/test splitting, feature encoding, feature selection, model training, and evaluation.
  • ✅ Correct handling of train/test split principle: The explicit separation of processing for training and test sets is critical to prevent data leakage and ensure a valid evaluation of model generalization. The diagram correctly shows distinct paths for these.
  • ✅ Acknowledgment of multiple encoding strategies: The inclusion of different encoding strategies ('Target encoding', 'Label encoding') for categorical variables in the training phase demonstrates an awareness of various techniques to handle such data, which can impact model performance.
  • ✅ Emphasis on feature selection, explainability, and interpretation: The stages of 'Feature Selection & Explainability' and 'Model interpretation' are important for building robust and trustworthy models, especially in healthcare. Their inclusion is a positive aspect.
  • 💡 High-level diagram; specifics of methods not shown: The diagram is a high-level overview. The scientific rigor of the actual implementation would depend on the specific algorithms chosen for each step (e.g., cleansing methods, feature selection algorithms, evaluation metrics), which are not detailed in the diagram itself but would be expected in the accompanying text.
  • 💡 Implication of consistent encoding application to test set: The process for encoding categorical variables in the 'Test Set' ('Categorical variables to numbers') is shown separately. It's crucial that any parameters learned during encoding (e.g., from target encoding or label mapping in the training set) are applied consistently to the test set, rather than re-learning from the test set. The diagram simplifies this, but the principle must be followed in practice.
  • 💡 Cross-validation not explicitly shown: The diagram doesn't explicitly show steps like cross-validation within the training phase, which is a common technique for robust model training and hyperparameter tuning. This might be an implicit part of 'Train relevant models' or detailed elsewhere.
Communication
  • ✅ Clear flow and structure: The flowchart uses a clear top-down and branching structure, which effectively illustrates the sequence and parallel processing of data. Arrows distinctly guide the reader through the pipeline.
  • ✅ Concise and appropriate labels: The labels within the boxes are generally concise and use appropriate terminology for a data analytics pipeline. This aids in understanding the function of each stage.
  • ✅ Clear distinction between training and test set processing: The diagram visually separates the processing for the training set and the test set, which is a crucial distinction in machine learning workflows.
  • 💡 Test set pathway to evaluation could be more explicit: While generally clear, the connection between the processed 'Test Set' and 'Model Evaluation' is not explicitly drawn with an arrow, though it is implied. Adding an arrow from the 'Numeric representation' of the Test Set to 'Model Evaluation' (perhaps showing the trained model being applied to it) would make the evaluation pathway more explicit.
  • ✅ Consistent visual style: The diagram uses a consistent visual style for boxes and arrows, contributing to a professional and easy-to-read presentation.
  • ✅ Appropriate level of detail for an overview: The level of detail is appropriate for a high-level overview of the pipeline. It successfully communicates the major stages without becoming overly cluttered.
  • 💡 Potential for color coding to enhance differentiation: Consider using subtle color coding to differentiate between data states (e.g., raw data, processed features, models) or types of operations (e.g., preprocessing, modeling, evaluation) to enhance visual segmentation and comprehension further.
Fig. 3 Distribution of the length of stay in the dataset
Figure/Table Image (Page 7)
Fig. 3 Distribution of the length of stay in the dataset
First Reference in Text
We examine the distribution of the LoS in the dataset, as shown in Fig. 3.
Description
  • Axes and Scale: The figure is a histogram visualizing the distribution of 'Length of Stay' (LoS) for patients in the dataset. The horizontal x-axis represents the Length of Stay, ranging from 0 up to 120 units, which are presumably days. The vertical y-axis, labeled 'Count', represents the number of patient records corresponding to each length of stay, and it is presented on a logarithmic scale, with major ticks at 10^2 (100), 10^3 (1,000), 10^4 (10,000), and 10^5 (100,000).
  • Shape of Distribution: The distribution is heavily right-skewed, meaning that the vast majority of patients have very short lengths of stay, with the frequency decreasing rapidly as the length of stay increases. The highest counts (appearing to exceed 10^5, or 100,000 patients) are for the shortest lengths of stay, likely 1 or 2 days. For example, the first bar, representing the shortest LoS, is the tallest.
  • Truncation at 120 Days: There is a noticeable and abrupt spike in the count at the 120-day mark on the x-axis. The count for LoS = 120 days is significantly higher than for stays immediately preceding it (e.g., 100-119 days), reaching a count of approximately 10^4 (10,000). This suggests an artificial limit or truncation in the data recording at 120 days, as mentioned in the text (page 5, 'We note that the providers of the data have truncated the length of stay to 120 days.').
  • Frequency Decline: Beyond the initial very short stays, the counts gradually decrease. For instance, around 20 days, the count is roughly 10^4 (10,000). By 40 days, it drops to around 10^3 (1,000). For lengths of stay around 60, 80, and 100 days, the counts are progressively lower, well below 10^3.
Scientific Validity
  • ✅ Appropriate visualization choice: A histogram is an appropriate visualization technique for understanding the distribution of a continuous or discrete numerical variable like Length of Stay (LoS). It effectively shows the frequency of different LoS values.
  • ✅ Justified use of logarithmic scale: The use of a logarithmic scale on the y-axis is scientifically sound and necessary here, given the highly skewed nature of LoS data where short stays are very common and long stays are rare. Without it, the variation in frequencies for longer stays would be invisible.
  • ✅ Accurately depicts typical LoS distribution characteristics: The figure clearly illustrates the right-skewed nature of LoS data, which is a common characteristic in healthcare datasets. This visual confirmation is important for subsequent modeling choices (e.g., transformations or using models robust to skewed data).
  • ✅ Highlights data truncation issue: The prominent spike at 120 days strongly suggests data truncation, as confirmed by the authors in the text. This is a critical feature of the dataset that the histogram successfully highlights, and it has important implications for data analysis and model interpretation (e.g., LoS values are capped).
  • 💡 Binning details not specified: The figure itself does not provide information on the binning strategy (e.g., width of each bar). While the overall shape is clear, the exact count for precise LoS values (e.g., exactly 1 day vs. 2 days) is hard to discern from the bars at the very beginning due to the scale and binning, though the general trend is evident.
  • ✅ Strongly supports reference text: The figure strongly supports the reference text's statement that it shows the distribution of LoS in the dataset. The visual evidence is direct and clear.
Communication
  • ✅ Appropriate chart type: The histogram effectively uses bars to represent the frequency of different lengths of stay. The choice of a histogram is appropriate for visualizing the distribution of a continuous variable.
  • ✅ Clear axis labels: The x-axis ('Length of Stay') and y-axis ('Count') are clearly labeled. The units for length of stay appear to be days, although not explicitly stated on the axis label itself, it's implied by the context of hospital stays and the integer values.
  • ✅ Effective use of logarithmic scale for y-axis: The y-axis uses a logarithmic scale (10^2, 10^3, 10^4, 10^5), which is crucial for visualizing data with a wide range of frequencies, as is the case here. This allows both the high counts for short stays and the lower counts for longer stays to be visible on the same plot.
  • 💡 Bin width information: The x-axis ticks are at intervals of 20 (0, 20, 40, ..., 120). This provides a good overview, but the exact bin widths are not explicitly stated, though they appear to be relatively narrow, perhaps 1 day or a small number of days.
  • ✅ Clean and uncluttered design: The plot is clean and lacks clutter. The single color for the bars is appropriate and does not distract from the data.
  • 💡 Lack of annotation for the 120-day spike: The sudden spike at 120 days is visually prominent. While the text later explains this as truncation, the figure itself doesn't indicate this. A note in the caption or an annotation on the graph about the 120-day truncation would make the figure more self-contained in explaining this feature.
  • ✅ Informative title: The title 'Distribution of the length of stay in the dataset' is informative and accurately describes the content of the figure.
Fig. 4 A density plot of the distribution of the length of stay.
Figure/Table Image (Page 8)
Fig. 4 A density plot of the distribution of the length of stay.
First Reference in Text
This strategy is based on the distribution of the LoS as shown earlier in Figs. 3 and 4.
Description
  • Axes and Scale: The figure presents a density plot illustrating the distribution of patient Length of Stay (LoS). The x-axis shows LoS values, numerically scaled from 0 to 120, presumably in days. The y-axis, labeled 'Density', ranges from 0.00 to 0.16.
  • Shape of Distribution and Peak Density: The plot depicts a highly right-skewed distribution. The density is very low near LoS = 0, rises sharply to a peak value of approximately 0.16 at an LoS of around 2-3 days, and then declines steadily as LoS increases, forming a long tail extending towards 120 days. This indicates that very short hospital stays are most common, with the likelihood of a stay decreasing as its length increases.
  • Methodology and Properties: The caption specifies that the plot was generated using kernel density estimation (KDE) with a Gaussian kernel. KDE is a technique used to estimate the underlying probability distribution of a dataset by smoothing out the data points. A Gaussian kernel is a common choice, using a bell-shaped curve for smoothing. The caption also correctly notes that the total area under a density curve is 1.
  • Comparison to Histogram (Fig. 3): Unlike the histogram in Figure 3, this density plot does not show a distinct spike at LoS = 120 days. The smoothing nature of KDE tends to average out such sharp, isolated features, resulting in a curve that tapers off more gently towards the maximum LoS shown.
Scientific Validity
  • ✅ Appropriate visualization technique: A density plot is an appropriate method for visualizing the estimated probability distribution of a continuous variable like LoS, offering a smoothed alternative to a histogram.
  • ✅ Sound statistical basis: The use of kernel density estimation with a specified Gaussian kernel is a standard statistical technique. The statement that the area under the curve is 1 is a fundamental property of probability density functions and is correctly noted.
  • ✅ Supports understanding of LoS distribution for binning strategy: The plot effectively illustrates the skewness and the concentration of data at shorter LoS values, which is consistent with the information from Figure 3 and typical for LoS data. This visualization supports the authors' strategy to bin LoS, particularly for shorter durations where density changes rapidly.
  • 💡 Kernel bandwidth not specified: While the Gaussian kernel is common, the choice of bandwidth for the KDE is not mentioned. Bandwidth selection can significantly affect the smoothness and appearance of the density plot, potentially masking or overemphasizing certain features. However, the current plot appears reasonably smooth without obvious artifacts of poor bandwidth choice for a general overview.
  • 💡 Smoothing obscures data truncation detail: The density plot, due to its smoothing nature, obscures the sharp truncation at 120 days that was evident in the histogram (Fig. 3). While this is an inherent characteristic of KDE, it means this particular plot is less effective at highlighting that specific data artifact compared to the histogram.
  • ✅ Supports claims in reference text: The figure, in conjunction with Fig. 3, supports the reference text's claim that the LoS distribution informs their binning strategy by showing where the majority of data points lie and how the frequency changes.
Communication
  • ✅ Appropriate chart type: The density plot is a suitable choice for visualizing the continuous distribution of Length of Stay, providing a smoothed representation compared to a histogram.
  • 💡 X-axis labeling: The y-axis is clearly labeled 'Density'. While the x-axis is not explicitly named on the plot itself, its numerical scale (0-120) and the figure title clearly indicate it represents Length of Stay (presumably in days). Adding an explicit x-axis label like 'Length of Stay (days)' directly on the plot would improve clarity.
  • ✅ Clean and uncluttered design: The plot is clean and uses a single line, making the distribution's shape easy to discern. The gridlines are subtle and do not clutter the visual.
  • ✅ Informative caption: The caption is informative, stating that it's a density plot, the area under the curve is 1 (a fundamental property of density plots), and specifying the method used (kernel density estimation with a Gaussian kernel) including a citation. This helps in understanding how the plot was generated.
  • 💡 Smoothing effect on truncation visibility: The figure effectively highlights the high concentration of shorter stays and the long tail, which is consistent with the histogram in Fig. 3. However, the smoothing inherent in density plots means the sharp truncation effect at 120 days (visible in Fig. 3) is less pronounced here, appearing as a gentle tapering off.

Results

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

Table 1 Descriptive statistics regarding the LoS variable
Figure/Table Image (Page 9)
Table 1 Descriptive statistics regarding the LoS variable
First Reference in Text
Table 1 summarizes basic statistical properties of the LoS variable.
Description
  • Variable Described: The table provides a summary of descriptive statistics for the 'Length of Stay' (LoS) variable, which typically refers to the duration a patient stays in a hospital. The unit for LoS is implied to be days.
  • Mean LoS: The 'Mean' (average) LoS is reported as 5.41 days.
  • Standard Deviation: The 'std. deviation' (standard deviation), a measure of the amount of variation or dispersion of a set of values, is 7.97 days. A standard deviation larger than the mean often suggests a skewed distribution with some very high values.
  • Minimum LoS: The 'Minimum' LoS observed in the dataset is 1 day.
  • 25th Percentile (Q1): The '25th percentile' (also known as the first quartile) is 2 days. This means that 25% of the patients had an LoS of 2 days or less.
  • 50th Percentile (Median/Q2): The '50th percentile' (also known as the median or second quartile) is 3 days. This indicates that half of the patients had an LoS of 3 days or less, and half had an LoS of 3 days or more. The median being lower than the mean (3 vs 5.41) further supports the idea of a right-skewed distribution (many short stays and fewer very long stays).
  • 75th Percentile (Q3): The '75th percentile' (also known as the third quartile) is 6 days. This means that 75% of the patients had an LoS of 6 days or less, or conversely, 25% of patients had an LoS longer than 6 days.
  • Maximum LoS: The 'Maximum' LoS observed in the dataset is 120 days. This aligns with the truncation point mentioned elsewhere in the paper (Fig. 3).
Scientific Validity
  • ✅ Appropriate selection of statistics: The selection of descriptive statistics (mean, standard deviation, min, max, quartiles) is appropriate for summarizing a numerical variable like LoS and provides a good initial understanding of its central tendency, spread, and range.
  • ✅ Statistics consistent with skewed distribution: The reported values, particularly the mean (5.41) being notably higher than the median (3), and the large standard deviation (7.97) relative to the mean, correctly suggest a right-skewed distribution. This is consistent with the visual evidence from Figure 3 (histogram) and Figure 4 (density plot).
  • ✅ Reflects data truncation at maximum value: The maximum value of 120 days aligns with the data truncation noted in the paper (e.g., related to Figure 3). This is an important characteristic of the dataset that these statistics reflect.
  • ✅ Useful for informing analytical choices: The table provides a useful summary that informs subsequent analytical choices. For instance, the skewness indicated might necessitate data transformations or the use of non-parametric methods or models robust to such distributions.
  • 💡 Consider adding skewness and kurtosis values: While the provided statistics are good, measures of skewness and kurtosis could also be included to quantitatively describe the shape of the distribution further, complementing the qualitative inference from the mean/median comparison.
  • ✅ Strongly supports reference text: The table strongly supports the reference text by providing a clear summary of basic statistical properties of the LoS variable.
Communication
  • ✅ Clear structure and labeling: The table is well-structured with clear labels for each statistical measure and their corresponding values. This makes it easy to read and understand.
  • ✅ Concise and accurate title: The title is concise and accurately reflects the content of the table.
  • ✅ Efficient presentation of key statistics: The table effectively presents key descriptive statistics in a compact format, allowing for a quick overview of the LoS variable's characteristics.
  • 💡 Explicitly state units for LoS: The units for LoS (presumably days) are not explicitly stated in the table or its immediate caption, although it is implied by the context of hospital stays and the integer values. Adding '(days)' next to 'LoS variable' in the caption or as a note would enhance clarity.
  • 💡 Consider adding the number of observations (N): The number of observations (N) is not included. While not always mandatory for descriptive statistics, providing N would give context to the scale of the dataset these statistics are derived from.
Fig. 5 This figure depicts the distribution of the LoS variable for newborns
Figure/Table Image (Page 10)
Fig. 5 This figure depicts the distribution of the LoS variable for newborns
First Reference in Text
Figure 5 shows the distribution of the LoS variable for newborns.
Description
  • Plot Type and Subject: The figure is a density plot showing the distribution of the 'Length of Stay' (LoS) variable specifically for newborns. A density plot is a smoothed version of a histogram, representing the probability distribution of a continuous variable; the area under the curve sums to 1.
  • Axes and Scales: The x-axis represents the Length of Stay, scaled from 0 to 9 units, which are presumably days. The y-axis, labeled 'Density', ranges from 0.00 to 0.35, indicating the probability density at each LoS value.
  • Shape of Distribution and Peak: The distribution for newborns is sharply peaked and right-skewed. The highest density occurs around an LoS of 2-3 days, where the density value reaches approximately 0.37 (the peak of the curve is slightly above the 0.35 y-axis tick).
  • Density Decline: After the peak, the density drops off rapidly. For example, at an LoS of 1 day, the density is around 0.20. By an LoS of 5 days, the density has fallen to approximately 0.05, and it becomes very low for LoS values of 6 days and beyond, approaching zero by 9 days.
  • Comparison to Overall LoS Distribution: Compared to the overall LoS distribution shown in Figure 4 (which goes up to 120 days), this distribution for newborns is much more concentrated at the lower end of the LoS scale, with a much shorter tail.
Scientific Validity
  • ✅ Justified subpopulation analysis: Presenting a separate LoS distribution for newborns is a valid approach, as this subpopulation likely has distinct LoS characteristics compared to the general patient population, justifying separate modeling.
  • ✅ Appropriate visualization method: A density plot is an appropriate choice for visualizing the distribution of LoS for newborns, providing a clear, smoothed representation of the data's underlying probability distribution.
  • ✅ Clinically plausible distribution: The plot accurately depicts a distribution that is highly concentrated at short LoS values, which is clinically expected for many newborn cases (e.g., routine births).
  • ✅ Strongly supports reference text: The figure strongly supports the reference text by clearly showing the distribution of the LoS variable specifically for the newborn cohort.
  • 💡 Kernel bandwidth not specified: As with Figure 4, the choice of bandwidth for the kernel density estimation is not specified. While the plot appears reasonable, this parameter can influence the smoothness and specific shape of the curve.
  • 💡 Clarity on maximum LoS for newborns: The x-axis extends to 9 days. It's unclear if this represents the maximum LoS for newborns in the dataset or if longer stays were possible but had negligible density. If there's a truncation specific to newborns (different from the general 120-day truncation), it would be useful to note.
Communication
  • ✅ Appropriate chart type: The use of a density plot is appropriate for showing the smoothed distribution of the LoS for newborns.
  • ✅ Clear y-axis label, understandable x-axis: The y-axis is clearly labeled 'Density'. The x-axis, while not explicitly labeled, has clear numerical ticks from 0 to 9, which, combined with the legend 'Length of Stay', makes its meaning clear (presumably days). Adding an explicit x-axis label 'Length of Stay (days)' would be a minor improvement.
  • ✅ Clean and easy-to-read design: The plot is clean, with a single line representing the distribution, making it easy to interpret the shape. The gridlines are helpful for estimating values.
  • ✅ Clear legend: The legend 'Length of Stay' is clear and correctly identifies the variable being plotted.
  • ✅ Informative title: The title is informative and accurately describes the content and specific subpopulation (newborns) of the figure.
  • ✅ Effectively communicates key distribution characteristics: The plot effectively communicates that the LoS for newborns is concentrated at very short durations, with a rapid decrease in density for longer stays.
Table 2 This table depicts the frequency of occurrence of the top 20 APR DRG...
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Table 2 This table depicts the frequency of occurrence of the top 20 APR DRG descriptions in the dataset

Figure/Table Image (Page 10)
Table 2 This table depicts the frequency of occurrence of the top 20 APR DRG descriptions in the dataset
First Reference in Text
Table 2 shows the top 20 APR DRG descriptions based on their frequency of occurrence in the dataset.
Description
  • Content Overview and APR DRG Explanation: The table lists the top 20 most frequently occurring All Patient Refined Diagnosis Related Groups (APR DRG) descriptions in the dataset, along with their absolute frequencies. APR DRGs are a system used to classify hospital cases into groups expected to have similar hospital resource use, based on diagnosis, procedures, age, sex, and the presence of complications or comorbidities.
  • Most Frequent DRG: The most frequent APR DRG description is 'Neonate birthwt > 2499 g, normal newborn or neonate w other problem', with a frequency of 195,238 occurrences.
  • Other Highly Frequent DRGs: The second most frequent is 'Vaginal delivery', occurring 142,275 times, followed by 'Septicemia & disseminated infections' with 93,349 occurrences.
  • Range of Frequencies: The frequencies for the top 20 DRGs range from 195,238 down to 22,151 for 'Alcohol abuse & dependence', which is the 20th most frequent DRG listed.
  • Diversity of Conditions: The list includes a diverse set of medical conditions and procedures, such as childbirth-related DRGs (vaginal delivery, Cesarean delivery, neonate conditions), infections (septicemia), chronic diseases (heart failure, chronic obstructive pulmonary disease), surgical procedures (knee/hip joint replacement), acute conditions (renal failure, CVA & precerebral occlusion w infarct), and mental health/substance abuse conditions (schizophrenia, bipolar disorders, alcohol abuse).
Scientific Validity
  • ✅ Provides dataset composition insight: Presenting the frequency of the top 20 APR DRGs is a valid and informative way to describe the composition of the dataset. It highlights the most common patient groups and conditions encountered.
  • ✅ Important context for subsequent analysis: This information is crucial for understanding the context of any subsequent analysis, as models might perform differently or be more relevant for more frequent DRGs. It sets the stage for understanding which patient populations are most represented.
  • ✅ Strongly supports reference text: The table directly supports the reference text by listing the top 20 APR DRG descriptions and their frequencies.
  • ✅ Highlights dataset scope: The diversity of conditions in the top 20 (from births to chronic illnesses to mental health) indicates the broad scope of the dataset being analyzed, which is important for assessing the generalizability of findings.
  • 💡 Primarily descriptive; further analysis needed for deeper insights: While descriptive, this table primarily serves to characterize the data. Further scientific insight would come from linking these DRGs to outcomes like Length of Stay (LoS), which is explored in other parts of the paper (e.g., Figure 6).
  • 💡 Assumes accuracy of underlying data and coding: The accuracy of the frequencies depends on the correctness of the underlying data processing and DRG coding, which is assumed to be standard for the SPARCS dataset.
Communication
  • ✅ Clear two-column layout: The table uses a clear two-column format, making it easy to associate each APR DRG description with its frequency.
  • ✅ Unambiguous column headers: The column headers 'APR DRG Description' and 'Frequency' are unambiguous and accurately describe the data within them.
  • ✅ Informative title: The title is informative and clearly states the content of the table – the top 20 APR DRG descriptions by frequency.
  • ✅ Clear presentation of descriptions and frequencies: The APR DRG descriptions, while sometimes lengthy, are presented as they are in the classification system, which is necessary for accuracy. The frequency values are clearly displayed as integers.
  • 💡 Consider adding percentage frequencies: While the table shows absolute frequencies, adding a column for the percentage of total occurrences for each DRG could provide additional relative context and enhance understanding of their prevalence within the entire dataset.
  • 💡 Length of the table: The table is quite long due to the detailed descriptions. While this is inherent to the nature of DRG descriptions, for presentation in a constrained format, perhaps only the top 10 could be shown in the main text with the full list in supplementary materials, if space is an issue. However, as presented, it is complete for the top 20.
Fig. 6 A 3-d plot showing the distribution of the LoS for the top-20 most...
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Fig. 6 A 3-d plot showing the distribution of the LoS for the top-20 most frequently occuring APR DRG descriptions.

Figure/Table Image (Page 11)
Fig. 6 A 3-d plot showing the distribution of the LoS for the top-20 most frequently occuring APR DRG descriptions.
First Reference in Text
Figure 6 shows the distribution of the LoS variable for the top 20 most frequently occurring APR DRG descriptions shown in Table 2.
Description
  • Plot Type and Purpose: The figure is a three-dimensional plot designed to show the distribution of Length of Stay (LoS) for each of the top 20 most frequently occurring APR DRG (All Patient Refined Diagnosis Related Groups) descriptions. APR DRGs are a system for classifying hospital cases based on diagnoses, procedures, and other patient factors.
  • Axes Description: The x-axis (horizontal, extending from left to right in the foreground) represents the Length of Stay, with numerical labels from 0 to 8, presumably in days. The y-axis (extending into the depth of the plot, from front to back) represents the different APR DRG descriptions. These are categorical, and the labels for individual DRGs are listed along this axis, starting with 'Neonate birthwt >2499g...' at the front and ending with 'Alcohol abuse & dependence' at the back. The z-axis (vertical) represents the density or frequency of occurrence of the LoS, scaled from 0.0 to 1.0.
  • Individual LoS Distributions: For each APR DRG along the y-axis, a separate LoS distribution (like a smoothed histogram or density curve) is plotted along the x-axis, with the height of the curve at any LoS point indicating its density (z-value). Each DRG's distribution has a distinct color.
  • Observed Distribution Shapes and Variations: Visually, most distributions appear to be right-skewed, with peaks at very short LoS values (e.g., 1-3 days) and then tapering off. The height of these peaks (density) varies across different DRGs. For example, the distribution for 'Neonate birthwt >2499g...' (front-most, light blue) shows a high peak at a very short LoS. Other DRGs further back show peaks of varying heights and slightly different shapes.
  • Comparative Aspect: The plot attempts to allow comparison of LoS distributions across these 20 common DRGs. For instance, one might try to see if certain DRGs typically have longer or shorter LoS, or more spread-out distributions, though precise comparison is challenging due to the 3D perspective.
Scientific Validity
  • ✅ Valid analytical goal: Attempting to visualize LoS distributions for multiple categories (APR DRGs) simultaneously is a valid analytical goal, as it can reveal patterns or differences in LoS based on patient condition/procedure.
  • ✅ Appropriate use of density distributions: The use of density plots for each DRG is appropriate for showing the shape of the LoS distribution.
  • 💡 3D representation challenges scientific interpretation: However, 3D plots for this type of data (multiple distributions) often suffer from interpretability issues. Occlusion (where some distributions hide others) and perspective distortion can make it difficult to accurately compare heights (densities) and shapes, especially in a static image. The scientific value derived might be limited by these perceptual challenges.
  • 💡 Limited support for quantitative comparison: The figure aims to support the idea that LoS distributions vary by APR DRG. While some general differences in peak height and spread can be vaguely discerned, the plot does not allow for rigorous quantitative comparison. For instance, determining if the peak LoS for 'Heart failure' is significantly different from 'Other pneumonia' is very difficult from this visual alone.
  • ✅ Reasonable selection of DRGs: The selection of the top 20 APR DRGs (as listed in Table 2) is a reasonable approach to focus on the most common patient groups.
  • 💡 Supports general claim but effectiveness is limited: The figure supports the general claim in the reference text that it shows LoS distributions for these DRGs. However, the effectiveness in conveying detailed insights from these distributions is questionable due to the chosen 3D format.
  • 💡 Potential truncation of LoS x-axis view: The x-axis only goes up to LoS = 8 days. Given that the overall LoS distribution (Fig. 3) goes up to 120 days, and Table 1 shows a mean LoS of 5.41 and 75th percentile of 6, this plot might be truncating the view of the tails for many DRGs, potentially missing important information about longer stays within these common conditions.
Communication
  • 💡 Potential interpretability challenges with 3D plots: The 3D plot attempts to convey a lot of information (LoS distribution for 20 different DRGs simultaneously). While ambitious, 3D surface or density plots can be difficult to interpret accurately due to occlusion, perspective distortion, and difficulty in precisely reading values from the z-axis.
  • 💡 Poor legibility of APR DRG labels: The y-axis representing APR DRG descriptions is categorical. The labels for these DRGs are crucial for interpretation but are quite small and overlap significantly, making it very difficult to identify which distribution corresponds to which specific DRG without extensive zooming or external reference to Table 2.
  • 💡 Difficulty in reading z-axis values precisely: The x-axis (Length of Stay) and z-axis (density) are continuous. The x-axis ticks (0-8) are somewhat clear, but the z-axis scale (0.0 to 1.0) is harder to map to specific peaks without a clearer color bar or gridlines on the surfaces.
  • 💡 Color differentiation for 20 categories: The use of different colors for each DRG's distribution helps to visually separate them to some extent, but with 20 categories, the color distinctions might not be sufficient for all viewers, especially if there are similarities in color.
  • 💡 Occlusion due to viewing angle in static 3D plot: The viewing angle chosen makes some distributions in the 'front' more visible, while those in the 'back' are partially obscured. An interactive 3D plot would be more effective for exploration, but in a static format, this is a limitation.
  • 💡 Alternative 2D visualizations might be clearer: A series of 2D density plots (one for each DRG, or grouped by similarity) or a heatmap might have been a more effective way to communicate these distributions clearly and allow for easier comparison, avoiding the complexities of 3D representation in a static image.
  • ✅ Informative caption: The caption accurately describes what the plot intends to show and identifies the axes, which is helpful.
Table 3 The regression results produced by varying the encoding scheme and the...
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Table 3 The regression results produced by varying the encoding scheme and the model.

Figure/Table Image (Page 11)
Table 3 The regression results produced by varying the encoding scheme and the model.
First Reference in Text
Our results are shown in Table 3.
Description
  • Table Purpose and R² Score Explanation: The table presents the performance, measured by the R² Score, of different regression models when applied to data for non-newborns, using various feature encoding schemes. The R² Score, or coefficient of determination, is a statistical measure of how well the regression predictions approximate the real data points; an R² of 1 indicates that the regression predictions perfectly fit the data, while an R² of 0 indicates that the model does not explain any of the variability in the response data around its mean.
  • One Hot Encoding with Linear Regression: The first row shows that using 'One Hot' encoding with a 'Linear Regression' model resulted in an R² Score of 0.36. 'One Hot encoding' is a technique to convert categorical data (non-numeric data like 'type of admission') into a numerical format by creating new binary (0 or 1) columns for each category. 'Linear Regression' is a statistical method to model the relationship between a dependent variable (like length of stay) and one or more independent variables by fitting a linear equation.
  • Target Encoding with Random Forest Regressor: The second row indicates that using 'Target' encoding with a 'Random Forest Regressor' model achieved an R² Score of 0.396. 'Target encoding' is a technique where each category of a categorical variable is replaced with a statistical measure (e.g., the mean) of the target variable (length of stay) for that category. A 'Random Forest Regressor' is an ensemble learning method that operates by constructing multiple decision trees during training and outputting the mean prediction of the individual trees for regression tasks.
  • Combined One Hot and Target Encoding with Linear Regression: The third row shows the result of combining 'One Hot and Target' encoding methods with a 'Linear Regression' model, yielding the highest R² Score in the table: 0.42. This suggests that using both types of encoding together provided more useful information for the linear regression model in this specific case.
Scientific Validity
  • ✅ Systematic comparison of methods: Comparing different encoding schemes and model types is a standard and valid approach in machine learning to identify the best-performing combination for a given dataset and task. This systematic exploration is good practice.
  • ✅ Appropriate evaluation metric (R² Score): The R² score is a common and appropriate metric for evaluating the goodness-of-fit of regression models. It provides a standardized way to compare how much variance in the dependent variable is explained by each model.
  • ✅ Provides empirical evidence for best performing combination: The results indicate that the combination of 'One Hot and Target' encoding with Linear Regression performed best among the tested options for non-newborn data. This provides empirical evidence for this specific combination's effectiveness on this dataset.
  • 💡 Limited scope of tested combinations: The table only presents a limited set of combinations. It would be beneficial to know if other models (e.g., Random Forest with One Hot, or other regression algorithms like Gradient Boosting) were also tested, or why these specific combinations were chosen for presentation. For instance, it's not shown how 'One Hot and Target' encoding performs with Random Forest Regressor.
  • 💡 Moderate R² scores indicate room for improvement: The R² scores, while showing relative differences, are all below 0.5 (specifically 0.36, 0.396, 0.42). This indicates that a substantial portion of the variance in Length of Stay for non-newborns is not explained by these models using the current features. While the best model explains 42% of the variance, 58% remains unexplained, suggesting limitations in predictive power or the need for additional informative features.
  • 💡 Lack of statistical significance or confidence intervals for R²: The table doesn't include information about the statistical significance of the R² values or confidence intervals, which would add more rigor to the comparison. However, for a comparative table of model performance, R² alone is often presented.
  • ✅ Supports reference text: The table accurately supports the reference text stating that results are shown in Table 3.
Communication
  • ✅ Clear and logical structure: The table has a clear three-column structure ('Encodings', 'Model', 'R² Score'), which makes it easy to compare the performance of different model and encoding combinations.
  • ✅ Concise and accurate headers: The column headers are concise and accurately describe the data they contain.
  • ✅ Informative caption with important context: The caption clearly states the purpose of the table and specifies that the data pertains to non-newborns, which is crucial context.
  • ✅ Appropriate terminology: The use of terms like 'One Hot', 'Target', 'Linear Regression', and 'Random Forest Regressor' is standard in machine learning and appropriate for the target audience.
  • ✅ Efficient presentation of results: The table is compact and presents the key results efficiently. The R² scores are easy to read and compare.
Fig. 7 SHAP Value plot for newborns
Figure/Table Image (Page 12)
Fig. 7 SHAP Value plot for newborns
First Reference in Text
Figures 7 and 8 show the SHAP values plots obtained for the features in the newborn partition of the dataset.
Description
  • Plot Type and SHAP Explanation: This figure is a SHAP (SHapley Additive exPlanations) summary plot for the newborn dataset. SHAP values are a game theory approach to explain the output of any machine learning model. They quantify the contribution of each feature to the prediction for an individual instance, indicating how much each feature has pushed the model's output away from the baseline or average prediction.
  • Axes Interpretation: The y-axis lists various input features used in the model, ordered from top to bottom by their global importance (sum of absolute SHAP values across all samples). The x-axis represents the SHAP value itself; positive values indicate the feature pushed the prediction higher (e.g., longer Length of Stay - LoS), while negative values indicate the feature pushed the prediction lower (e.g., shorter LoS).
  • Dot and Color Interpretation: Each dot on the plot represents a single newborn patient in the dataset. The color of the dot indicates the original value of that feature for that patient: red for high values and blue for low values, as shown by the vertical color bar on the right labeled 'Feature value'. The horizontal spread of dots for each feature shows the distribution of SHAP values for that feature.
  • Top Feature: APRDRGCode: The top-ranked feature is 'APRDRGCode' (All Patient Refined Diagnosis Related Groups Code). For this feature, there's a wide spread of SHAP values. Red dots (high target-encoded APRDRG values, often associated with more complex/severe DRGs) tend to have positive SHAP values (increasing predicted LoS), while blue dots (low target-encoded APRDRG values) are more mixed but include many with negative SHAP values.
  • Second Feature: APRSeverityofIllnessCode: The second feature, 'APRSeverityofIllnessCode', shows a clearer pattern: red dots (high severity) are predominantly on the positive SHAP value side (increasing LoS), and blue dots (low severity) are mostly on the negative SHAP value side (decreasing LoS).
  • Feature: BirthWeight: The fourth feature, 'BirthWeight', also shows a distinct pattern. Red dots (high birth weight) are mostly associated with negative SHAP values (decreasing LoS), while blue dots (low birth weight) are predominantly associated with positive SHAP values (increasing LoS). This indicates that lower birth weight contributes to predictions of longer hospital stays for newborns.
  • Other Features and Overall Impact: Other important features shown include 'CCSProcedureCode', 'PatientDisposition', 'OperatingCertificateNumber', and 'APRRiskofMortality'. Features towards the bottom, like 'CCSDiagnosisCode' and 'APRMedicalSurgicalDescription', have SHAP values clustered more tightly around zero, indicating less overall impact on the LoS predictions for newborns.
Scientific Validity
  • ✅ Appropriate interpretability method: SHAP plots are a robust and widely accepted method for model interpretability, providing insights into both global feature importance and local feature contributions, including their directionality. Using SHAP is appropriate for understanding the drivers of LoS predictions.
  • ✅ Illustrates direction and magnitude of feature effects: The plot effectively demonstrates not just which features are important, but also how their values affect the LoS prediction for newborns (e.g., low birth weight increasing predicted LoS). This goes beyond simple feature ranking.
  • ✅ Clear ranking of global feature importance: The ordering of features by their mean absolute SHAP value provides a clear ranking of global feature importance for the newborn model, which is a valuable output.
  • 💡 Interpretation of encoded categorical features: The interpretation of 'high' and 'low' feature values (colors) for categorical features like 'APRDRGCode' or 'CCSProcedureCode' depends on how they were encoded. The text mentions these SHAP plots are based on a Random Forest Regressor with target-encoded features. Thus, a 'high' value for such a code means its target-encoded representation was high (which itself correlates with higher average LoS). This context is crucial for accurate interpretation and should ideally be reiterated when discussing these specific features.
  • 💡 Model-specific interpretation: The plot is specific to the model trained for newborns. The feature importances and effects shown are conditional on this specific model's architecture and training data.
  • ✅ Supports claims in reference text: The plot strongly supports the textual claim that it shows SHAP values for features in the newborn partition and helps identify influential features like 'BirthWeight' and 'APRSeverityofIllnessCode'.
Communication
  • ✅ Standard and informative visualization: The SHAP summary plot is a standard and generally effective way to visualize feature importance and effects. The vertical ordering of features by global importance is helpful.
  • ✅ Clear color coding and x-axis labeling: The color coding (red for high feature values, blue for low) provides an intuitive way to see how the magnitude of a feature impacts the prediction. The x-axis label 'SHAP value (impact on model output)' clearly explains what the horizontal position of dots represents.
  • 💡 Abbreviated feature names: Feature names like 'APRDRGCode', 'APRSeverityofIllnessCode', 'CCSProcedureCode' are dataset-specific. While standard in healthcare, providing full names or brief explanations in an appendix or the main text could improve accessibility for a broader audience. For example, explaining what 'APRDRGCode' stands for.
  • 💡 Potential for point overlap: The plot can become dense where many points overlap, especially around SHAP values of zero. This can make it slightly harder to discern the exact distribution of SHAP values for less impactful instances of a feature.
  • ✅ Clear color bar: The color bar on the right clearly indicates 'High' and 'Low' feature values corresponding to the red and blue colors, respectively. The label 'Feature value' is standard but could be more specific if the features were all on a similar, interpretable scale (which is not the case here).
Fig. 8 1-D SHAP plot, in order of decreasing feature importance: top to bottom...
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Fig. 8 1-D SHAP plot, in order of decreasing feature importance: top to bottom (for non-newborns)

Figure/Table Image (Page 12)
Fig. 8 1-D SHAP plot, in order of decreasing feature importance: top to bottom (for non-newborns)
First Reference in Text
Figures 7 and 8 show the SHAP values plots obtained for the features in the newborn partition of the dataset.
Description
  • Plot Type and Purpose: Figure 8 is a SHAP (SHapley Additive exPlanations) summary plot, intended to show feature importance and effects for a model predicting Length of Stay (LoS) for non-newborns (as per the caption). SHAP values quantify how much each feature contributes to pushing a model's prediction away from a baseline value.
  • Axes and Feature Ordering: Features are listed on the y-axis, ordered by their global importance from top to bottom. The x-axis represents the SHAP value, indicating the impact on the model output (LoS prediction). Positive SHAP values suggest the feature contributes to a higher predicted LoS, while negative values suggest a contribution to a lower predicted LoS. The scale ranges from approximately -20 to +80.
  • Dot and Color Interpretation: Each dot represents an individual patient. The color of the dot indicates the feature's value for that patient: red for high values, blue for low values (according to the vertical color bar on the right). The horizontal position of the dot shows its SHAP value.
  • Top Feature: APR Severity of Illness Code: The most important feature is 'APR Severity of Illness Code'. High values of this feature (red dots) are generally associated with high positive SHAP values (increasing predicted LoS), while low values (blue dots) are associated with negative SHAP values (decreasing predicted LoS).
  • Other Important Features: Other highly ranked features include 'APR DRG Code', 'Patient Disposition', 'CCS Procedure Code', and 'APR Medical Surgical Description'. For 'APR DRG Code', for instance, higher target-encoded values (red dots) tend to have positive SHAP values.
  • Features: Operating Certificate Number and Age Group: 'Operating Certificate Number' appears as a moderately important feature. 'Age Group' is also listed, where higher age groups (red dots) tend to have positive SHAP values, suggesting older patients have predictions of longer LoS.
  • Less Important Features: Features like 'Payment Typology 2', 'Health Service Area', and 'Zip Code - 3 digits' are ranked lower, with their SHAP values clustered more closely around zero, indicating less overall impact on the model's predictions for non-newborns.
Scientific Validity
  • ✅ Valid interpretability method: SHAP plots are a scientifically sound method for model interpretation, providing valuable insights into feature effects.
  • ✅ Demonstrates feature influence effectively: The plot effectively displays both the magnitude and direction of feature influences on LoS predictions for the specific model being analyzed.
  • 💡 Critical inconsistency with reference text regarding the dataset partition: There is a critical inconsistency: the caption states Figure 8 is for 'non-newborns', while the reference text states 'Figures 7 and 8 show the SHAP values plots obtained for the features in the newborn partition of the dataset.' This discrepancy must be resolved. Based on the features displayed (e.g., 'Age Group', and the general nature of other top features like 'APR Severity of Illness Code', 'APR DRG Code'), the plot visually appears more consistent with a non-newborn adult population rather than newborns (where 'BirthWeight' was a key feature in Fig. 7). If the visual and caption are correct, the reference text is erroneous for Figure 8.
  • ✅ Clinically plausible feature importance (if for non-newborns): Assuming the caption is correct and this plot is for non-newborns, the identified top features (e.g., severity of illness, DRG code, patient disposition) are clinically plausible drivers of LoS in a general adult population.
  • 💡 Interpretation of encoded categorical features: The interpretation of encoded categorical features (like APR DRG Code) depends on the encoding scheme used (e.g., target encoding, as mentioned for the Random Forest Regressor used to generate these plots). A 'high' value for such features implies a high target-encoded value.
Communication
  • ✅ Standard and effective visualization: The SHAP summary plot is a standard and effective visualization for feature importance and impact. The features are clearly ranked by global importance.
  • ✅ Clear color coding and axis labeling: The color coding (red for high feature values, blue for low) and the x-axis label 'SHAP value (impact on model output)' are clear and aid interpretation.
  • 💡 Major contradiction between caption and reference text: The caption states this plot is for 'non-newborns'. However, the reference text explicitly says 'Figures 7 and 8 show the SHAP values plots obtained for the features in the newborn partition of the dataset.' This is a significant contradiction that confuses the reader. The figure content (feature names and their apparent impact) seems more aligned with a general adult population than newborns (e.g., 'Age Group' is present, which is less relevant for newborns compared to 'BirthWeight' in Fig 7). Assuming the caption is correct for the visual, the reference text needs correction.
  • 💡 Abbreviated feature names: Feature names are abbreviations (e.g., 'APR DRG Code', 'APR MDC Code'). While standard in this domain, full names or a glossary could improve readability for a broader audience.
  • ✅ Clear color bar: The vertical color bar clearly defines 'High' and 'Low' feature values, which is good. The label 'Feature value' is standard.
  • 💡 Point density: The plot is dense with points, especially around SHAP value 0, which is typical for such plots but can make discerning individual point distributions for less impactful features slightly challenging.
Fig. 9 A 2-D plot showing the relationship between SHAP values for one feature,...
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Fig. 9 A 2-D plot showing the relationship between SHAP values for one feature, "APR Severity of Illness Code", and the feature values themselves (non-newborns)

Figure/Table Image (Page 13)
Fig. 9 A 2-D plot showing the relationship between SHAP values for one feature, "APR Severity of Illness Code", and the feature values themselves (non-newborns)
First Reference in Text
From Fig. 9, we observe that as the severity of illness code increases from 1-4, there is a corresponding increase in the SHAP values.
Description
  • Plot Type and Context: The figure is a 2D plot, specifically a SHAP dependence plot, illustrating the relationship between the values of a single feature, 'APR Severity of Illness Code', and their corresponding SHAP (SHapley Additive exPlanations) values for the non-newborn patient dataset. SHAP values quantify the impact of a feature on the model's prediction (in this case, likely Length of Stay).
  • Axes Description: The x-axis represents the 'APRSeverityofillnessCode', which appears to take discrete values, likely 1 (Minor), 2 (Moderate), 3 (Major), and 4 (Extreme), based on common medical severity scales, although only the numerical values 1.0, 2.0, 3.0, 4.0 are directly indicated by the clusters of points. The y-axis shows the 'SHAP value for APRSeverityofillnessCode', ranging from approximately -2 to 14.
  • Data Points (Blue Dots): Each blue dot represents an individual patient instance. Its horizontal position indicates the patient's APR Severity of Illness Code, and its vertical position indicates the SHAP value for that severity code for that specific patient, showing how much that severity level contributed to the LoS prediction for them.
  • Feature Value Distribution (Grey Bars): Superimposed on the plot are light grey bars centered around the feature values (1, 2, 3, 4). The height of these bars seems to indicate the frequency or distribution of each severity code value in the dataset. The tallest grey bar is for severity code 1, followed by 2, then 3, and the shortest is for severity code 4, indicating that lower severity codes are more common.
  • Observed Trend: A clear positive trend is visible: as the 'APRSeverityofillnessCode' increases from 1 to 4, the corresponding SHAP values generally increase. For severity code 1, SHAP values are clustered around 0, mostly slightly negative (e.g., -1 to +1). For severity code 2, SHAP values are mostly positive, centered around +2 to +3. For severity code 3, SHAP values are higher, mainly between +3 and +6. For severity code 4, the SHAP values are highest, ranging from approximately +5 to over +12.
  • Variability in SHAP Values: There is also a vertical spread of SHAP values for each severity code, indicating that even for the same severity level, its impact on the LoS prediction can vary depending on the other feature values for a given patient (interaction effects).
Scientific Validity
  • ✅ Appropriate method for feature effect visualization: SHAP dependence plots are a scientifically sound and widely used method for understanding how a specific feature's values influence model predictions, including non-linear relationships and interaction effects (indicated by vertical dispersion).
  • ✅ Strongly supports claims in reference text: The plot strongly supports the observation made in the reference text: 'as the severity of illness code increases from 1-4, there is a corresponding increase in the SHAP values.' This positive monotonic relationship is clearly visible.
  • ✅ Provides clinically intuitive model insight: The visualization provides valuable insight into the model's behavior, confirming that it has learned a clinically intuitive relationship: higher severity of illness contributes to predictions of longer hospital stays.
  • ✅ Useful contextual information from feature distribution: The inclusion of the grey bars showing the distribution of the feature values themselves is useful context, as it shows that the model's understanding of higher severity codes is based on fewer instances compared to lower severity codes.
  • 💡 Focuses on a single feature's main effect: The plot is specific to one feature ('APR Severity of Illness Code') and the non-newborn model. It doesn't show how this feature interacts with others, although the vertical spread of points hints at such interactions.
Communication
  • ✅ Effective plot type combination: The plot type, a SHAP dependence plot combined with a histogram-like representation of feature value distribution, is effective for showing the relationship between a feature's value and its impact on the model output, as well as the prevalence of those feature values.
  • ✅ Clear labeling and caption: The axes are clearly labeled: 'APRSeverityofillnessCode' for the x-axis and 'SHAP value for APRSeverityofillnessCode' for the y-axis. The caption also clearly states the feature and the population (non-newborns).
  • 💡 Clarity of grey bars representing feature distribution: The use of blue dots for individual SHAP values and grey bars for the distribution of feature values is visually distinct. However, the grey bars are quite faint and their y-axis scale is not explicitly defined, making it hard to gauge the exact frequency they represent, though their relative heights are discernible.
  • ✅ Main trend is clearly communicated: The plot clearly shows the positive trend: as the APR Severity of Illness Code increases, the SHAP values tend to increase. This main message is well-communicated.
  • ✅ Good use of point density to show SHAP value distribution: The density of the blue dots effectively conveys the concentration of SHAP values for each feature value. The vertical spread of dots at each feature value also indicates the variability of the feature's impact across different instances.
  • 💡 X-axis tick alignment for discrete feature values: The x-axis ticks are at 0.5 intervals (0.5, 1.0, 1.5...4.5) for a feature that likely takes integer values (1, 2, 3, 4 for severity). This might be a default setting of the plotting tool. Aligning ticks with the actual discrete feature values (1, 2, 3, 4) or centering the bars/dot clusters over these integer values would be more intuitive.
Fig. 10 A density plot showing the relationship between APR Severity of Illness...
Full Caption

Fig. 10 A density plot showing the relationship between APR Severity of Illness Code and the LoS.

Figure/Table Image (Page 13)
Fig. 10 A density plot showing the relationship between APR Severity of Illness Code and the LoS.
First Reference in Text
To further understand the relationship between the APR Severity of Illness code and the LoS, we created the plot in Fig. 10.
Description
  • Plot Type and Variables: The figure is a 2D density plot, also known as a heatmap, which visualizes the joint distribution of two variables: 'APR Severity of Illness Code' on the x-axis and 'Length of Stay' (LoS) on the y-axis. The plot uses color intensity to represent the density of data points (patient records) at specific combinations of severity code and LoS.
  • Axes and Scales: The x-axis, 'APR Severity of Illness Code', ranges from 0.0 to 4.0. Based on typical medical severity scales and the concentration of data, the relevant discrete values are likely 1 (Minor), 2 (Moderate), 3 (Major), and 4 (Extreme). The y-axis, 'Length of Stay', ranges from 1 to 9 days.
  • Color Scale for Density: A color bar on the right side of the plot indicates the density scale, ranging from 0 (darkest color, typically purple/blue in such schemes, representing low density) to 7 (brightest color, typically yellow, representing high density).
  • Highest Density Region: The highest density of data points (brightest yellow area) is observed for an 'APR Severity of Illness Code' of 1 and a 'Length of Stay' of approximately 2 days. This indicates that the most common scenario is minor severity with a 2-day hospital stay.
  • Trend with Increasing Severity: As the 'APR Severity of Illness Code' increases from 1 to 4, the distribution of 'Length of Stay' tends to shift upwards, and the peak density decreases. For severity code 2, the LoS distribution has a high density around 2-3 days. For severity code 3, the LoS distribution is more spread out, with a noticeable density around 3-5 days. For severity code 4, the density is lower overall, but the LoS tends to be longer, with some concentration around 4-7 days visible within the 9-day LoS range shown.
  • Methodology: The plot was generated using kernel density estimation (KDE) with a Gaussian kernel, which is a statistical method to estimate the probability density function of a random variable, here applied in two dimensions to show the joint density.
Scientific Validity
  • ✅ Appropriate visualization technique: A 2D density plot is an appropriate and effective method for visualizing the relationship between an ordinal categorical variable (APR Severity of Illness Code) and a continuous variable (LoS), especially for identifying concentrations and trends in large datasets.
  • ✅ Strongly supports claims in reference text: The plot strongly supports the claims made in the reference text, specifically that 'the most frequently occurring APR Severity of Illness code is 1 (Minor), and that the most frequently occurring LoS is 2 days.' This corresponds to the brightest yellow region in the plot.
  • ✅ Provides valuable insight into LoS drivers: The visualization provides clear evidence of how the LoS distribution shifts with increasing severity of illness, which is a clinically intuitive and important finding for understanding factors influencing LoS.
  • ✅ Sound statistical basis: The use of kernel density estimation with a Gaussian kernel is a standard statistical technique for generating such plots.
  • 💡 Truncation of LoS y-axis: The y-axis for LoS is capped at 9 days. While this focuses on the most frequent LoS durations, it truncates the view for longer stays, especially for higher severity codes where LoS can extend beyond 9 days. This is a limitation if one wants to understand the full LoS distribution for severe cases from this plot alone, though it is consistent with other plots focusing on shorter LoS.
  • 💡 Kernel bandwidth not specified: The choice of bandwidth for the kernel density estimation is not specified. Bandwidth can influence the smoothness and appearance of the density contours. However, the current plot appears to provide a reasonable representation without obvious artifacts of poor bandwidth choice.
Communication
  • ✅ Effective plot type: The 2D density plot (heatmap) is an effective choice for visualizing the joint distribution of two variables, one of which is discrete/ordinal (APR Severity of Illness Code) and the other continuous (Length of Stay).
  • ✅ Clear axis labels and scales: The axes are clearly labeled: 'APR Severity of Illness Code' for the x-axis and 'Length of Stay' for the y-axis. The numerical scales are also clear.
  • ✅ Clear color bar and good color scale choice: The color bar on the right, with values from 0 to 7, clearly indicates how color intensity maps to data density. The use of a perceptually uniform color scale (e.g., viridis or similar, as it appears to be) is good practice.
  • ✅ Informative caption: The caption is informative, specifying the variables, the type of plot, and the method used for generation (kernel density estimation with Gaussian kernel), including a citation.
  • ✅ Effectively highlights key relationships and concentrations: The plot effectively highlights the areas of highest concentration, such as severity code 1 with LoS around 2 days. The shift in LoS distribution with increasing severity is also visually apparent.
  • 💡 X-axis tick alignment for discrete feature values: The x-axis ticks are at 0.5 intervals for a feature that likely takes integer values (1, 2, 3, 4 for severity). While the density clouds are centered over these integers, aligning the major ticks directly with 1, 2, 3, 4 would be slightly more intuitive.
Fig. 11 A density plot showing the distribution of the birth weight values (in...
Full Caption

Fig. 11 A density plot showing the distribution of the birth weight values (in grams) versus the LoS.

Figure/Table Image (Page 14)
Fig. 11 A density plot showing the distribution of the birth weight values (in grams) versus the LoS.
First Reference in Text
Similarly, Fig. 11 shows the relationship between the birth weight and the length of stay.
Description
  • Plot Type and Variables: The figure is a 2D density plot (heatmap) illustrating the joint distribution of newborn 'Birth Weight' (in grams) on the x-axis and 'Length of Stay' (LoS, presumably in days) on the y-axis. Color intensity represents the density of data points (newborn records) at specific combinations of birth weight and LoS.
  • Axes and Scales: The x-axis, 'Birth Weight', is scaled from approximately 1000 grams to 8000 grams, with major ticks at 2000, 4000, 6000, and 8000 grams. The y-axis, 'Length of Stay', ranges from 1 to 9 days.
  • Color Scale for Density: A color bar on the right side of the plot indicates the density scale, ranging from 0.0000 (darkest color, typically purple/blue, representing low density) to 0.0012 (brightest color, typically yellow, representing high density).
  • Highest Density Region: The highest density of data points (brightest yellow area) is concentrated in the region where 'Birth Weight' is between approximately 2500 and 4000 grams, and 'Length of Stay' is very short, primarily around 2 days. This indicates that the most common scenario is a normal birth weight with a short hospital stay.
  • Trend for Lower Birth Weights: For lower birth weights (e.g., below 2500 grams), the density plot suggests that the Length of Stay tends to be longer and more variable. There are visible areas of moderate density (greenish colors) extending to higher LoS values (e.g., 4-7 days) for birth weights around 1500-2500 grams. This implies an inverse relationship: lower birth weights are associated with longer hospital stays.
  • Trend for Higher Birth Weights: For very high birth weights (e.g., above 4500-5000 grams), the density of data points is very low across all LoS values shown, indicating such cases are rare in this dataset.
  • Methodology: The plot was generated using kernel density estimation (KDE) with a Gaussian kernel, a statistical method to estimate the probability density function of data, applied here in two dimensions.
Scientific Validity
  • ✅ Appropriate visualization technique: A 2D density plot is an appropriate and effective method for visualizing the joint distribution of two continuous variables (Birth Weight and LoS), especially for identifying areas of high concentration and general trends in large datasets.
  • ✅ Strongly supports claims in reference text: The plot strongly supports the claim in the reference text that 'The most common length of stay is two days,' as the highest density region is centered around LoS = 2 days for the most common birth weights.
  • ✅ Provides valuable insight into LoS drivers for newborns: The visualization provides clear evidence of the clinically expected relationship: lower birth weights are generally associated with longer and more variable hospital stays for newborns. This is an important factor influencing LoS in this population.
  • ✅ Sound statistical basis: The use of kernel density estimation with a Gaussian kernel is a standard statistical technique for generating such plots.
  • 💡 Truncation of LoS y-axis: The y-axis for LoS is capped at 9 days. While this covers the majority of newborn stays (as seen in Fig. 5), it might truncate the view for extremely low birth weight newborns who could have very long stays. This is a minor limitation if the focus is on the most common patterns.
  • 💡 Kernel bandwidth not specified: The choice of bandwidth for the kernel density estimation is not specified in the caption for this specific figure, though a general method is cited. Bandwidth can influence the smoothness and appearance of the density contours.
Communication
  • ✅ Effective plot type: The 2D density plot (heatmap) is an effective choice for visualizing the joint distribution of two continuous variables: Birth Weight and Length of Stay.
  • ✅ Clear axis labels and scales: The axes are clearly labeled: 'Birth Weight' (with units implicitly grams from the caption) for the x-axis and 'Length of Stay' for the y-axis. The numerical scales are also clear.
  • ✅ Clear color bar and good color scale choice: The color bar on the right, with values from 0.0000 to 0.0012, clearly indicates how color intensity maps to data density. The color scheme appears to be perceptually uniform, which is good practice.
  • ✅ Informative caption: The caption is informative, specifying the variables, units for birth weight, the type of plot, and the method used for generation (kernel density estimation with Gaussian kernel), including a citation.
  • ✅ Effectively highlights key relationships and concentrations: The plot effectively highlights the main concentration of data points, showing that most newborns have birth weights in the 2500-4000 gram range and short LoS. The inverse relationship between birth weight and LoS for lower birth weights is also visually suggested.
  • 💡 Explicit units on x-axis label: The x-axis label 'Birth Weight' could explicitly include '(grams)' on the axis itself for immediate clarity, although the caption provides this.
Fig. 12 Confusion matrix for classification of non-newborns.
Figure/Table Image (Page 14)
Fig. 12 Confusion matrix for classification of non-newborns.
First Reference in Text
The confusion matrix in Fig. 12 shows that the highest density of correctly classified samples is in or close to the diagonal region.
Description
  • Plot Type and Purpose: The figure displays a confusion matrix, which is a table used to evaluate the performance of a classification model. This specific matrix is for the classification of Length of Stay (LoS) for non-newborns into five predefined classes or bins.
  • Classes and Labels: The classes, representing binned LoS in days, are labeled along both the rows (assumed to be True Labels) and columns (assumed to be Predicted Labels) as: '1' (1 day), '2' (2 days), '3' (3 days), '4-6' (4 to 6 days), and '>6' (more than 6 days).
  • Correct Classifications (Diagonal): The numbers within each cell represent the count of samples. The diagonal cells show the number of correctly classified samples for each class: 19,227 for class '1'; 15,728 for class '2'; 4,262 for class '3'; 25,218 for class '4-6'; and 35,052 for class '>6'.
  • Misclassifications (Off-Diagonal): Off-diagonal cells show misclassifications. For instance, 11,401 samples that truly belonged to class '1' (LoS of 1 day) were incorrectly predicted as class '2' (LoS of 2 days). Similarly, 10,781 samples of true class '4-6' were misclassified as class '2'.
  • Color Coding and Scale: A color bar on the right side indicates the scale for the cell counts, ranging from 5,000 at the bottom (lighter color) to 35,000 at the top (darker color). The caption states that lighter colors represent lower numbers, which is consistent with the color bar.
  • Visual Pattern of Classification: Visually, the diagonal elements are generally darker, indicating higher counts, which supports the reference text's statement that the highest density of correctly classified samples is in or close to the diagonal region. Many misclassifications appear in cells adjacent to the diagonal, suggesting confusion between neighboring LoS bins.
Scientific Validity
  • ✅ Appropriate evaluation tool: A confusion matrix is a standard and appropriate tool for evaluating the performance of a multi-class classification model, providing detailed insight into correct and incorrect predictions for each class.
  • ✅ Strongly supports claims in reference text: The matrix strongly supports the claims in the reference text: the diagonal elements generally have the highest counts in their respective rows/columns, and misclassifications are often concentrated in adjacent classes (e.g., class '1' being confused with '2', class '2' with '1' or '3').
  • ✅ Data allows for comprehensive performance metric calculation: The presented data allows for the calculation of per-class precision, recall, and F1-score, as well as overall accuracy, providing a comprehensive performance overview. The overall accuracy calculated from the matrix (sum of diagonal / total sum) is approximately 47.0%, which is consistent with the 46.98% accuracy reported in the text for the Multinomial Logistic Regression model used for this non-newborn classification.
  • 💡 Impact of binning strategy: The choice of LoS bins (1, 2, 3, 4-6, >6 days) influences the classification task and the interpretation of the matrix. The broadness of the '>6' class means that it lumps together a wide range of longer stays, and the model's ability to distinguish between, for example, a 7-day stay and a 30-day stay is not assessed by this matrix.
  • 💡 Model and dataset specific results: The matrix represents the performance of a specific model (Multinomial Logistic Regression, as per text) on a particular dataset split (presumably a test set). Performance could vary with different models or data.
Communication
  • ✅ Standard and clear format: The confusion matrix is presented in a standard grid format, which is familiar for classification performance evaluation. The numerical values within each cell are clearly legible.
  • ✅ Effective color coding for visual assessment: The color coding, with lighter shades for lower counts and darker shades for higher counts (as indicated by the color bar ranging from 5000 to 35000), provides a quick visual impression of where the classifications are concentrated.
  • 💡 Explicit axis titles (True/Predicted Label): The class labels ('1', '2', '3', '4-6', '>6') are used for both rows and columns. While common, explicitly labeling the y-axis as 'True Label' and the x-axis as 'Predicted Label' would enhance clarity for readers less familiar with confusion matrices.
  • ✅ Informative caption: The caption is informative, explaining that the figure is a confusion matrix for non-newborns and how to interpret the diagonal elements and color coding.
  • ✅ Effectively communicates model performance: The figure effectively communicates the model's performance across different LoS classes, highlighting both correct classifications and common misclassification patterns.
Fig. 13 Confusion matrix for classification of newborns.
Figure/Table Image (Page 15)
Fig. 13 Confusion matrix for classification of newborns.
First Reference in Text
The confusion matrix in Fig. 13 shows that the majority of data samples lie in or close to the diagonal region.
Description
  • Plot Type and Purpose: Figure 13 presents a confusion matrix, a tool used to summarize the performance of a classification model, in this case, for predicting the Length of Stay (LoS) for newborns. The LoS has been categorized into five classes.
  • Classes and Labels: The LoS classes are labeled along the rows (True Labels) and columns (Predicted Labels) as: '1' (1 day), '2' (2 days), '3' (3 days), '4-6' (4 to 6 days), and '>6' (more than 6 days).
  • Correct Classifications (Diagonal): The diagonal cells show the number of correctly classified newborn LoS instances for each class. These are: 140 for class '1'; 11,713 for class '2'; 261 for class '3'; 170 for class '4-6'; and 1,071 for class '>6'. The highest number of correct classifications is for class '2' (11,713 instances).
  • Misclassifications (Off-Diagonal): Off-diagonal cells represent misclassifications. For example, 1,301 newborns with a true LoS of 1 day (class '1') were incorrectly predicted to have an LoS of 2 days (class '2'). Similarly, 4,947 newborns with a true LoS of 2 days were mispredicted as class '3'.
  • Color Coding and Scale: A color bar on the right indicates the scale for the cell counts, ranging from 0 (lighter color, bottom) to 10,000 (darker color, top). The caption confirms that lighter colors represent lower numbers.
  • Visual Pattern of Classification: Visually, the cell for (True '2', Predicted '2') is the darkest, reflecting the 11,713 correct classifications. Significant misclassifications appear in cells adjacent to the diagonal, such as true '2' being predicted as '3' (4,947 instances) or true '1' being predicted as '2' (1,301 instances). This supports the reference text's claim that most samples lie in or close to the diagonal.
Scientific Validity
  • ✅ Appropriate evaluation tool: A confusion matrix is an appropriate and standard method for evaluating the performance of a multi-class classification model, providing a detailed breakdown of correct and incorrect predictions per class.
  • ✅ Supports claims in reference text: The matrix supports the reference text's claim that 'the majority of data samples lie in or close to the diagonal region.' The highest values are on the diagonal, and significant off-diagonal values are often in adjacent cells.
  • ✅ Reveals class-specific performance: The matrix reveals the model's strengths and weaknesses for newborn LoS prediction. For example, it performs very well for class '2' (LoS of 2 days) in terms of raw correct counts, but has more difficulty with class '1', '3', and '4-6', where misclassifications into neighboring classes are common.
  • ✅ Allows for verification of reported accuracy: The overall accuracy for this Random Forest Classification model for newborns is stated in the text as 60.08%. The data in the matrix (sum of diagonal / total sum) should align with this reported accuracy. Sum of diagonal = 140+11713+261+170+1071 = 13355. Total sum = sum of all cells. This detailed breakdown is valuable.
  • 💡 Impact of binning strategy: The choice of LoS bins (1, 2, 3, 4-6, >6 days) is consistent with Fig. 12 and impacts the classification task. The performance metrics are relative to these defined bins.
  • 💡 Highlights challenges in predicting certain LoS classes for newborns: The relatively low number of correct classifications for classes '1' (140), '3' (261), and '4-6' (170) compared to class '2' (11,713) suggests either class imbalance or that these classes are harder to predict accurately with the current model and features for newborns.
Communication
  • ✅ Standard and clear format: The confusion matrix is presented in a standard grid format, which is appropriate for visualizing classification performance. The numerical values within each cell are clearly legible.
  • ✅ Effective color coding: The color coding, with lighter shades for lower counts and darker shades for higher counts (color bar from 0 to 10000), helps in quickly identifying areas of high and low classification counts.
  • 💡 Explicit axis titles (True/Predicted Label): The class labels ('1', '2', '3', '4-6', '>6') are used for both rows (True Labels) and columns (Predicted Labels). Explicitly titling the axes as 'True Label' and 'Predicted Label' would be a minor improvement for universal clarity.
  • ✅ Informative caption: The caption clearly explains that the figure is a confusion matrix for newborns and how to interpret the diagonal elements and color coding.
  • ✅ Effectively communicates model performance: The figure effectively communicates the model's performance for newborn LoS classification, showing strengths and weaknesses across classes.
Fig. 14 Shows the density plot of the predicted length of stay versus actual...
Full Caption

Fig. 14 Shows the density plot of the predicted length of stay versus actual length of stay for the classifier model for non-newborns.

Figure/Table Image (Page 15)
Fig. 14 Shows the density plot of the predicted length of stay versus actual length of stay for the classifier model for non-newborns.
First Reference in Text
The density plot in Fig. 14 shows the relationship between the actual LoS and the predicted LoS.
Description
  • Plot Type and Purpose: Figure 14 is a 2D density plot, often referred to as a heatmap, which illustrates the relationship between the 'Actual Length of Stay' (LoS) and the 'Predicted Length of Stay' for non-newborns, as determined by a classifier model. Color intensity represents the density of data points (patient cases) at each combination of actual and predicted LoS.
  • Axes and Scales: The x-axis, 'Actual Length of Stay', ranges from 1 to 8 days. The y-axis, 'Predicted Length of Stay', also ranges from 1 to 8 days. This suggests that both actual and predicted LoS values are likely binned or represent discrete day counts within this range for the purpose of this classifier's evaluation.
  • Color Scale for Density: A color bar on the right side of the plot shows the density scale, ranging from 0.02 (darker blue/purple, indicating low density) to 0.12 (brighter yellow, indicating high density).
  • Concentration along the Diagonal: The highest density of points (brightest yellow regions) generally falls along or very close to the main diagonal (where Actual LoS = Predicted LoS). For example, when the Actual LoS is 1 day, the Predicted LoS also shows its highest density around 1 day. Similarly, for an Actual LoS of 2 days, the highest density of predictions is clustered around 2-3 days. This pattern indicates that the classifier often predicts the LoS correctly or close to the actual value, especially for shorter stays.
  • Pattern for Longer Actual LoS: As the Actual LoS increases (e.g., to 3, 4, 5 days), the peak density of predictions still tends to be around the actual value, but the clusters become more diffuse (spread out vertically) and the peak density values are lower compared to shorter stays. This suggests that the classifier's predictions become less precise or more varied for longer actual LoS values within this 1-8 day range.
  • Methodology: The plot was generated using kernel density estimation (KDE) with a Gaussian kernel, a statistical method for estimating the probability density function of a random variable, applied here to visualize the joint distribution of actual and predicted LoS values.
Scientific Validity
  • ✅ Appropriate visualization technique: A 2D density plot is an appropriate visualization for comparing actual versus predicted values from a classification model, especially when the output represents binned categories that can be mapped to a numerical scale. It effectively shows where the model's predictions concentrate relative to the true values.
  • ✅ Supports claims in reference text: The plot visually supports the reference text's statement that 'For a LoS of 2 days, the centroid of the predicted LoS cluster is between 2 and 3 days.' The brightest region for Actual LoS = 2 is indeed centered vertically between predicted LoS of 2 and 3.
  • ✅ Provides good visual summary of classifier performance: The plot provides a good visual summary of the classifier's performance. The concentration along the diagonal indicates the model's ability to correctly classify LoS, while the spread shows the extent and nature of misclassifications (e.g., tending to predict slightly longer stays for actual LoS of 2 days).
  • 💡 Truncation of LoS axes limits view of longer stays: The plot is limited to LoS values up to 8 days. This is consistent with the error analysis in Figure 15, which also focuses on this range. However, it means the plot doesn't show performance for the '>6 days' class if it extends beyond 8 days, or how the classifier handles the general '>8 days' category if that's how the bin is defined in other contexts.
  • 💡 Interpretation of 'Predicted LoS' from classifier: The term 'Predicted Length of Stay' for a classifier output needs careful interpretation. It likely represents the LoS value corresponding to the predicted class bin (e.g., the midpoint or a representative value of the bin). The smoothing from KDE helps visualize the distribution of these predictions.
  • 💡 Kernel bandwidth not specified: The choice of bandwidth for the kernel density estimation is not specified in this figure's caption (though a general citation [61] is given for the method). Bandwidth selection can influence the appearance of the density contours.
Communication
  • ✅ Effective plot type: The 2D density plot (heatmap) is an effective way to visualize the agreement between actual and predicted Length of Stay (LoS) values from a classifier model.
  • ✅ Clear axis labels and scales: The axes are clearly labeled 'Actual Length of Stay' (x-axis) and 'Predicted Length of Stay' (y-axis). The numerical scales (1 to 8 days) are also clear.
  • ✅ Clear color bar and appropriate color scale: The color bar on the right, with values from 0.02 to 0.12, clearly indicates how color intensity maps to data density. The color scheme (likely viridis or similar) is perceptually uniform, which is good practice.
  • ✅ Informative caption: The caption is informative, specifying the variables, the model type (classifier for non-newborns), and the method used for generation (kernel density estimation with Gaussian kernel), including a citation.
  • ✅ Effectively highlights model performance: The plot effectively highlights that the model's predictions are most concentrated along the diagonal, especially for shorter LoS values, indicating correct or nearly correct classifications. The spread off the diagonal shows where the classifier makes errors.
Fig. 15 Shows the distribution of correctly predicted LoS values for each class...
Full Caption

Fig. 15 Shows the distribution of correctly predicted LoS values for each class used in our model.

Figure/Table Image (Page 16)
Fig. 15 Shows the distribution of correctly predicted LoS values for each class used in our model.
First Reference in Text
A quantitative depiction of our model errors is shown in Fig. 15.
Description
  • Plot Type and Purpose: Figure 15 is a heatmap that displays the distribution of prediction errors for a Length of Stay (LoS) model, specifically for non-newborns. The values in the cells represent proportions.
  • Axes/Categories Description: The columns represent the actual LoS classes, categorized as 1, 2, 3, 4, 5, 6, 7, 8 (presumably days), and 'More than 8' days. The rows represent the magnitude of the prediction error, binned as: '0 < err <= 1' (error is greater than 0 but less than or equal to 1 day), '1 < err <= 2', '2 < err <= 3', '3 < err <= 4', '4 < err <= 5', and 'err > 5' (error is greater than 5 days).
  • Cell Value Interpretation: Each cell in the heatmap shows the proportion of predictions for a given actual LoS class (column) that fall into a specific error magnitude bin (row). For example, for an actual LoS of 2 days (column '2'), the cell in the '0 < err <= 1' row has a value of 0.51. This means that 51% of the time when the actual LoS was 2 days, the model's prediction had an error of 1 day or less.
  • Color Scale: A color scale on the right ranges from 0.1 (darker blue) to 0.5 (brighter, more towards yellow/orange), indicating the proportion in each cell. Higher values (brighter colors) mean a larger proportion of predictions fall into that error category for that actual LoS.
  • Error Distribution for Short LoS: For shorter actual LoS values (e.g., 1 to 3 days), the highest proportions are concentrated in the smallest error bin ('0 < err <= 1'). For example, for actual LoS = 1, the proportion is 0.28; for LoS = 2, it's 0.51; for LoS = 3, it's 0.52. This indicates the model is relatively accurate for short stays.
  • Error Distribution for Longer LoS: As the actual LoS increases, the errors tend to become larger. For actual LoS = 8 days, the proportion of predictions with an error of 1 day or less is 0.1, while the proportion with an error between 1 and 2 days is 0.1, and the proportion with an error between 4 and 5 days is 0.09, and error > 5 days is 0.5.
  • Error Distribution for 'More than 8' LoS Class: For the 'More than 8' actual LoS class, the largest proportion of errors (0.5) falls into the 'err > 5' bin, indicating significant errors for very long stays, likely due to the truncation of this class.
  • Interpretation of 'Zero Error': The caption explains that an error of 0 would mean the predicted LoS is exactly the actual LoS. The top row ('0 < err <=1') implies that a zero error would fall into this bin, suggesting good performance. For example, the text interprets the 0.51 for LoS=2 as 51% of predicted LoS having an error of less than 1 day, which includes zero error.
Scientific Validity
  • ✅ Appropriate visualization for error analysis: The heatmap is an appropriate method to visualize the distribution of prediction errors across different actual classes and error magnitudes, providing a quantitative depiction as stated in the reference text.
  • ✅ Illustrates common LoS prediction model behavior: The figure clearly demonstrates that the model performs better (smaller errors) for shorter actual LoS values and that performance degrades for longer LoS values. This is a common finding in LoS prediction tasks.
  • 💡 Potential misalignment between figure's error bins and textual interpretation of specific error values: The interpretation provided in the reference text for LoS=2 (51% have zero error, 23% have an error of 1 day) is slightly confusing when compared to the figure's row label '0 < err <= 1'. The figure's label suggests this bin includes errors from just above 0 up to 1. The text seems to imply this bin is specifically for 'zero error' and then another for 'error of 1 day'. The caption's explanation ('error of less than or equal to one day') for the top row is more consistent with the figure's row label. The text's interpretation of how the 0.51 is broken down further (51% zero error, 23% 1 day error) cannot be directly derived from this single cell value of 0.51 in the figure. The figure shows that 51% of predictions for actual LoS=2 have an absolute error between 0 and 1 day (inclusive of 0 and 1 if errors are discrete days). The second row for LoS=2 shows 0.23 for error between 1 and 2 days. This suggests the text interpretation of the figure's data for LoS=2 might be misaligned with the figure's binning or contains additional breakdown not directly shown.
  • ✅ Correctly identifies impact of class truncation on errors: The large errors for the 'More than 8' class (50% of predictions having an error > 5 days) are correctly attributed in the text to the truncation of this class, which lumps together a wide range of actual LoS values. This is a valid observation and limitation.
  • 💡 Definition of error calculation not explicit in figure: The definition of 'error' (e.g., absolute difference between predicted LoS class midpoint and actual LoS class midpoint) is not explicitly defined in the figure's context, but the binned magnitudes are clear. The caption clarifies it's the difference between actual and predicted LoS.
Communication
  • ✅ Effective visualization choice: The heatmap is a generally effective way to visualize the distribution of prediction errors across different actual LoS classes and error magnitudes.
  • ✅ Clear row and column labels: The column labels (1, 2, ..., 8, More than 8) clearly indicate the actual LoS classes. The row labels (0< err <=1, 1< err <=2, etc.) clearly define the error bins.
  • ✅ Clear color scale: The color scale on the right (0.1 to 0.5) helps in quickly identifying cells with higher proportions of errors. The use of a sequential color scheme is appropriate.
  • ✅ Highly informative and essential caption: The caption is very detailed and accurately explains how to interpret the rows (error magnitudes) and columns (actual LoS classes), which is crucial for understanding this somewhat complex figure. It also specifies that the data is for non-newborns.
  • 💡 Figure title could be more precise: The title 'Fig. 15 Shows the distribution of correctly predicted LoS values for each class used in our model' is slightly misleading, as the figure primarily shows the distribution of errors in predicted LoS values, not just correctly predicted ones. The reference text 'A quantitative depiction of our model errors' is more accurate. The detailed caption clarifies this, but the main title could be improved to reflect 'error distribution'.
  • ✅ Legible numerical values: The numerical values within the cells are legible and directly represent the proportions, which is good.
Fig. 16 Scatter plot showing an instance of a linear regression fit to the data...
Full Caption

Fig. 16 Scatter plot showing an instance of a linear regression fit to the data (newborns).

Figure/Table Image (Page 16)
Fig. 16 Scatter plot showing an instance of a linear regression fit to the data (newborns).
First Reference in Text
Figures 16 and 17 show the scatter plots for the linear regression models.
Description
  • Plot Type and Subject: Figure 16 is a scatter plot that visually represents the performance of a linear regression model for predicting Length of Stay (LoS) in newborns. Each orange dot on the plot corresponds to an individual newborn patient case.
  • Axes Description: The x-axis is labeled 'Actual Length of Stay' and ranges from 0 to 120 (presumably days). The y-axis is labeled 'Predicted Length of Stay' and also ranges from 0 to 120 (days). This setup allows for a direct comparison between what the model predicted and what actually occurred.
  • Overlay Lines: Two lines are overlaid on the scatter plot: A blue line labeled 'Exact Line'. This line represents a perfect prediction scenario where the Predicted LoS exactly equals the Actual LoS (i.e., a line with a slope of 1 passing through the origin). A green line labeled 'Best Fit Line'. This is the linear regression line calculated from the data, representing the model's best linear estimate of Predicted LoS based on Actual LoS.
  • Data Distribution and Regression Fit: The orange data points are clustered more densely at lower LoS values (e.g., 0-20 days) and become sparser as LoS increases. The green 'Best Fit Line' appears to pass closely through the dense cluster of points at lower LoS and generally follows the trend of the data. It is quite close to the blue 'Exact Line', especially for LoS values up to around 60-80 days.
  • R² Score and Interpretation: The caption states that the R² score for this linear regression model on newborn data is 0.82. The R² score, or coefficient of determination, measures how well the regression predictions approximate the real data points. An R² of 0.82 indicates that 82% of the variance in the Predicted LoS can be explained by the Actual LoS through this linear model, suggesting a strong fit for this newborn dataset.
  • Performance at Longer Stays: For very long actual stays (e.g., Actual LoS > 100 days), there are fewer data points, and the 'Best Fit Line' might show some deviation from the 'Exact Line', but overall the two lines are quite close across much of the range.
Scientific Validity
  • ✅ Appropriate visualization for regression performance: A scatter plot with the regression line and an ideal fit line (y=x) is a standard and highly appropriate method for visualizing the performance of a linear regression model, allowing for qualitative assessment of the fit.
  • ✅ High R² score indicates good model fit for newborns: The reported R² score of 0.82 is very high for LoS prediction tasks, especially using a simple linear regression model. This suggests that for the newborn dataset, the features used (or perhaps a strong linear component in the relationship) allow for a strong predictive capability with this model. The visual proximity of the best fit line to the exact fit line is consistent with a high R² value.
  • ✅ Supports claims in reference text: The plot clearly supports the reference text's explanation of the 'exact line' and what a perfect model would look like. It allows viewers to judge how close the current model comes to this ideal.
  • ✅ Visual evidence consistent with reported R²: The visual evidence in the plot (points clustering around the best fit line, which is close to the exact fit line) is consistent with an R² of 0.82. This indicates a strong linear relationship captured by the model for this specific dataset (newborns).
  • 💡 Clarification of axes in evaluation context: The plot shows 'Actual Length of Stay' on the x-axis and 'Predicted Length of Stay' on the y-axis. Typically, in evaluating regression models, the independent variables (features) are used to predict the dependent variable (LoS). A scatter plot of actual LoS vs. predicted LoS is standard for evaluation. If the x-axis is meant to be a primary predictor rather than the actual outcome, the labeling might be slightly unconventional for an evaluation plot, but it's a common way to show actual vs. predicted.
  • 💡 Ambiguity of 'instance' in caption: The term 'instance of a linear regression fit' in the caption suggests this might be one example or a specific run. However, given the R² score, it likely represents the overall model fit for the newborn dataset. If it's just an 'instance', the generalizability of the R² score might be questioned.
Communication
  • ✅ Appropriate chart type: The scatter plot is a standard and effective way to visualize the relationship between actual and predicted values in a regression model.
  • ✅ Clear labels and legend: The axes are clearly labeled 'Actual Length of Stay' and 'Predicted Length of Stay'. The legend clearly distinguishes between the 'Best Fit Line' (green) and the 'Exact Line' (blue).
  • ✅ Effective use of reference line ('Exact Line'): The inclusion of the 'Exact Line' (y=x line) provides an excellent visual reference for perfect prediction, making it easy to assess the model's performance relative to this ideal.
  • ✅ Informative caption: The caption is informative, specifying the dataset (newborns), the R² score (0.82), and explaining the meaning of the blue line. This makes the figure largely self-contained.
  • 💡 Potential for overplotting with many data points: The data points (orange dots) are numerous, which can lead to overplotting, especially for shorter LoS values where data is concentrated. However, the overall trend and the fit of the regression line are still discernible.
  • ✅ Effectively communicates model fit: The plot effectively conveys that for newborns, the linear regression model provides a reasonably good fit, with predictions generally aligning with actual values, especially for shorter stays.
Fig. 17 Scatter plot for linear regression. (non-newborns).
Figure/Table Image (Page 17)
Fig. 17 Scatter plot for linear regression. (non-newborns).
First Reference in Text
Figures 16 and 17 show the scatter plots for the linear regression models.
Description
  • Plot Type and Subject: Figure 17 is a scatter plot illustrating the performance of a linear regression model used to predict Length of Stay (LoS) for the non-newborn patient dataset. Each small orange dot represents an individual patient case.
  • Axes Description: The x-axis, labeled 'Actual Length of Stay', ranges from 0 to 120 (presumably days). The y-axis, labeled 'Predicted Length of Stay', also ranges from 0 to 120 (days). This allows for a direct comparison of the model's predictions against the actual outcomes.
  • Overlay Lines: Two distinct lines are overlaid on the scatter of data points: A blue line, labeled 'Exact Line', represents the ideal scenario where Predicted LoS perfectly matches Actual LoS (a y=x line with a slope of 1). A green line, labeled 'Best Fit Line', represents the linear regression model's prediction line based on the input features.
  • Data Distribution and Regression Fit: The orange data points are densely packed, particularly for Actual LoS values below approximately 20 days, forming a wide band. The green 'Best Fit Line' has a noticeably shallower slope than the blue 'Exact Line'. This indicates that, on average, the model tends to under-predict longer LoS and may over-predict very short LoS relative to a perfect fit.
  • R² Score and Interpretation: The caption states that the R² score for this linear regression model on non-newborn data is 0.42. The R² score (coefficient of determination) quantifies how well the regression predictions fit the actual data. An R² of 0.42 means that 42% of the variance in the Predicted LoS is explained by the model using the Actual LoS (or more accurately, by the features used to predict LoS). This suggests a moderate fit, weaker than the 0.82 R² score observed for newborns in Figure 16.
  • Variability and Spread of Predictions: There is considerable scatter of data points around the 'Best Fit Line', indicating substantial variability in predictions for any given Actual LoS. Many points lie far from both the 'Best Fit Line' and the 'Exact Line', especially as Actual LoS increases.
Scientific Validity
  • ✅ Appropriate visualization for regression assessment: Displaying a scatter plot of actual versus predicted values, along with the regression line and an ideal fit line, is a standard and appropriate method for evaluating the performance of a linear regression model.
  • ✅ R² score consistent with visual representation: The R² score of 0.42 indicates a moderate linear relationship captured by the model for the non-newborn dataset. The visual representation (significant spread of points, divergence between best fit and exact lines) is consistent with this R² value, indicating that while there is some predictive capability, a large portion of the variance remains unexplained by this linear model.
  • ✅ Highlights model limitations for non-newborns: The plot, particularly the divergence of the 'Best Fit Line' from the 'Exact Line' and the wide scatter, clearly illustrates the limitations of the linear regression model for the non-newborn dataset, especially when compared to its performance on the newborn dataset (Fig. 16).
  • ✅ Supports claims in reference text: The plot effectively supports the reference text's explanation of the 'exact line' and its role in evaluating model performance.
  • 💡 Overplotting obscures detailed error distribution: The significant overplotting makes it difficult to assess the density distribution of errors or to identify if there are specific regions of Actual LoS where the model performs particularly poorly beyond the general trend. This is a limitation of using a simple scatter plot for very large datasets without transparency or density indications.
  • ✅ Standard actual vs. predicted plot: The plot shows 'Actual Length of Stay' on the x-axis and 'Predicted Length of Stay' on the y-axis. This is a standard actual vs. predicted plot for model evaluation.
Communication
  • ✅ Appropriate chart type: The scatter plot is a standard and appropriate method for visualizing the relationship between actual and predicted values in a regression model.
  • ✅ Clear labels and legend: The axes are clearly labeled 'Actual Length of Stay' and 'Predicted Length of Stay'. The legend clearly distinguishes the 'Best Fit Line' (green) from the 'Exact Line' (blue).
  • ✅ Effective use of reference line ('Exact Line'): The inclusion of the 'Exact Line' (y=x line) is crucial as a reference for perfect prediction, allowing for easy visual assessment of the model's deviation.
  • ✅ Informative caption: The caption is informative, specifying the dataset (non-newborns), the R² score (0.42), and explaining the meaning of the blue line. This enhances the figure's self-containedness.
  • 💡 Severe overplotting due to high data density: The data points (orange dots) are very dense, leading to significant overplotting, especially for shorter LoS values. This makes it difficult to discern the true distribution of points and individual predictions in these regions. Techniques like using transparency (alpha blending) or plotting a 2D density/heatmap instead could improve clarity for such dense data.
  • ✅ General trend discernible despite overplotting: Despite overplotting, the general trend and the significant spread of predictions around the best fit line are visible, indicating a weaker fit compared to Figure 16 (newborns).
Fig. 18 Shows the density plot of the predicted length of stay versus actual...
Full Caption

Fig. 18 Shows the density plot of the predicted length of stay versus actual length of stay for the classifier model for non-newborns.

Figure/Table Image (Page 17)
Fig. 18 Shows the density plot of the predicted length of stay versus actual length of stay for the classifier model for non-newborns.
First Reference in Text
Figure 18 shows a density plot depicting the relationship between the predicted length of stay and the actual length of stay.
Description
  • Plot Type and Variables: Figure 18 is a 2D density plot that visualizes the relationship between the 'Actual Length of Stay' (LoS) on the x-axis and the 'Predicted Length of Stay' on the y-axis for a classifier model applied to non-newborn patients. The density of data points (patient cases) is represented by the intensity of the orange/brown shading; darker/more intense areas indicate a higher concentration of predictions.
  • Axes and Scales: Both the x-axis ('Actual Length of Stay') and y-axis ('Predicted Length of Stay') are scaled from 1 to 8, presumably representing days or LoS class bins.
  • Overlay Lines: Two lines are overlaid on the density plot: A blue line labeled 'Exact Line', representing a perfect prediction where Predicted LoS equals Actual LoS (a y=x line). A green line labeled 'Best Fit Line', which is described in the caption as 'The best fit regression line to our predictions'. This line shows the general trend of the model's predictions relative to the actual values.
  • Data Density Distribution: The density cloud is most intense (darkest orange/brown) for shorter actual LoS values (e.g., 1-3 days), with predictions also concentrated in these shorter LoS ranges. The cloud generally follows the diagonal but is quite broad, indicating variability in predictions.
  • Relationship between Best Fit and Exact Lines: The green 'Best Fit Line' has a shallower slope than the blue 'Exact Line'. It starts slightly above the 'Exact Line' for very short actual LoS and then falls below the 'Exact Line' as actual LoS increases. This suggests a tendency for the classifier model to, on average, over-predict very short stays and under-predict longer stays within this 1-8 day range.
  • Methodology: The plot was generated using kernel density estimation (KDE) with a Gaussian kernel, a statistical method to estimate the probability density of the data, which is then visualized as the shaded regions.
Scientific Validity
  • ✅ Appropriate visualization for classifier performance: Using a 2D density plot to compare actual versus predicted values from a classifier (where predictions are likely class labels mapped to representative LoS values) is an appropriate way to visualize the model's performance and error patterns.
  • ✅ Useful reference lines for interpretation: The inclusion of an 'Exact Line' (y=x) provides a clear benchmark for perfect prediction. The 'Best Fit Line' helps to summarize the systematic trend in the model's predictions.
  • ✅ Illustrates typical classifier performance characteristics: The plot supports the general understanding of the classifier's behavior: it captures some of the relationship between actual and predicted LoS, but there's considerable variance and some systematic deviation (as shown by the best fit line's slope). This is consistent with the performance of many real-world classifiers on complex tasks.
  • ✅ Strongly supports reference text: The plot effectively visualizes the information presented in the reference text regarding the two lines and their meaning.
  • 💡 Interpretation of 'Predicted LoS' from classifier: The interpretation of 'Predicted Length of Stay' from a classifier model is important. It likely refers to the representative value of the predicted LoS class bin. The density plot then shows the distribution of these representative values against the actual LoS (also likely binned or its representative value).
  • 💡 Limited view due to axis range (1-8 days): The axes are limited to 1-8 days. This focuses on shorter stays but doesn't show how the classifier performs for the '>6' or potentially longer LoS categories if they extend beyond 8 days. This is consistent with the error analysis in Fig. 15.
Communication
  • ✅ Comprehensive visualization choice: The 2D density plot combined with regression lines is a comprehensive way to visualize classifier performance in terms of agreement between predicted and actual (binned) LoS.
  • ✅ Clear labels and legend: The axes are clearly labeled 'Actual Length of Stay' and 'Predicted Length of Stay'. The legend clearly distinguishes the 'Best Fit Line' (green) from the 'Exact Line' (blue).
  • ✅ Effective use of reference and fit lines: The inclusion of both the 'Exact Line' (ideal prediction) and the 'Best Fit Line' (trend in predictions) provides valuable context for interpreting the density cloud.
  • ✅ Highly informative caption: The caption is highly informative, explaining the plot type, variables, model context (classifier for non-newborns), the method of generation, and the meaning of the two lines. This significantly aids understanding.
  • 💡 Missing color bar for density scale: The color scheme for the density plot (shades of orange/brown) effectively highlights areas of high concentration, although a color bar indicating the density scale is missing, which would add precision.
  • ✅ Clearly communicates model performance characteristics: The plot effectively communicates that while there's a general positive correlation, the classifier's predictions show considerable spread and the 'Best Fit Line' deviates from the 'Exact Line', indicating imperfect classification.
Fig. 19 This figure shows the three CCS diagnosis codes that produced the top...
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Fig. 19 This figure shows the three CCS diagnosis codes that produced the top three R² scores using linear regression.

Figure/Table Image (Page 18)
Fig. 19 This figure shows the three CCS diagnosis codes that produced the top three R² scores using linear regression.
First Reference in Text
Hence, in order to understand which CCS diagnosis codes produce good model fits, we produced the plot in Fig. 19.
Description
  • Plot Type and Context: Figure 19 is a bar chart that displays the R² (R-squared) scores obtained from linear regression models built separately for different Clinical Classifications Software (CCS) diagnosis codes. CCS codes are used to group patient diagnoses and procedures into a manageable number of clinically meaningful categories.
  • Axes and R² Score Explanation: The x-axis, labeled 'CCS Diagnosis Codes', shows six specific numerical CCS codes: 101, 100, 109, 159, 657, and 659. The y-axis, labeled 'r squared score', ranges from 0.0 to 0.6. The R² score is a statistical measure that represents the proportion of the variance in the dependent variable (Length of Stay) that is predictable from the independent variable(s) in a regression model. A score closer to 1 indicates a better fit.
  • Top Performing CCS Diagnosis Codes: The chart highlights the performance for six specific CCS codes. The first three bars represent the codes with the highest R² scores: CCS code 101 has the highest R² score, approximately 0.62. CCS code 100 has an R² score of about 0.54. CCS code 109 has an R² score of approximately 0.50.
  • Lowest Performing CCS Diagnosis Codes (shown): The last three bars represent the codes with the lowest R² scores among those selected for display: CCS code 159 has an R² score of about 0.21. CCS code 657 has an R² score of roughly 0.18. CCS code 659 has the lowest R² score shown, approximately 0.14.
  • Selection Criteria for Displayed Codes: The caption clarifies that these are specifically the top three and bottom three R² scores from the analysis when using linear regression for individual CCS diagnosis codes.
Scientific Validity
  • ✅ Appropriate visualization for comparing R² scores: Using a bar chart to compare R² scores across different categories (CCS diagnosis codes) is an appropriate and standard visualization method.
  • ✅ Demonstrates variability in model performance by diagnosis code: The figure effectively demonstrates that model performance (as measured by R²) varies significantly depending on the specific CCS diagnosis code when separate linear regression models are built for each. This supports the idea that a one-size-fits-all model may not be optimal for all diagnostic categories.
  • ✅ Highlights differential predictability for specific conditions: The R² scores presented (e.g., 0.62 for CCS code 101) indicate that for certain specific cardiac-related conditions (as per Table 4: Coronary atherosclerosis and other heart disease), a linear regression model can explain a substantial portion of the variance in Length of Stay. Conversely, for conditions like 'Urinary tract infections' (CCS 159, R² ~0.21) or 'Schizophrenia and other psychotic disorders' (CCS 659, R² ~0.14), the linear model has much lower explanatory power.
  • ✅ Supports stated research goal: The figure and caption, in conjunction with the reference text and Tables 4 and 5, clearly support the goal of identifying CCS codes that produce good or poor model fits with linear regression.
  • 💡 Selective presentation (top/bottom 3): The figure only shows the top 3 and bottom 3 R² scores. While this highlights the extremes, it doesn't provide a view of the overall distribution of R² scores across all 285 CCS codes. This is a selective presentation, but appropriate for illustrating the range of performance.
  • 💡 Contextual interpretation of 'good model fit': The term 'good model fits' is relative. An R² of 0.62 might be considered good in some contexts, especially for complex outcomes like LoS, while in others it might be moderate. The interpretation depends on the field and specific application.
Communication
  • ✅ Appropriate chart type: The bar chart is a straightforward and effective way to compare the R² scores for different CCS diagnosis codes.
  • ✅ Clear axis labels: The x-axis ('CCS Diagnosis Codes') and y-axis ('r squared score') are clearly labeled. The numerical labels for the CCS codes on the x-axis are distinct.
  • ✅ Easy visual comparison of R² scores: The bars are clearly differentiated, and their heights directly correspond to the R² scores, making visual comparison easy.
  • ✅ Informative caption: The caption is informative, specifying that the plot shows the top three and bottom three R² scores for CCS diagnosis codes using linear regression, and it lists these codes. This greatly aids interpretation.
  • ✅ Clean and uncluttered design: The use of a single color for all bars is appropriate as the primary comparison is based on height. The plot is clean and uncluttered.
  • 💡 Clinical meaning of CCS codes not directly in figure: While the CCS codes are numerically identified, providing the actual diagnosis descriptions (as done in Tables 4 and 5 in the text) directly on the plot or in a more closely associated legend could make the figure more self-contained regarding the clinical meaning of these codes. However, given the space constraints of a bar chart with potentially long descriptions, referencing the tables is a reasonable compromise.
Table 4 CCS Diagnosis codes, descriptions and R² Scores for the top 3 CCS codes...
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Table 4 CCS Diagnosis codes, descriptions and R² Scores for the top 3 CCS codes in Fig. 19

Figure/Table Image (Page 18)
Table 4 CCS Diagnosis codes, descriptions and R² Scores for the top 3 CCS codes in Fig. 19
First Reference in Text
We provide the following descriptions in Tables 4 and 5 for the 3 CCS Diagnosis Codes in Fig. 19 with the top R2 Scores using linear regression.
Description
  • Table Purpose and Terminology: Table 4 lists the top three Clinical Classifications Software (CCS) diagnosis codes that yielded the highest R² (R-squared) scores when individual linear regression models were used to predict Length of Stay (LoS) for patients within each specific CCS category. CCS codes are a system for categorizing patient diagnoses into clinically meaningful groups. The R² score indicates the proportion of variance in LoS explained by the model, with higher scores indicating a better fit.
  • Top CCS Code (101): The CCS Diagnosis Code '101' is associated with 'Coronary atherosclerosis and other heart disease' and achieved an R² Score of 0.617. This was the highest R² score among all CCS codes when modeled with linear regression.
  • Second CCS Code (100): The CCS Diagnosis Code '100', described as 'Acute myocardial infarction' (commonly known as a heart attack), yielded the second-highest R² Score of 0.538.
  • Third CCS Code (109): The CCS Diagnosis Code '109', which corresponds to 'Acute cerebrovascular disease' (conditions affecting blood flow to the brain, like a stroke), had the third-highest R² Score of 0.497.
Scientific Validity
  • ✅ Provides valuable clinical context to Figure 19: Presenting the descriptions for the CCS codes that achieved the highest R² scores is a valid way to provide context and clinical meaning to the numerical results shown in Figure 19. It helps identify which types of medical conditions are better predicted by the linear regression models.
  • ✅ Consistency with Figure 19 data: The R² scores reported (0.617, 0.538, 0.497) are consistent with the bar heights for CCS codes 101, 100, and 109 respectively in Figure 19, confirming the data linkage.
  • ✅ Highlights predictability of specific conditions: The fact that specific, relatively well-defined acute and chronic conditions (related to heart disease and stroke) yield higher R² scores suggests that LoS for these conditions might have more consistent drivers that a linear model can capture, compared to broader or more heterogeneous categories.
  • ✅ Supports reference text: The table supports the reference text by providing the descriptions for the top 3 CCS codes mentioned in relation to Figure 19.
  • 💡 Contextualizes individual model performance vs. aggregate: While these R² scores are the 'top 3', it's important to remember they are for individual linear regression models for each CCS code. The overall model for all non-newborns (Table 3) had an R² of 0.42. Some specific conditions are better modeled individually by a linear approach than the aggregate.
Communication
  • ✅ Clear and logical structure: The table has a clear three-column layout ('CCS Diagnosis Code', 'CCS Diagnosis Description', 'R² Score'), making it easy to read and associate the information.
  • ✅ Concise and accurate headers: The column headers are concise and accurately describe their content.
  • ✅ Informative caption: The caption is informative, clearly stating that the table lists the top 3 CCS codes from Figure 19 with their descriptions and R² scores. This provides good context.
  • ✅ Inclusion of full diagnosis descriptions: Presenting the full diagnosis description alongside the code enhances understanding, as the codes themselves are not inherently meaningful to all readers.
  • ✅ Appropriate precision for R² scores: The R² scores are presented to three decimal places, which is an appropriate level of precision for this metric.
Table 5 CCS Diagnosis codes, descriptions and R² Scores for the lowest 3 CCS...
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Table 5 CCS Diagnosis codes, descriptions and R² Scores for the lowest 3 CCS codes in Fig. 19

Figure/Table Image (Page 18)
Table 5 CCS Diagnosis codes, descriptions and R² Scores for the lowest 3 CCS codes in Fig. 19
First Reference in Text
Similarly, the following table shows the 3 CCS Diagnosis Codes in Fig. 19 for the lowest R2 Scores using linear regression.
Description
  • Table Purpose and Terminology: Table 5 presents information on the three Clinical Classifications Software (CCS) diagnosis codes that resulted in the lowest R² (R-squared) scores when individual linear regression models were used to predict Length of Stay (LoS). CCS codes categorize patient diagnoses into broader groups. The R² score measures how much of the variability in LoS is explained by the model; lower scores indicate a poorer model fit.
  • CCS Code 159 (Highest of the Lowest): The CCS Diagnosis Code '159', described as 'Urinary tract infections', yielded an R² Score of 0.209. This is the highest R² score among the three lowest presented.
  • CCS Code 657: The CCS Diagnosis Code '657', which corresponds to 'Mood disorders', resulted in an R² Score of 0.182.
  • CCS Code 659 (Lowest R² Score): The CCS Diagnosis Code '659', described as 'Schizophrenia and other psychotic disorders', had the lowest R² Score among the three, at 0.135. This indicates that the linear regression model explained only 13.5% of the variance in LoS for this category.
Scientific Validity
  • ✅ Provides context for poorly performing models: Presenting the descriptions for the CCS codes that achieved the lowest R² scores complements Table 4 and Figure 19 by highlighting conditions where the simple linear regression approach is least effective for predicting LoS.
  • ✅ Consistency with Figure 19 data: The R² scores (0.209, 0.182, 0.135) are consistent with the bar heights for CCS codes 159, 657, and 659 respectively in Figure 19, ensuring data consistency.
  • ✅ Highlights complexity of predicting LoS for certain conditions: The low R² scores for conditions like mood disorders and schizophrenia suggest that LoS for these psychiatric conditions is likely influenced by a more complex interplay of factors that are not well captured by a simple linear model based on the available features, or that LoS for these conditions is inherently more variable.
  • ✅ Supports reference text: The table effectively supports the reference text by providing the descriptions for the 3 CCS codes with the lowest R² scores as depicted in Figure 19.
  • 💡 Underscores need for better models/features for these codes: These low R² scores reinforce the need for more sophisticated models or additional/different features when trying to predict LoS for these specific diagnostic categories. The paper later discusses the lack of patient vitals, medications, or income level data which could be particularly relevant for mental health conditions.
Communication
  • ✅ Clear and logical structure: The table is well-structured with three clear columns ('CCS Diagnosis Code', 'CCS Diagnosis Description', 'R² Score'), facilitating easy association of the information.
  • ✅ Concise and accurate headers: The column headers are concise and accurately represent the data within each column.
  • ✅ Informative caption: The caption is informative, clearly stating that the table lists the lowest 3 CCS codes from Figure 19, along with their descriptions and R² scores. This provides necessary context.
  • ✅ Inclusion of full diagnosis descriptions: Including the full diagnosis description is crucial for understanding the clinical relevance of the poorly performing CCS codes.
  • ✅ Appropriate precision for R² scores: The R² scores are presented to three decimal places, maintaining consistency with Table 4 and offering appropriate precision.
Fig. 20 The labels for each row on the left show combinations of different...
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Fig. 20 The labels for each row on the left show combinations of different input features.

Figure/Table Image (Page 19)
Fig. 20 The labels for each row on the left show combinations of different input features.
First Reference in Text
We trained a CatBoost Regressor [65] on the complete dataset in order to determine the relationship between combinations of features and the prediction accuracy as determined by the R² correlation score.
Description
  • Plot Type and Model: Figure 20 is a horizontal bar chart that displays the R² (R-squared) correlation scores achieved by a CatBoost Regressor model when trained with different combinations of input features. The CatBoost Regressor is a machine learning algorithm based on gradient boosting on decision trees.
  • Feature Combinations (Y-axis): The y-axis lists various combinations of input features. These combinations start with single features (e.g., ['APRSeverityofillnessCode'], ['APRDRGCode']) and progressively include more features. For example, a later combination is ['APRMDCCode', 'APRSeverityofIllnessCode', 'APRDRGCode', 'PatientDisposition', 'CCSProcedureCode']. The features listed are codes used in healthcare data, such as APRDRGCode (All Patient Refined Diagnosis Related Groups Code) and APRSeverityofIllnessCode.
  • R² Score (X-axis): The x-axis represents the 'r squared score', ranging from 0.0 to 0.4. The R² score indicates the proportion of the variance in the dependent variable (Length of Stay) that is predictable from the independent variables (the feature combination used). A higher R² score signifies a better model fit.
  • Performance of Single Features: The length of each horizontal bar corresponds to the R² score achieved with the feature combination listed on its left. For instance, using only ['APRSeverityofillnessCode'] yields an R² score of approximately 0.29. Using only ['APRDRGCode'] yields an R² score of about 0.33.
  • Performance of Combined Features: As more features are combined, the R² score generally increases, but with diminishing returns. The combination of ['APRMDCCode', 'APRSeverityofIllnessCode', 'APRDRGCode', 'PatientDisposition'] achieves an R² score of about 0.42.
  • Plateau in Performance: Adding further features beyond the combination of 'APRMDCCode', 'APRSeverityofIllnessCode', 'APRDRGCode', and 'PatientDisposition' (e.g., adding 'CCSProcedureCode', 'CCSDiagnosisCode', 'TypeofAdmission', 'APRMedicalSurgicalDescription', 'FacilityName') results in very marginal increases in the R² score. The top several bars, representing combinations with 4 or more features, all show R² scores clustered very closely around 0.42 to 0.43. This suggests that a model with just four key features ('APR MDC Code', 'APR Severity of Illness Code', 'APR DRG Code', 'Patient Disposition') performs nearly as well as models with many more features.
Scientific Validity
  • ✅ Valid approach for feature selection/importance assessment: The approach of systematically adding features and observing the impact on model performance (R² score) is a valid method for identifying a parsimonious set of important features and understanding when adding more features yields diminishing returns. This is a form of forward feature selection.
  • ✅ Appropriate evaluation metric (R²): The R² score is an appropriate metric for evaluating the goodness-of-fit of the CatBoost Regressor model in this context.
  • ✅ Strongly supports claims in reference text regarding feature sufficiency: The figure strongly supports the inference made in the reference text: that a combination of four specific features ('APR MDC Code', 'APR Severity of Illness Code', 'APR DRG Code', 'Patient Disposition') achieves an R² score very close to the maximum observed, and adding further features provides minimal improvement. The plateau effect is clearly visible.
  • 💡 Model-specific results: The results are specific to the CatBoost Regressor model. Other models might show different sensitivities to feature combinations or achieve different overall R² scores.
  • 💡 Order of feature combination not fully detailed in figure: The order in which features were added to form combinations is not explicitly detailed in the figure itself, but the y-axis implies a somewhat structured addition. The scientific validity of the 'minimal set' conclusion depends on a reasonable exploration of feature combinations, which appears to have been done by progressively adding features to core sets.
  • ✅ Consistent with other reported results (Table 6): The highest R² score achieved is around 0.43, which is consistent with the CatBoost regression result for non-newborns reported in Table 6 (0.432). This consistency is good.
Communication
  • ✅ Effective chart type for comparison: The horizontal bar chart is an effective way to compare the R² scores for different feature combinations, with longer bars clearly indicating better performance.
  • 💡 Readability of y-axis feature combination labels: The y-axis labels, representing combinations of input features, are quite long and somewhat difficult to parse quickly due to their programmatic list format (e.g., "['APRMDCCode', 'APRSeverityofIllnessCode', 'APRDRGCode', 'PatientDisposition', 'CCSProcedureCode']"). While accurate, a more summarized or grouped naming convention might improve readability if possible, or ensure sufficient vertical spacing.
  • ✅ Clear x-axis label and scale: The x-axis, labeled 'r squared score', is clear, and the scale (0.0 to 0.4) is appropriate for the data shown.
  • ✅ Clear model indication and informative caption: The title 'CatBoost Regressor' at the top right clearly indicates the model used. The caption further clarifies the content.
  • ✅ Effectively demonstrates diminishing returns: The plot effectively demonstrates the incremental improvement (or lack thereof) in R² score as more features are added, clearly showing a plateau in performance.
  • ✅ Appropriate use of color: The use of a single color for the bars is appropriate as the comparison is based on length.

Discussion

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

Fig. 21 A random forest tree that represents a best-fit model to the data for...
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Fig. 21 A random forest tree that represents a best-fit model to the data for newborns.

Figure/Table Image (Page 19)
Fig. 21 A random forest tree that represents a best-fit model to the data for newborns.
First Reference in Text
The most significant result we obtain is shown in Figs. 21 and 22, which provides an interpretable working of the decision trees using random forest modeling.
Description
  • Plot Type: Decision Tree: Figure 21 displays a single decision tree, stated to be from a random forest model, used to predict Length of Stay (LoS) for newborns. A decision tree is a flowchart-like structure where each internal node represents a test on an attribute (e.g., 'BirthWeight <= 1550.0'), each branch represents the outcome of the test ('True' or 'False'), and each leaf node represents a class label or a continuous value (in this case, the predicted LoS, shown as 'value').
  • Node Information: Each node in the tree contains several pieces of information: the condition for splitting (e.g., 'BirthWeight <= 1550.0'), 'squared_error' (a measure of the variance or error in LoS for the samples at that node), 'samples' (the number of newborn cases that reach that node), and 'value' (the average LoS for the samples at that node, which serves as the LoS prediction if the node is a leaf).
  • Root Node Details: The root node splits based on 'BirthWeight <= 1550.0'. It has a 'squared_error' of 65.53, covers 199,467 samples, and has an average LoS ('value') of 3.74 days.
  • Branching and Feature Splits: The tree branches out based on conditions involving features like 'CCSProcedureCode', 'APRDRGCode', 'PatientDisposition', and 'APRSeverityofIllnessCode'. For example, if 'BirthWeight <= 1550.0' is true and 'CCSProcedureCode <= 0.5' is also true, the predicted LoS ('value') at that subsequent node is 51.61 days for 2,864 samples.
  • Leaf Nodes and Predictions: The leaf nodes represent the final predicted LoS for newborns following a particular path down the tree. For instance, for a newborn with 'BirthWeight > 1550.0' (first split is False), 'APRDRGCode <= 625.5' (second split is True), 'APRDRGCode <= 582.0' (third split is True), and 'squared_error = 7.15' (this seems like a typo in the image, leaf nodes don't have further splits, this node leads to a predicted 'value' of 1.57 days based on 1,242 samples). A more complete path: if BirthWeight > 1550.0 (False), APRDRGCode > 625.5 (False), and APRSeverityofIllnessCode > 3.5 (False), the predicted LoS is 2.66 days (based on 189,574 samples).
  • Reported Performance (R² Score): The caption states that this specific 4-level decision tree achieves an R² score of 0.65. R² (coefficient of determination) indicates that 65% of the variance in LoS for newborns can be explained by this single tree model.
Scientific Validity
  • ✅ Valid method for model interpretability: Visualizing a single decision tree is a common and valid technique to provide insight into the decision-making process of more complex ensemble models like random forests, thereby enhancing interpretability as claimed in the reference text.
  • ✅ Clinically relevant features used: The features used for splitting (BirthWeight, CCSProcedureCode, APRDRGCode, PatientDisposition, APRSeverityofIllnessCode) are clinically relevant variables that are expected to influence the length of stay for newborns.
  • ✅ Respectable R² for a single shallow tree: The R² score of 0.65 for a single tree of limited depth (4 levels) is a respectable performance for predicting a complex outcome like LoS. It demonstrates that even a simplified rule-based structure can capture a significant portion of the variability.
  • ✅ Tree structure aligns with clinical intuition: The structure of the tree aligns with clinical intuition. For example, the root split on 'BirthWeight <= 1550.0' correctly identifies very low birth weight as a primary driver of LoS, with the 'True' branch (low birth weight) leading to significantly higher predicted LoS values (e.g., initial node value of 48.31 days). This supports the reference text.
  • 💡 Illustrative nature of a single tree from an ensemble: It is important to recognize that this single tree is an illustration from a random forest. The overall random forest model (an ensemble of many such trees) is expected to have better predictive performance (as shown in Table 7, R²=0.767 for Random Forest Regression for newborns) but is less directly interpretable than a single tree. The caption's R² of 0.65 correctly refers to this specific tree's performance.
  • 💡 Nuance in 'best-fit model' phrasing: The term 'best-fit model' in the caption might be slightly misconstrued if taken to mean this single tree is the complete best model. It's a representative tree that fits the data well for its structure, chosen to illustrate the random forest's workings.
Communication
  • ✅ Clear and standard visualization: The decision tree diagram is a standard and effective way to visualize the rules learned by the model, making it interpretable.
  • ✅ Informative node labels: The labels within each node (splitting condition, squared_error, samples, value) are clearly presented and provide necessary information for understanding the tree's logic.
  • ✅ Manageable tree depth for readability: The limited depth of the tree (4 levels as mentioned in the caption) makes it visually manageable and relatively easy to follow the decision paths in a static figure format.
  • ✅ Informative caption and clear path indicators: The caption is informative, specifying that it's a tree from a random forest for newborns and providing its R² score (0.65). The arrows labeled 'True' and 'False' clearly indicate the path based on the condition.
  • 💡 Phrasing of 'best-fit model': The term 'best-fit model' in the caption for a single tree from a random forest could be slightly nuanced. It's more accurately an illustrative or representative tree. However, the context of demonstrating interpretability makes this understandable. The R² score provided is for this specific tree.
Fig. 22 A random forest tree using only a tree of depth 3 that represents a...
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Fig. 22 A random forest tree using only a tree of depth 3 that represents a best-fit model to the data for non-newborns.

Figure/Table Image (Page 19)
Fig. 22 A random forest tree using only a tree of depth 3 that represents a best-fit model to the data for non-newborns.
First Reference in Text
The most significant result we obtain is shown in Figs. 21 and 22, which provides an interpretable working of the decision trees using random forest modeling.
Description
  • Plot Type: Decision Tree (Depth 3): Figure 22 displays a single decision tree of depth 3, selected from a random forest model, designed to predict Length of Stay (LoS) for non-newborn patients. A decision tree uses a series of feature-based rules to arrive at a prediction. 'Depth 3' means there are at most three decision points from the root to any leaf.
  • Node Information: Each node in the tree provides: the condition for splitting (e.g., 'APR DRG Code <= 62.67'), 'mse' (mean squared error, a measure of the average squared difference between the estimated values and the actual value), 'samples' (the number of non-newborn cases at that node), and 'value' (the average LoS for samples at that node, serving as the LoS prediction if it's a leaf node).
  • Root Node Details: The root node considers all 1,044,369 samples, has an mse of 64.65, and an average LoS ('value') of 5.72 days. It splits based on 'APR DRG Code <= 62.67'. APR DRG Code refers to the All Patient Refined Diagnosis Related Groups Code, a patient classification system.
  • Key Splitting Features: The tree branches based on conditions involving 'APR DRG Code', 'APR Severity of Illness Code', and 'Patient Disposition'. For example, if 'APR DRG Code <= 62.67' is True, the next split is on 'APR Severity of Illness Code <= 24.6'. If that is also True, the next split is on 'Patient Disposition <= 20.71'.
  • Example Leaf Node Prediction: The leaf nodes provide the final LoS predictions for specific patient segments. For instance, if APR DRG Code > 62.67 (False at root), then APR DRG Code > 813.55 (False at next node), and APR Severity of Illness Code > 91.81 (False at the third level), the predicted LoS ('value') is 46.26 days for 3,182 samples in that leaf.
  • Reported Performance (R²) and Purpose: The caption states that this specific 3-level decision tree achieves an R² score of 0.28. This means it explains 28% of the variance in LoS for non-newborns. The caption also explicitly states this shallow tree is shown for readability and to demonstrate rule-based interpretation, not for optimal predictive power.
Scientific Validity
  • ✅ Valid method for showcasing model interpretability: Visualizing a single, shallow decision tree is a valid and widely used technique to illustrate the interpretability of tree-based ensemble models like random forests, as stated in the reference text. It allows for understanding the types of rules the model learns.
  • ✅ Clinically relevant top-level features: The features used for splitting at the top levels (APR DRG Code, APR Severity of Illness Code, Patient Disposition) are clinically relevant and expected to be strong predictors of LoS for a general non-newborn population. This supports the reference text's claim about these being important top-level features.
  • ✅ R² score reflects illustrative purpose, not optimal prediction: The R² score of 0.28 for this single, depth-3 tree is modest. This is expected, as a single shallow tree will not perform as well as a full random forest ensemble (which achieved R² of 0.396 for non-newborns per Table 6) or a more complex model like CatBoost (R² of 0.432). The caption appropriately contextualizes this by emphasizing readability and interpretability over raw predictive power.
  • ✅ Supports specific example interpretation in text: The example interpretation given in the reference text for the right-most branch (APR DRG Code > 813.55 and APR Severity of Illness Code < 91 leading to LoS of ~46 days) can be traced in the figure and is correctly described (value is 44.21 or 46.26 depending on the exact path). This demonstrates the rule-based nature of the model.
  • 💡 Reinforces illustrative nature of the single tree: It's important that readers understand this is an illustrative tree and not the full random forest model. The caption does a good job of conveying this by mentioning the depth limitation for readability.
Communication
  • ✅ Clear and standard visualization for interpretability: The decision tree diagram is a standard and effective way to visualize classification/regression rules. The limited depth (3 levels) makes it readable in a static format, as intended by the authors.
  • ✅ Informative node labels: Labels within each node (splitting condition, mse, samples, value) are clearly presented and provide the necessary information to follow the tree's logic.
  • ✅ Clear branch labels: The 'True' and 'False' branch labels clearly indicate the decision paths.
  • ✅ Highly informative and contextualizing caption: The caption is very detailed, explaining the tree's depth, its purpose (for non-newborns), its R² score (0.28), and the rationale for showing a shallow tree (readability). This greatly aids understanding and manages expectations about its performance relative to a full model.
  • 💡 Subtle color coding could be explained if meaningful: The color-coding of nodes (though subtle shades of beige/orange) helps to visually group them by level or some other property, though this isn't explicitly explained, the structure is clear enough without it.
Table 6 This table summarizes the R² scores for three different regression...
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Table 6 This table summarizes the R² scores for three different regression models we investigated.

Figure/Table Image (Page 20)
Table 6 This table summarizes the R² scores for three different regression models we investigated.
First Reference in Text
Table 6 we see that in the case of data concerning non-newborns, the catboost regression performs the best, with an R² score of 0.432.
Description
  • Table Purpose and Context: Table 6 presents a comparison of performance for three different regression models used to predict Length of Stay (LoS) for non-newborn patients. Performance is measured by the R² score and the p-value.
  • Metrics Explained (R² and p-value): The R² score (coefficient of determination) indicates the proportion of the variance in the LoS that is predictable from the independent variables in the model. A score closer to 1 suggests a better fit. The p-value in this context likely refers to the statistical significance of the overall regression model or the R² value, indicating the probability of observing the results if there were no true relationship.
  • Catboost Regression Performance: 'Catboost regression' achieved the highest R² score of 0.432. CatBoost is a gradient boosting on decision trees algorithm. The p-value for this model is reported as < 1 e-2 (less than 0.01), indicating statistical significance.
  • Random Forest Regression Performance: 'Random Forest Regression' yielded an R² score of 0.396. Random Forest is an ensemble learning method that constructs multiple decision trees. Its p-value is also < 1 e-2.
  • Linear Regression Performance: 'Linear Regression' resulted in an R² score of 0.42. Linear regression is a statistical method modeling the linear relationship between variables. Its p-value is also < 1 e-2.
  • Comparative Model Performance: Based on the R² scores, Catboost regression (0.432) performed slightly better than Linear Regression (0.42), which in turn performed better than Random Forest Regression (0.396) for the non-newborn dataset.
Scientific Validity
  • ✅ Valid comparative methodology: Comparing different regression models using R² and p-values is a standard and scientifically valid approach to identify the best-performing model for a specific dataset and prediction task.
  • ✅ Appropriate use of R² and p-values: The R² score is an appropriate metric for assessing the goodness-of-fit of regression models. The p-values confirm the statistical significance of the model fits, suggesting the observed R² values are unlikely due to random chance.
  • ✅ Strongly supports claims in reference text: The table strongly supports the claims made in the reference text: Catboost regression performs best with an R² of 0.432, and all models have p-values < 0.01, indicating statistical significance.
  • 💡 Moderate R² scores indicate unexplained variance: The R² values, while statistically significant, are moderate (all below 0.45). This indicates that while the models capture some of the variance in LoS for non-newborns, a substantial portion remains unexplained. This highlights the complexity of LoS prediction and suggests potential for improvement with other features or more complex models not tested here.
  • 💡 Performance contingent on model tuning and feature engineering: The table presents results for three specific models. The choice of these models is reasonable (linear baseline, tree-based ensemble, gradient boosting). However, the performance is contingent on the specific hyperparameter tuning and feature engineering used for each model, which are not detailed in this table but are crucial for fair comparison.
  • 💡 Dataset-specific results: The results are specific to the non-newborn dataset. Different models might perform differently on other datasets or subpopulations (like newborns, as shown in Table 7).
Communication
  • ✅ Clear and logical structure: The table has a clear three-column structure ('Model name', 'R² score', 'p value'), making it easy to compare the performance metrics for each model.
  • ✅ Concise and accurate headers: The column headers are concise and accurately describe the data they contain.
  • ✅ Informative caption with crucial context: The caption is informative, stating the table's purpose (summarizing R² scores for different regression models) and specifying the dataset (non-newborns).
  • ✅ Clear model identification: The model names ('Catboost regression', 'Random Forest Regression', 'Linear Regression') are standard and clearly identify the algorithms used.
  • ✅ Comprehensive metrics presented: Presenting both R² scores and p-values provides a good overview of model fit and statistical significance.
  • 💡 Presentation of p-values: The p-values are all reported as '< 1 e-2', which is a common way to denote very small p-values. This is acceptable, though providing the exact p-value or a more precise upper bound (e.g., <0.001) could be slightly more informative if space permits, but not critical.
Table 7 This table summarizes the R² scores for three different regression...
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Table 7 This table summarizes the R² scores for three different regression models we investigated.

Figure/Table Image (Page 20)
Table 7 This table summarizes the R² scores for three different regression models we investigated.
First Reference in Text
From Table 7 that refers to data from newborns, the linear regression performs the best, with an R² score of 0.82.
Description
  • Table Purpose and Context: Table 7 provides a summary of the performance of three different regression models when applied to predict Length of Stay (LoS) specifically for the newborn patient dataset. The performance is evaluated using the R² score and the p-value.
  • Metrics Explained (R² and p-value): The R² score, or coefficient of determination, measures the proportion of the variance in the dependent variable (LoS) that can be predicted from the independent variables (features used in the model). A score closer to 1 indicates a better model fit, meaning the model explains a larger portion of the LoS variability. The p-value indicates the statistical significance of the model's R² score, suggesting the likelihood of observing such a fit by chance if no true relationship existed.
  • Linear Regression Performance: 'Linear Regression', a statistical method that models a linear relationship between variables, achieved the highest R² score of 0.82 for the newborn data. The p-value is reported as < 1 e-2 (less than 0.01), indicating high statistical significance.
  • Random Forest Regression Performance: 'Random Forest Regression', an ensemble learning method using multiple decision trees, yielded an R² score of 0.767. Its p-value is also < 1 e-2.
  • Catboost Regression Performance: 'Catboost regression', a gradient boosting on decision trees algorithm, resulted in an R² score of 0.730. Its p-value is also < 1 e-2.
  • Comparative Model Performance for Newborns: For the newborn dataset, Linear Regression (R² = 0.82) performed the best, followed by Random Forest Regression (R² = 0.767), and then Catboost regression (R² = 0.730). All models showed highly statistically significant results.
Scientific Validity
  • ✅ Valid comparative methodology: Comparing different regression models using R² and p-values is a standard and valid approach for identifying the most suitable model for a given dataset and prediction task.
  • ✅ Appropriate use of R² and p-values: The R² score is an appropriate metric for assessing the goodness-of-fit of these regression models. The p-values correctly confirm the statistical significance of the model fits.
  • ✅ Strongly supports claims in reference text: The table strongly supports the claims made in the reference text: Linear Regression performs best for newborns with an R² score of 0.82, and all models have p-values < 0.01, indicating statistical significance.
  • ✅ High R² for Linear Regression is a significant finding for newborns: The exceptionally high R² score of 0.82 for Linear Regression on the newborn dataset is noteworthy, especially when compared to the non-newborn results (Table 6, max R² ~0.43). This suggests that LoS for newborns might be driven by a few key features with strong linear relationships (e.g., birth weight, as indicated in Fig. 7 and Fig. 21), which are well-captured by a simpler linear model.
  • ✅ Generally strong model performance for newborns: The performance of all three models is quite strong for the newborn dataset (all R² > 0.7), indicating good predictive capability for this subpopulation. This contrasts with the more moderate performance on the non-newborn dataset.
  • 💡 Performance contingent on upstream processing and tuning: As with Table 6, the model performance is contingent on the specific feature engineering (e.g., how 'BirthWeight' or 'APRDRGCode' were handled) and any hyperparameter tuning, which are not detailed in this summary table.
Communication
  • ✅ Clear and logical structure: The table is well-structured with clear columns for 'Model name', 'R² score', and 'p value', facilitating easy comparison.
  • ✅ Concise and accurate headers: The column headers are concise and accurately describe the content within them.
  • ✅ Informative caption with essential context: The caption clearly states the table's purpose (summarizing R² scores for different regression models) and, crucially, the specific dataset it pertains to (newborns).
  • ✅ Clear model identification: The model names ('Catboost regression', 'Random Forest Regression', 'Linear Regression') are standard and easily identifiable.
  • ✅ Comprehensive metrics presented: The presentation of both R² scores and p-values allows for a comprehensive assessment of both model fit and statistical significance.
  • ✅ Clear indication of p-values: Reporting p-values as '< 1 e-2' is acceptable for very small values, clearly indicating high statistical significance.
Table 8 Evalution of multi-class classifier metrics for logistic regression for...
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Table 8 Evalution of multi-class classifier metrics for logistic regression for non-newborns.

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Table 8 Evalution of multi-class classifier metrics for logistic regression for non-newborns.
First Reference in Text
We examine the performance of classifiers on non-newborn data, as shown in Tables 10 and 12.
Description
  • Table Purpose and Context: Table 8 presents a detailed evaluation of a multi-class logistic regression classifier model used for predicting Length of Stay (LoS) for non-newborn patients. The LoS is divided into five classes, labeled 'Class 0' through 'Class 4'.
  • Metrics Presented: For each class, the table reports four key performance metrics: 'Precision' (the proportion of correctly predicted positive instances out of all instances predicted as positive; i.e., TP / (TP + FP)), 'Recall' (also known as sensitivity, the proportion of correctly predicted positive instances out of all actual positive instances; i.e., TP / (TP + FN)), 'F1-score' (the harmonic mean of precision and recall, providing a single score that balances both; i.e., 2 (Precision Recall) / (Precision + Recall)), and 'Support' (the number of actual instances of each class in the dataset).
  • Per-Class Performance Highlights: Performance varies across classes. For example: 'Class 0' has Precision = 0.45, Recall = 0.56, F1-score = 0.50, with 16,685 samples. 'Class 1' has Precision = 0.44, Recall = 0.40, F1-score = 0.42, with 21,235 samples. 'Class 2' has Precision = 0.57, Recall = 0.11, F1-score = 0.19, with 18,520 samples. 'Class 3' has Precision = 0.38, Recall = 0.49, F1-score = 0.43, with 25,161 samples. 'Class 4' has Precision = 0.59, Recall = 0.71, F1-score = 0.65, with 24,331 samples.
  • Average Performance Scores: The table also includes two types of average scores across all classes: 'Macro avg' (macro average): Precision = 0.49, Recall = 0.46, F1-score = 0.44. The macro average computes the metric independently for each class and then takes the simple average, treating all classes equally. 'Weighted avg' (weighted average): Precision = 0.48, Recall = 0.47, F1-score = 0.45. The weighted average computes the metric for each class and then averages them, weighted by the number of true instances for each class (support).
  • Total Samples Evaluated: The total number of samples used for this evaluation (sum of 'Support' for all classes) is 105,932.
Scientific Validity
  • ✅ Appropriate selection of evaluation metrics: The use of precision, recall, F1-score, and support are standard and appropriate metrics for evaluating the performance of a multi-class classification model, providing a more nuanced view than accuracy alone, especially when class imbalance may be present (as suggested by varying support values).
  • ✅ Reporting both macro and weighted averages: Reporting both macro and weighted averages is good practice. Macro average gives equal weight to each class, useful if all classes are equally important. Weighted average accounts for class imbalance, reflecting performance on the majority classes more.
  • ✅ Highlights class-specific performance differences: The results show varied performance across classes. For instance, 'Class 2' has a very low recall (0.11) despite reasonable precision (0.57), indicating the model misses many actual instances of Class 2. Conversely, 'Class 4' has good recall (0.71) and precision (0.59), resulting in the highest F1-score (0.65) among the classes.
  • ✅ Moderate overall performance indicated: The overall weighted F1-score of 0.45 (and macro F1 of 0.44) suggests moderate performance for the logistic regression model on this multi-class task for non-newborns. The overall accuracy mentioned in the reference text (0.47 or 47%) is consistent with these F1-scores, which also hover around the mid-0.40s.
  • ✅ Consistency with overall accuracy mentioned in text: The reference text states: 'The overall accuracy is computed by dividing the total number of accurate predictions, which is 49,686 out of a total number of 105,932 samples, which yields a value of 0.47.' This overall accuracy is consistent with the performance metrics shown in Table 8, suggesting this table is indeed the one being implicitly referred to when discussing the logistic regression performance for non-newborns, despite the reference text citing Tables 10 and 12 for general classifier performance.
  • 💡 Class definitions (LoS bins) not in table: The table does not specify which LoS bins Class 0-4 correspond to. This information is crucial for interpreting the clinical significance of the per-class performance and would typically be found elsewhere in the methods or results section (e.g., as seen in Fig 12: 1, 2, 3, 4-6, >6 days).
Communication
  • ✅ Clear and logical structure: The table is well-structured with clear rows for each class and averaging methods, and columns for standard classification metrics. This makes it easy to read and compare performance across classes.
  • ✅ Standard and clear headers: The column headers ('Precision', 'Recall', 'F1-score', 'Support') are standard terms in machine learning and are unambiguous.
  • ✅ Highly informative caption: The caption is highly informative, specifying the model (logistic regression), the dataset (non-newborns), and explaining how the macro and weighted averages are computed. This is excellent for clarity.
  • ✅ Concise class labeling: The use of 'Class 0' through 'Class 4' is concise. While the exact meaning of these classes (presumably LoS bins) isn't in the table, it's likely defined elsewhere in the paper (e.g., corresponding to 1 day, 2 days, 3 days, 4-6 days, >6 days as seen in Fig 12).
  • ✅ Comprehensive set of metrics: Presenting precision, recall, and F1-score provides a balanced view of the classifier's performance, as looking at accuracy alone can be misleading, especially with imbalanced classes (which 'Support' values hint at).
  • 💡 Mismatch with provided reference text: The reference text provided (mentioning Tables 10 and 12) does not seem to directly correspond to this Table 8. This is a discrepancy that needs to be addressed in the main text to ensure readers are directed to the correct table when discussing these results.
Fig. 23 This figure applies to data concerning non-newborns.
Figure/Table Image (Page 21)
Fig. 23 This figure applies to data concerning non-newborns.
First Reference in Text
Not explicitly referenced in main text
Description
  • Plot Type: Multiclass ROC Curves: Figure 23 displays a set of Receiver Operating Characteristic (ROC) curves for a multiclass classification model (specified in the caption as the CatBoost classifier) applied to data concerning non-newborns. An ROC curve plots the True Positive Rate (TPR, or sensitivity) against the False Positive Rate (FPR, or 1-specificity) at various threshold settings. It illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.
  • Axes Description: The x-axis represents the 'False Positive Rate', ranging from 0.0 to 1.0. The y-axis represents the 'True Positive Rate', also ranging from 0.0 to 1.0.
  • Individual Curves and Classes: There are five distinct ROC curves shown, each corresponding to a one-vs-rest evaluation for one of the LoS classes (Length of Stay classes, presumably binned as Class 0, Class 1, Class 2, Class 3, and Class 4). For example, the curve 'Class 0 vs Rest' shows the performance of the CatBoost classifier in distinguishing instances of Class 0 from all other classes combined.
  • General Performance Indication: All five curves are positioned above the main diagonal (which would run from (0,0) to (1,1), representing random chance), indicating that the classifier performs better than random guessing for all classes. Curves that are further towards the top-left corner represent better performance.
  • Comparative Performance by Class: The performance varies by class. For instance, the curves for 'Class 0 vs Rest' (blue) and 'Class 4 vs Rest' (purple) appear to be furthest towards the top-left, suggesting better discrimination for these classes compared to, for example, 'Class 2 vs Rest' (green), which is closer to the diagonal.
  • Area Under the Curve (AUC): The caption states that 'The area under the ROC curve is 0.7844'. This value, the AUC, quantifies the overall ability of the classifier to discriminate between classes. An AUC of 1 represents a perfect classifier, while an AUC of 0.5 represents a classifier with no discriminative ability (equivalent to random chance). An AUC of 0.7844 indicates a reasonably good level of discriminative performance for the CatBoost classifier on this multiclass problem. This value likely represents a macro- or micro-averaged AUC across the five one-vs-rest scenarios.
Scientific Validity
  • ✅ Appropriate evaluation metrics (ROC and AUC): ROC curves and the Area Under the Curve (AUC) are standard and robust metrics for evaluating the performance of classification models, particularly for assessing their ability to distinguish between classes across different decision thresholds. Their use here is appropriate.
  • ✅ Provides nuanced performance insight: The figure effectively demonstrates the performance of the CatBoost classifier for non-newborns in a multiclass setting by breaking it down into one-vs-rest scenarios for each class. This allows for a nuanced understanding of where the model excels or struggles.
  • ✅ Consistent with per-class AUCs in Table 10: The varying performance across classes (e.g., better for Class 0 and Class 4 vs Rest, less so for Class 2 vs Rest) is a scientifically relevant finding, suggesting that the model's ability to identify specific LoS bins differs. This aligns with the AUC values presented in Table 10 for CatBoost (Class 0: 0.842, Class 4: 0.887, Class 2: 0.705).
  • ✅ Overall AUC consistent with Table 10: The overall AUC of 0.7844, as stated in the caption, matches the average AUC for CatBoost reported in Table 10 for non-newborns. This consistency strengthens the validity of the presented results.
  • ✅ Supports the general intent of the reference text: The figure supports the implicit claim in the reference text (though the reference text is slightly broader, mentioning 'different multiclass classifiers' while the figure focuses on CatBoost) by visualizing ROC curves for non-newborns. The figure itself is specific to CatBoost as per its detailed caption.
  • 💡 Class definitions (LoS bins) not directly in figure: The definitions of 'Class 0' through 'Class 4' (i.e., which LoS bins they represent) are not provided directly in the figure or its caption. This information is necessary for a full clinical interpretation of the per-class performance and is assumed to be available elsewhere in the paper (e.g., corresponding to bins like 1 day, 2 days, 3 days, 4-6 days, >6 days as suggested by Fig 12).
Communication
  • ✅ Appropriate chart type for multiclass performance: The use of multiple ROC curves on a single plot is a standard and effective way to compare the performance of a multiclass classifier on a one-vs-rest basis for each class.
  • ✅ Clear axis labels, scale, and title: The axes ('False Positive Rate', 'True Positive Rate') are clearly labeled and correctly scaled from 0.0 to 1.0. The title 'Multiclass ROC curve' is accurate.
  • ✅ Clear and effective legend: The legend clearly distinguishes the five different 'Class vs Rest' scenarios with distinct colors and line styles, making it easy to identify each curve.
  • ✅ Highly informative caption: The caption is highly informative, specifying that the data is for non-newborns, the classifier is CatBoost, and it provides the overall area under the ROC curve (AUC) of 0.7844. This context is crucial for interpretation.
  • 💡 Consider adding a diagonal chance line: While not strictly necessary for experienced readers, explicitly drawing the diagonal y=x line (representing random chance) could provide an immediate visual baseline for performance assessment.
  • ✅ Clean design and adequate resolution: The plot is clean and not overly cluttered, despite showing five curves. The resolution appears adequate for distinguishing the curves.
Table 9 In the first scenario, we developed a multiclass classifier using...
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Table 9 In the first scenario, we developed a multiclass classifier using logistic regression with the 2016 SPARCS dataset.

Figure/Table Image (Page 21)
Table 9 In the first scenario, we developed a multiclass classifier using logistic regression with the 2016 SPARCS dataset.
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and Metrics: Table 9 compares the performance (measured by 'Accuracy') of a multiclass logistic regression classifier across two different years of the SPARCS dataset (2016 and 2017) for two distinct patient categories: 'Newborns' and 'Non-newborns'. Accuracy, in this context, is the proportion of correct classifications made by the model out of the total number of classifications.
  • Experimental Scenarios: The caption clarifies the experimental setup: a classifier was developed (trained) using the 2016 SPARCS dataset. Its performance was then evaluated on the 2016 dataset (presumably a test set from 2016 data) and also on the 2017 SPARCS dataset (representing a test on unseen, future data).
  • Performance for Newborns: For the 'Category: Newborns': When tested on the 2016 data (the year it was trained on), the classifier achieved an Accuracy of 0.605. When this same 2016-trained classifier was tested on the 2017 data, the Accuracy dropped slightly to 0.604.
  • Performance for Non-newborns: For the 'Category: Non-newborns': When tested on the 2016 data, the classifier achieved an Accuracy of 0.606. When tested on the 2017 data, the Accuracy for non-newborns dropped to 0.590.
  • Observed Trend in Accuracy: The table shows a small decrease in accuracy for both categories when the model trained on 2016 data is applied to 2017 data, with the drop being more pronounced for non-newborns (0.606 to 0.590, a drop of 0.016) than for newborns (0.605 to 0.604, a drop of 0.001).
Scientific Validity
  • ✅ Valid approach for assessing temporal stability: Testing a model trained on data from one period (2016) on data from a subsequent period (2017) is a valid and important way to assess the model's temporal stability and generalizability. It helps understand if the model's performance degrades over time due to potential shifts in data distributions or underlying patterns (concept drift).
  • ✅ Accuracy as a relevant metric for this comparison: Accuracy is a standard metric for classification performance, though for multiclass problems with potential class imbalance, other metrics like F1-score, precision, and recall per class (as in Table 8) provide a more nuanced view. However, for a high-level comparison of temporal stability, overall accuracy can be informative.
  • ✅ Plausible results showing slight performance degradation: The observed slight decrease in accuracy when moving from 2016 to 2017 data is plausible and often expected in real-world applications, as healthcare practices, patient populations, or coding practices might evolve over time.
  • ✅ Supports reference text: The table directly supports the reference text's statement about comparing the logistic regression classifier's performance on 2016 data against 2017 data.
  • ✅ Highlights differential temporal stability between groups: The fact that the performance drop is minimal for newborns (0.001) compared to non-newborns (0.016) is an interesting finding. It might suggest that the factors influencing LoS for newborns are more stable over this one-year period, or that the model for newborns is more robust to temporal changes.
  • 💡 Lack of per-class performance details for 2017 data: The table only reports overall accuracy. It does not provide details on whether the performance degradation on 2017 data was uniform across all LoS classes or if specific classes were more affected. A more detailed comparison using per-class metrics or confusion matrices for the 2017 data would offer deeper insights.
Communication
  • ✅ Clear and logical table structure: The table structure is clear, with distinct sections for 'Category: Newborns' and 'Category: Non-newborns', and sub-rows for 'Year' and 'Accuracy'. This makes it easy to locate specific performance figures.
  • ✅ Unambiguous headers and labels: The column headers ('Year', 'Accuracy') are unambiguous. The category labels are also clear.
  • ✅ Highly informative caption: The caption is highly informative, explaining the two scenarios (training on 2016 data, testing on 2016 and 2017 data) and the model used (logistic regression). This context is crucial for understanding the results.
  • ✅ Appropriate precision for accuracy values: The accuracy values are presented to three decimal places, which is a common and appropriate level of precision for this metric.
  • ✅ Effectively communicates key finding (performance drop): The table effectively communicates a slight drop in accuracy when the model trained on 2016 data is applied to 2017 data, for both newborns and non-newborns.
Table 10 We report the AUC scores for the three different classifiers we used,...
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Table 10 We report the AUC scores for the three different classifiers we used, logistic regression, random forest and catboost.

Figure/Table Image (Page 21)
Table 10 We report the AUC scores for the three different classifiers we used, logistic regression, random forest and catboost.
First Reference in Text
We examine the performance of classifiers on non-newborn data, as shown in Tables 10 and 12.
Description
  • Table Purpose and AUC Metric: Table 10 presents the Area Under the ROC Curve (AUC) scores for three different machine learning classifiers: Logistic Regression, Random Forest, and CatBoost. These scores are specifically for the task of classifying Length of Stay (LoS) for non-newborn patients. The AUC is a measure of a classifier's ability to distinguish between classes, with a value of 1.0 representing a perfect classifier and 0.5 representing a classifier with no discriminative ability (random chance).
  • One-vs-Rest Scenarios for Multiclass Evaluation: The table shows AUC scores for five different 'one-vs-rest' scenarios, corresponding to 'class 0' through 'class 4'. In a one-vs-rest approach for a multi-class problem, the performance is evaluated by treating each class in turn as the positive class and all other classes as the negative class.
  • Logistic Regression Performance: For 'Logistic Regression': The AUC scores range from 0.498 (for class 3) to 0.595 (for class 4). The 'Average AUC' for Logistic Regression is 0.5522.
  • Random Forest Performance: For 'Random Forest': The AUC scores are generally higher, ranging from 0.702 (for class 2) to 0.885 (for class 4). The 'Average AUC' for Random Forest is 0.78.
  • CatBoost Performance: For 'CatBoost': This classifier shows the highest AUC scores across most classes, ranging from 0.705 (for class 2) to 0.887 (for class 4). The 'Average AUC' for CatBoost is 0.7844.
  • Comparative Classifier Performance: Overall, CatBoost has the highest average AUC (0.7844), followed closely by Random Forest (0.78), with Logistic Regression performing significantly lower (0.5522). This indicates that for the non-newborn dataset, CatBoost and Random Forest are substantially better at discriminating between the LoS classes than Logistic Regression.
  • Average AUC Calculation: The caption clarifies that the last column ('Average AUC') computes the average of the AUC scores from the preceding class-specific columns.
Scientific Validity
  • ✅ Appropriate and robust evaluation metric (AUC): Using AUC scores is a standard and robust method for evaluating and comparing the performance of classification models, especially when dealing with potentially imbalanced classes, as it is threshold-independent.
  • ✅ Valid comparison of multiple classifiers: Comparing multiple classifiers (Logistic Regression, Random Forest, CatBoost) is good practice to identify the most effective algorithm for the specific problem and dataset.
  • ✅ Standard approach for multiclass AUC evaluation: The one-vs-rest approach for calculating per-class AUCs in a multiclass setting is a common technique, providing insights into how well each class is distinguished from the others.
  • ✅ Clear demonstration of superior performance by ensemble methods: The results clearly indicate that tree-based ensemble methods (Random Forest and CatBoost) significantly outperform Logistic Regression for this LoS classification task on non-newborn data. The average AUCs around 0.78 for these models suggest a reasonably good discriminative ability.
  • ✅ Consistent with reference text and accompanying Figure 24: The table directly supports the reference text, which states that Table 10 shows classifier performance on non-newborn data. Figure 24, which visualizes this table's data, further confirms the findings.
  • ✅ Provides insights into class-specific discriminability: The performance varies across classes for all models. For example, all models perform best at distinguishing 'class 4' from the rest, and generally find 'class 2' and 'class 3' harder to distinguish. This class-specific information is valuable.
  • 💡 Method of averaging AUC for overall score: The method of averaging AUCs (simple arithmetic mean as implied by the caption) for the 'Average AUC' column is a common way to get an overall performance measure, though other averaging methods (e.g., weighted by class support) could also be considered if class importance varies significantly.
Communication
  • ✅ Clear and logical table structure: The table is well-structured, with classifiers as rows and different class-specific AUCs as columns, making comparison straightforward.
  • ✅ Clear and descriptive headers: The column headers ('Classifier used', 'One vs. rest for class 0' through 'class 4', 'Average AUC') are clear and accurately describe the content.
  • ✅ Highly informative caption: The caption is highly informative, specifying the classifiers, the metric (AUC scores), the dataset context (non-newborns), and how the average AUC is computed. This greatly aids understanding.
  • ✅ Appropriate precision for AUC scores: The AUC scores are presented to three or four decimal places, which is appropriate precision for this metric.
  • ✅ Efficient data presentation: The table efficiently summarizes a large amount of performance data, allowing for quick identification of the best performing models overall and for specific classes.
  • 💡 Class definitions not in table: The meaning of 'class 0' through 'class 4' (i.e., the LoS bins they represent) is not defined within this table. This information is crucial for a full interpretation and is assumed to be provided elsewhere in the paper (e.g., as in Fig 12: 1, 2, 3, 4-6, >6 days).
Table 11 We report the AUC scores for the three different classifiers we used,...
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Table 11 We report the AUC scores for the three different classifiers we used, logistic regression, random forest and catboost.

Figure/Table Image (Page 22)
Table 11 We report the AUC scores for the three different classifiers we used, logistic regression, random forest and catboost.
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and AUC Metric: Table 11 presents a comparison of Area Under the ROC Curve (AUC) scores for three different machine learning classifiers: Logistic Regression, Random Forest, and CatBoost. These results are specifically for the task of classifying Length of Stay (LoS) for newborn patients. The AUC score measures a classifier's ability to distinguish between classes; a value of 1.0 indicates a perfect classifier, while 0.5 suggests no discriminative ability beyond random chance.
  • One-vs-Rest Scenarios for Multiclass Evaluation: The table details AUC scores for five 'one-vs-rest' scenarios, corresponding to 'class 0' through 'class 4'. In this approach, each class is iteratively treated as the positive class, and all other classes combined are treated as the negative class, to evaluate its distinguishability.
  • Logistic Regression Performance (Newborns): For 'Logistic Regression': The AUC scores for individual classes range from 0.424 (for class 3) to 0.643 (for class 4). The 'Average AUC' for Logistic Regression on the newborn dataset is 0.522.
  • Random Forest Performance (Newborns): For 'Random Forest': This classifier achieved higher AUC scores, ranging from 0.550 (for class 2) to 0.954 (for class 4). The 'Average AUC' for Random Forest is 0.6798.
  • CatBoost Performance (Newborns): For 'CatBoost': CatBoost generally performed the best among the three, with AUC scores ranging from 0.565 (for class 2) to 0.964 (for class 4). The 'Average AUC' for CatBoost is 0.6962.
  • Comparative Classifier Performance (Newborns): Comparing the models for the newborn dataset, CatBoost has the highest average AUC (0.6962), followed by Random Forest (0.6798), and then Logistic Regression (0.522). This indicates that for newborns, CatBoost and Random Forest provide better overall discrimination between LoS classes than Logistic Regression. All models show particularly high AUCs for distinguishing 'class 4' (likely the longest LoS bin) from the rest.
  • Average AUC Calculation Method: The caption notes that the 'Average AUC' is computed by averaging the AUC scores from the preceding class-specific columns.
Scientific Validity
  • ✅ Appropriate use of AUC for evaluation: AUC is a standard and appropriate metric for evaluating and comparing classifier performance, especially in medical applications where distinguishing between different outcomes (LoS classes) is important.
  • ✅ Valid comparison of different classifiers: The comparison of multiple classifiers (Logistic Regression, Random Forest, CatBoost) provides valuable information on which algorithmic approaches are more effective for this specific task (LoS classification for newborns).
  • ✅ Plausible performance ranking of classifiers: The results, showing CatBoost and Random Forest outperforming Logistic Regression, are plausible, as tree-based ensemble methods are often more powerful for complex, non-linear relationships than simple logistic regression.
  • ✅ Consistent with Figure 25 and reference text: The table's data is consistent with the accompanying Figure 25, which visually represents these AUC scores. The reference text also correctly points to Table 11 for newborn classifier performance and notes the similarity in AUCs for Random Forest and CatBoost, especially for class 3.
  • ✅ Indicates fair to good model performance for newborns: The average AUCs around 0.68-0.70 for the better models (Random Forest, CatBoost) indicate fair to good discriminative ability for the newborn LoS classification task. The particularly high AUC for 'class 4' (0.954-0.964) suggests this class is well-separated by these models.
  • 💡 Performance dependent on LoS class definitions: The performance metrics are specific to the chosen LoS class bins. Different binning strategies could lead to different AUC values.
Communication
  • ✅ Clear and logical table structure: The table is clearly structured, with classifiers listed as rows and their AUC scores for different class-specific one-vs-rest scenarios and an average AUC in columns. This facilitates easy comparison.
  • ✅ Unambiguous and descriptive headers: Column headers like 'Classifier used', 'One vs. rest for class 0' through 'class 4', and 'Average AUC' are unambiguous and accurately describe the data presented.
  • ✅ Highly informative caption: The caption is highly informative, specifying the classifiers, the metric (AUC scores), the specific dataset context (newborns), and the method for calculating the average AUC. This is crucial for correct interpretation.
  • ✅ Appropriate precision for AUC scores: The AUC scores are presented to three or four decimal places, which is standard and appropriate precision for this metric.
  • ✅ Efficient presentation of comparative performance: The table effectively summarizes the comparative performance of the three classifiers on the newborn dataset, highlighting both overall and class-specific discriminative power.
  • 💡 Class definitions (LoS bins) not in table: The definitions of 'class 0' through 'class 4' (i.e., the specific LoS bins for newborns) are not provided within this table. This information, assumed to be elsewhere (e.g., Fig 13 shows bins 1, 2, 3, 4-6, >6 days), is needed for a full clinical interpretation of per-class performance.
Table 12 This table uses data for non-newborns.
Figure/Table Image (Page 22)
Table 12 This table uses data for non-newborns.
First Reference in Text
We examine the performance of classifiers on non-newborn data, as shown in Tables 10 and 12.
Description
  • Table Purpose and DeLong Test Explanation: Table 12 presents the results of the DeLong test, a statistical test used to compare the Area Under the ROC Curve (AUC) of two correlated Receiver Operating Characteristic (ROC) curves. This analysis is performed on data for non-newborns to compare the performance of three different classifiers: Logistic Regression, Random Forests, and CatBoost.
  • Comparison Structure: One-vs-Rest Classes: The comparisons are made for each of five binary classification scenarios, designated as 'One vs. rest for Class 0' through 'One vs. rest for Class 4'. In each scenario, one class is treated as positive, and all other classes are combined as negative.
  • Pairwise Model Comparisons: For each binary class scenario, pairwise comparisons between the three models are shown: Logistic regression vs. Random Forests, Random Forests vs. Catboost, and Catboost vs. Logistic regression.
  • DeLong Test Statistic Interpretation: The 'Delong test statistic' is reported for each comparison. The caption explains that a positive value indicates the AUC for the first model listed in the comparison is larger than the AUC for the second model. Conversely, a negative value means the second model's AUC is larger.
  • P-value Interpretation: The 'p-value' column indicates the statistical significance of the difference in AUCs. A small p-value (typically < 0.05) suggests that the observed difference is unlikely to be due to random chance.
  • Example Comparison Result: Example: For 'One vs. rest for Class 0', comparing 'Logistic regression vs. Random Forests', the DeLong statistic is -153.156, and the p-value is 0.0. This means Random Forests has a significantly larger AUC than Logistic Regression for distinguishing Class 0 from the rest. Comparing 'Random Forests vs. Catboost' for the same class, the statistic is -29.575 (p=0.0), indicating Catboost has a significantly larger AUC than Random Forests.
  • Overall Trends in Comparisons: Across most comparisons for all classes, the p-values are 0.0, indicating highly significant differences between the AUCs of the compared models. For instance, Catboost consistently shows significantly better AUCs than Logistic Regression (large positive statistics). Random Forests also consistently outperforms Logistic Regression (large negative statistics when Logistic is first). Catboost generally outperforms Random Forests (negative statistics when Random Forests is first), though the magnitude of the statistic is smaller than when comparing with Logistic Regression. An exception is for 'One vs. rest for Class 3', where Random Forests vs. Catboost has a p-value of 0.004 for a statistic of -2.68, still significant but less overwhelmingly so than p=0.0.
Scientific Validity
  • ✅ Appropriate statistical test for AUC comparison: The DeLong test is an appropriate and widely accepted statistical method for comparing the AUCs of two diagnostic tests or classifiers, especially when the ROC curves are correlated (e.g., when evaluated on the same set of cases).
  • ✅ Thorough pairwise comparison strategy: The pairwise comparison strategy for the three models across each one-vs-rest class scenario is a thorough way to assess relative performance.
  • ✅ Strongly supports claims in reference text regarding significant differences: The results presented in the table strongly support the reference text's conclusion that there are statistically significant differences between the AUCs of the pairwise model comparisons. The consistently small p-values (mostly 0.0) confirm this.
  • ✅ Results align with classifier ranking from Table 10: The DeLong test statistics consistently favor CatBoost over Random Forest, and both over Logistic Regression, for most class-specific scenarios. This supports the conclusion that CatBoost performs best overall, followed by Random Forest, for the non-newborn dataset, aligning with the average AUCs reported in Table 10.
  • ✅ Correctly identifies specific comparison nuances: The one exception noted in the text for Class 3 (Random Forests vs. Catboost, p=0.004) is correctly identified in the table. While still statistically significant at α=0.05, it highlights that the difference between these two better-performing models might be less pronounced for certain specific class distinctions.
  • 💡 Class definitions not directly in table: The definitions of 'Class 0' through 'Class 4' are not in the table itself, which is a minor limitation for full interpretation without referring to other parts of the paper (e.g., Fig 12 defines them as LoS bins 1, 2, 3, 4-6, >6 days).
Communication
  • ✅ Clear and logical table structure: The table is well-structured with clear columns for 'Binary classes used', 'Models compared', 'Delong test statistic', and 'p-value'. This facilitates understanding of the pairwise comparisons.
  • ✅ Unambiguous headers: The column headers are unambiguous and accurately describe the data they contain.
  • ✅ Highly informative caption: The caption is highly informative, explaining the purpose of the table (DeLong test for pairwise AUC comparison), the data context (non-newborns), how to interpret the DeLong test statistic, and the setup for binary classifiers (one-vs-rest). This is excellent for self-containedness.
  • ✅ Clear presentation of comparisons and p-values: The model comparisons are clearly listed (e.g., 'Logistic regression vs. Random Forests'). The p-values are reported with sufficient precision to assess statistical significance.
  • 💡 Table length due to repetition: The repetition of model comparisons for each 'One vs. rest for Class X' makes the table quite long. While thorough, a more condensed format might be possible if space were a major constraint, but as is, it's very explicit.
Table 13 This table uses data for newborns.
Figure/Table Image (Page 24)
Table 13 This table uses data for newborns.
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and DeLong Test Explanation: Table 13 presents the results of the DeLong test, which is a statistical method used to compare the Area Under the ROC Curve (AUC) of two machine learning models, particularly when their predictions are correlated (e.g., tested on the same dataset). This analysis is conducted on data specifically for newborns to compare the performance of three classifiers: Logistic Regression, Random Forests, and CatBoost in predicting Length of Stay (LoS). The AUC is a measure of how well a model can distinguish between different classes; a higher AUC indicates better performance.
  • Comparison Structure: One-vs-Rest Classes: The comparisons are performed for five different binary classification scenarios, labeled 'One vs. rest for Class 0' through 'One vs. rest for Class 4'. In each 'one-vs-rest' scenario, one specific LoS class is treated as the positive class, and all other LoS classes are grouped together as the negative class. This allows for a detailed assessment of how well each model distinguishes each specific LoS class from the others.
  • Pairwise Model Comparisons: For each binary class scenario, three pairwise comparisons between the models are shown: 1) Logistic regression vs. Random Forests, 2) Random Forests vs. Catboost, and 3) Catboost vs. Logistic regression.
  • DeLong Test Statistic Interpretation: The 'Delong test statistic' is provided for each comparison. According to the caption, a positive value for this statistic means the first model listed in the pair has a larger AUC (better performance) than the second model. A negative value means the second model has a larger AUC.
  • P-value Interpretation: The 'p-value' column indicates the statistical significance of the observed difference in AUCs. A small p-value (typically less than 0.05) suggests that the difference in performance between the two models is statistically significant and not likely due to random chance.
  • Example Comparison Results and Key Trends: Key findings include: For 'One vs. rest for Class 0', Random Forests (statistic -11.83, p < 1e-10) and Catboost (statistic -12.102 vs. Random Forests, p < 1e-10) significantly outperform Logistic Regression and Catboost significantly outperforms Random Forests. For 'One vs. rest for Class 1', Random Forests significantly outperforms Logistic Regression (statistic -24.305, p < 1e-10), but Catboost is significantly outperformed by Random Forests (statistic 6.823 for Random Forests vs. Catboost, p < 1e-10). For 'One vs. rest for Class 3', the comparison between 'Random Forests vs. Catboost' yields a DeLong test statistic of -0.914 with a p-value of 0.180, indicating no statistically significant difference in AUC between these two models for this specific class distinction.
  • Overall Performance Summary: Generally, Random Forests and Catboost significantly outperform Logistic Regression across most class distinctions for newborns. The differences between Random Forests and Catboost are more nuanced, with one sometimes outperforming the other depending on the specific class being evaluated, and in one case (Class 3), their performance is not significantly different.
Scientific Validity
  • ✅ Appropriate statistical test for AUC comparison: The DeLong test is an appropriate statistical method for comparing the AUCs of correlated ROC curves, which is the case when different models are evaluated on the same dataset. Its use here is scientifically sound.
  • ✅ Thorough and detailed comparison strategy: The pairwise comparison of models for each one-vs-rest class scenario provides a thorough and detailed assessment of relative model performance, allowing for nuanced conclusions.
  • ✅ Strongly supports claims and specific interpretations in reference text: The table's results strongly support the claims made in the reference text. Specifically, the p-values are indeed less than 0.05 for most comparisons, indicating significant differences. The exception noted in the text for 'One vs. rest for class 3', Random Forests vs. Catboost, is accurately reflected in the table with a p-value of 0.180, correctly leading to the conclusion of no statistically significant difference for that specific comparison.
  • ✅ Provides meaningful insights into relative model strengths: The finding that Random Forests and Catboost generally outperform Logistic Regression for newborns is consistent with the expectation that ensemble tree-based methods can capture more complex relationships than linear models. The nuanced differences between Random Forest and Catboost are also important findings.
  • ✅ Consistency with related data in Table 11: The reference text also mentions that for Class 3, Random Forests vs Catboost, 'From Table 11 we observe that the AUCs of these two classifiers are very similar.' Table 11 shows for Class 3: Random Forest AUC = 0.671, Catboost AUC = 0.673. This similarity in AUCs (0.671 vs 0.673) is consistent with the non-significant p-value (0.180) from the DeLong test in Table 13 for this comparison.
  • 💡 Class definitions (LoS bins) not directly in table: The definitions of 'Class 0' through 'Class 4' (i.e., the specific LoS bins for newborns) are not provided directly within Table 13. This information is necessary for a full clinical interpretation of which specific LoS distinctions are harder or easier for the models to make, and is assumed to be available elsewhere (e.g., Fig 13 shows bins 1, 2, 3, 4-6, >6 days).
Communication
  • ✅ Clear and logical table structure: The table is well-organized with clear columns for 'Binary classes used', 'Models compared', 'Delong test statistic', and 'p-value', allowing for straightforward interpretation of pairwise model comparisons.
  • ✅ Unambiguous headers: The column headers are unambiguous and accurately describe the data contained within them.
  • ✅ Highly informative and comprehensive caption: The caption is exceptionally detailed and informative. It clearly explains the purpose of the table (DeLong test for pairwise AUC comparison), the specific dataset (newborns), how to interpret the DeLong test statistic (positive value means first model's AUC is larger), and the setup for the binary classifiers (one-vs-rest). This level of detail is excellent for ensuring the table is self-contained and easily understood.
  • ✅ Clear presentation of comparisons and p-values: The pairwise model comparisons (e.g., 'Logistic regression vs. Random Forests') are clearly listed. The p-values are presented with sufficient precision to assess statistical significance effectively.
  • ✅ Explicit presentation despite length: While the repetition of model comparisons for each 'One vs. rest for Class X' makes the table lengthy, it also makes it very explicit and easy to follow each specific comparison without cross-referencing.
Table 14 We report the Brier scores computed for the performance of the...
Full Caption

Table 14 We report the Brier scores computed for the performance of the different classifier models we developed.

Figure/Table Image (Page 24)
Table 14 We report the Brier scores computed for the performance of the different classifier models we developed.
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and Brier Score Explanation: Table 14 presents the Brier scores for three different classifier models—Logistic Regression, Random Forest classifier, and Catboost classifier—evaluated on data for non-newborns. The Brier score is a measure of the accuracy of probabilistic predictions; it is the mean squared difference between the predicted probability assigned to the possible outcomes and the actual outcome. A lower Brier score indicates better calibration and accuracy of the probabilistic predictions, with a perfect score being 0.
  • Logistic Regression Brier Score: For 'Logistic Regression', the Brier score is 0.754.
  • Random Forest Classifier Brier Score: For the 'Random Forest classifier', the Brier score is 0.644.
  • Catboost Classifier Brier Score: For the 'Catboost classifier', the Brier score is 0.635.
  • Comparative Performance: Comparing the scores, the Catboost classifier has the lowest Brier score (0.635), indicating it has the best probabilistic prediction accuracy among the three models for the non-newborn dataset. Random Forest classifier (0.644) performs slightly worse than Catboost, and Logistic Regression (0.754) performs considerably worse than the other two.
Scientific Validity
  • ✅ Appropriate evaluation metric (Brier score): The Brier score is an appropriate and well-established metric for evaluating the accuracy and calibration of probabilistic predictions from classifier models. Its use here is scientifically sound.
  • ✅ Valid comparison of classifiers: The comparison of Brier scores across different classifiers provides a valid means of assessing which model yields more accurate probability estimates for the class outcomes.
  • ✅ Plausible performance ranking: The results indicate that Catboost and Random Forest classifiers provide better calibrated probabilities than Logistic Regression for the non-newborn LoS classification task. The lower Brier scores for these ensemble methods are plausible given their ability to model complex relationships.
  • ✅ Supports interpretation from detailed text: The table directly supports the interpretation in the reference text (even though the provided `reference_text` field in the prompt was 'Not explicitly referenced in main text', I am using the text provided with the OCR'd page 24 for Table 14): Catboost has the lowest Brier score, indicating the best performance, followed by Random Forest, then Logistic Regression.
  • 💡 Interpretation of absolute Brier score values: The absolute values of the Brier scores (e.g., 0.635 for Catboost) are somewhat high, considering a perfect score is 0 and the range for a multi-class Brier score (as defined in the paper's methods for R classes) can go up to R. For 5 classes, the Brier score (as defined in the paper: sum over (prob_i,c - I_i,c)^2, then averaged) for a model that always predicts 1/5 for each class would be 0.8. Scores in the 0.6-0.7 range indicate that the models are better than random guessing but still have considerable room for improvement in terms of probability calibration.
Communication
  • ✅ Clear and simple structure: The table is simple and clearly structured with two columns: 'Type of classifier' and 'Brier score', making it easy to read and compare the scores.
  • ✅ Unambiguous headers: The column headers are unambiguous and accurately describe the content.
  • ✅ Informative caption with essential context: The caption clearly states the purpose of the table (reporting Brier scores for different classifiers) and specifies the dataset context (non-newborns).
  • ✅ Clear classifier identification: The classifier types are standard and clearly identified.
  • ✅ Appropriate precision for Brier scores: The Brier scores are presented to three decimal places, which is a common level of precision for this metric.
Table 15 We report the Brier scores computed for the performance of the...
Full Caption

Table 15 We report the Brier scores computed for the performance of the different classifier models we developed.

Figure/Table Image (Page 24)
Table 15 We report the Brier scores computed for the performance of the different classifier models we developed.
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and Brier Score Explanation: Table 15 presents the Brier scores for three different classifier models—Logistic Regression, Random Forest classifier, and Catboost classifier—when evaluated on data specifically for newborns. The Brier score is a proper score function that measures the accuracy of probabilistic predictions. It is calculated as the mean squared difference between the predicted probability assigned to the possible outcomes and the actual outcome. A lower Brier score indicates better calibrated and more accurate probabilistic predictions, with a perfect score being 0.
  • Logistic Regression Brier Score (Newborns): For 'Logistic Regression', the Brier score is 0.780.
  • Random Forest Classifier Brier Score (Newborns): For the 'Random Forest classifier', the Brier score is 0.532. This is the lowest score among the three models.
  • Catboost Classifier Brier Score (Newborns): For the 'Catboost classifier', the Brier score is 0.635.
  • Comparative Performance (Newborns): Comparing the Brier scores for the newborn dataset, the Random Forest classifier has the lowest score (0.532), indicating the best probabilistic prediction accuracy among the three. The Catboost classifier (0.635) performs next best, and Logistic Regression (0.780) performs considerably worse than the other two in terms of Brier score.
Scientific Validity
  • ✅ Appropriate evaluation metric (Brier score): The Brier score is an appropriate and well-established metric for evaluating the accuracy and calibration of probabilistic predictions from classifier models. Its use for comparing these classifiers is scientifically sound.
  • ✅ Valid comparison of classifiers: The comparison of Brier scores across different classifiers provides a valid method for assessing which model yields more accurate probability estimates for the class outcomes in the newborn dataset.
  • ✅ Supports primary claim in reference text: The table directly supports the reference text's claim that 'for newborns, the random forest classifier performs the best, followed by the catboost classifier and logistic regression.' The Brier scores are 0.532 (Random Forest), 0.635 (Catboost), and 0.780 (Logistic Regression), which matches this ranking.
  • 💡 Nuance in 'very similar' performance claim: The reference text also states, 'The performance of the random forest classifier and catboost classifier are very similar.' While Random Forest (0.532) is numerically better than Catboost (0.635), the difference (0.103) might be considered 'similar' in some contexts, especially compared to the much larger difference with Logistic Regression (0.780). However, without statistical tests on the Brier scores themselves, 'similarity' is a qualitative judgment. The DeLong test for AUCs (Table 13) showed some significant differences between RF and Catboost for newborns, suggesting their performance isn't always identical.
  • ✅ Indicates potentially better probability calibration for newborn models: The Brier scores for newborns (lowest 0.532) are generally lower (better) than for non-newborns (lowest 0.635 from Table 14). This suggests the models might be providing better calibrated probabilities for the newborn LoS classification task.
  • ✅ Brier scores indicate models are better than random: The range of the Brier score needs to be considered. For a multi-class problem with R classes, as defined in the paper's methods, the score can range from 0 to R. For 5 classes, a score of 0.532 is substantially better than random (which would be higher, e.g., 0.8 if predicting 1/5 for each class) and indicates reasonable calibration.
Communication
  • ✅ Clear and simple structure: The table is clearly structured with two columns: 'Type of classifier' and 'Brier score', which allows for easy comparison of the scores.
  • ✅ Unambiguous headers: The column headers are unambiguous and accurately describe the data within them.
  • ✅ Informative caption with essential context: The caption clearly states the purpose of the table (reporting Brier scores for different classifiers) and specifies the crucial context that this data is for newborns.
  • ✅ Clear classifier identification: The classifier types ('Logistic Regression', 'Random Forest classifier', 'Catboost classifier') are standard and clearly identified.
  • ✅ Appropriate precision for Brier scores: The Brier scores are presented to three decimal places, which is a common and appropriate level of precision for this metric.
Table 16 Model parameter and hyperparameter values used
Figure/Table Image (Page 24)
Table 16 Model parameter and hyperparameter values used
First Reference in Text
Not explicitly referenced in main text
Description
  • Table Purpose and Terminology: Table 16 lists the specific parameter and hyperparameter values that were used for three types of machine learning models investigated in the study: Logistic Regression, Random Forest Regression, and Decision Tree Regression. Parameters are learned from the data during model training, while hyperparameters are set before the learning process begins and control aspects of the learning algorithm itself.
  • Logistic Regression Parameters: For 'Logistic Regression': The optimizer used was 'Adam optimizer'. The 'Learning rate' for the Adam optimizer was set to 1e-3 (or 0.001). 'Weight decay', a regularization technique to prevent overfitting, was set to 1e-4 (or 0.0001). The 'Number of epochs', representing the number of times the entire training dataset was passed through the algorithm, was 10. The Adam optimizer is an algorithm for first-order gradient-based optimization of stochastic objective functions, commonly used in training neural networks and other machine learning models.
  • Random Forest Regression Hyperparameters: For 'Random Forest Regression': The 'Number of estimators' (which is the number of decision trees in the forest) was set to 10. The 'Maximum depth' of each tree in the forest was limited to 10 levels. Random Forest is an ensemble learning method that builds multiple decision trees and merges their outputs.
  • Decision Tree Regression Hyperparameter: For 'Decision Tree Regression': The 'Maximum depth' of the decision tree was set to 5 levels. A decision tree is a model that uses a tree-like graph of decisions and their possible consequences.
Scientific Validity
  • ✅ Promotes reproducibility: Providing the model parameters and hyperparameters is crucial for the reproducibility of machine learning research. This table attempts to fulfill that need for some of the models.
  • ✅ Common and reasonable hyperparameter values reported: The listed values for learning rate, weight decay, number of epochs (for Logistic Regression likely implemented via a framework like PyTorch as mentioned for linear regression earlier), number of estimators, and maximum depth are common hyperparameters for these respective models. The values themselves (e.g., max depth of 10 or 5) are reasonable starting points or could be results from a hyperparameter tuning process.
  • 💡 Context of parameter selection (default vs. tuned): The paper mentions using tenfold cross-validation to determine the best parameters (page 6). If these values are the result of such tuning, it adds to their validity. However, the table itself doesn't state if these are defaults or tuned values.
  • 💡 Significant omission: CatBoost parameters missing: A significant omission is the lack of parameters for the CatBoost Regressor. CatBoost was reported as the best performing model for non-newborns (Table 6) and used for feature importance analysis (Figure 20). Without its parameters, reproducing or fully understanding the CatBoost results is difficult. This makes the table incomplete in its stated goal of providing parameters for 'the different classifier models we developed'.
  • 💡 Implementation details for Logistic Regression: For Logistic Regression, the use of 'Adam optimizer' suggests an implementation beyond the standard scikit-learn `LogisticRegression` (which uses solvers like 'lbfgs', 'liblinear'). Given the mention of PyTorch for linear regression (page 9), it's plausible this logistic regression was also implemented in a framework allowing optimizers like Adam. Clarifying the specific implementation library would be beneficial.
Communication
  • ✅ Clear table structure: The table has a clear three-column structure: 'Type of Model', 'Parameter', and 'Value', which is easy to follow.
  • ✅ Clear and standard labels: The labels for models, parameters, and their values are generally clear and use standard machine learning terminology.
  • ✅ Concise caption: The caption is concise and accurately describes the table's content.
  • ✅ Effective listing of parameters: The table effectively lists key parameters for three types of models, aiding in understanding the model configurations.
  • 💡 Parameter naming for Logistic Regression: For Logistic Regression, listing 'Adam optimizer, Learning rate' as a single parameter name is a bit unconventional. It would be clearer to have 'Optimizer' as one parameter (Value: Adam) and 'Learning rate' as a separate parameter. The same applies to 'Adam optimizer, Weight decay' and 'Adam optimizer, Number of epochs'.
  • 💡 Omission of CatBoost parameters: The table is titled 'Model parameter and hyperparameter values used', but it omits parameters for the CatBoost model, which was reported as a key model in other results (e.g., Table 6, Figure 20). This makes the table incomplete with respect to the models discussed in the paper.
Fig. 24 A bar chart that depicts the data in Table 10 for non-newborns
Figure/Table Image (Page 23)
Fig. 24 A bar chart that depicts the data in Table 10 for non-newborns
First Reference in Text
Not explicitly referenced in main text
Description
  • Chart Type and Purpose: Figure 24 is a grouped bar chart that visually represents the Area Under the ROC Curve (AUC) scores from Table 10 for three different classifiers—Logistic Regression, Random Forest, and Catboost—when applied to data for non-newborns. The AUC measures a classifier's ability to distinguish between classes, with higher values indicating better performance.
  • Axes Description: The y-axis represents the AUC score, scaled from 0 to 1. The x-axis has five categories, each corresponding to a 'one-vs-rest' evaluation scenario for a specific class: 'One vs. rest for class 0', 'One vs. rest for class 1', 'One vs. rest for class 2', 'One vs. rest for class 3', and 'One vs. rest for class 4'.
  • Bar Grouping and Legend: Within each of the five x-axis categories, there are three bars, each representing one of the classifiers. According to the legend: Blue bars represent 'Logistic Regression'. Orange bars represent 'Random Forest'. Green bars represent 'Catboost'. The height of each bar corresponds to the AUC score achieved by that classifier for that specific 'one-vs-rest' class scenario.
  • Logistic Regression Performance: Visually, for all five class scenarios, the blue bars (Logistic Regression) are consistently the shortest, indicating the lowest AUC scores, generally around 0.5 to 0.6.
  • Random Forest and Catboost Performance: The orange bars (Random Forest) and green bars (Catboost) are consistently much taller than the blue bars, indicating significantly better performance. For most classes, the orange and green bars are of very similar height. For example, for 'One vs. rest for class 0', both Random Forest and Catboost have AUCs around 0.83-0.84. For 'One vs. rest for class 4', both have AUCs close to 0.88-0.89.
  • Overall Comparative Performance: The chart clearly shows that Random Forest and Catboost substantially outperform Logistic Regression in distinguishing each class from the rest for the non-newborn dataset. The performance of Random Forest and Catboost is very similar across all class scenarios, with Catboost often having a slight edge.
Scientific Validity
  • ✅ Appropriate visualization technique: A grouped bar chart is an appropriate and standard method for visually comparing performance metrics (like AUC) of multiple models across several categories or scenarios.
  • ✅ Accurate representation of Table 10 data: The figure accurately represents the AUC data presented in Table 10 for non-newborns. The relative heights of the bars correspond to the numerical values in the table.
  • ✅ Effectively highlights key comparative findings: The visualization effectively highlights the key findings from Table 10: the superior performance of Random Forest and Catboost compared to Logistic Regression, and the generally comparable performance between Random Forest and Catboost for non-newborns.
  • ✅ Supports discussion of classifier performance: The chart supports the discussion of classifier performance on non-newborn data by providing a clear visual summary that is easier to interpret at a glance than the raw numbers in a table.
  • 💡 Relies on external context for class definitions: The definitions of 'class 0' through 'class 4' are not directly provided in the figure, but it is explicitly linked to Table 10, where this context is assumed or provided elsewhere in the paper (e.g., Figure 12 shows LoS bins 1, 2, 3, 4-6, >6 days).
Communication
  • ✅ Effective chart type for comparison: The grouped bar chart is an effective choice for comparing the AUC scores of the three different classifiers across the five 'one-vs-rest' class scenarios.
  • ✅ Clear axis labels and scale: The y-axis, representing the AUC score, is clearly labeled and scaled from 0 to 1. The x-axis clearly labels the five 'One vs. rest for class X' scenarios.
  • ✅ Clear and effective legend: The legend clearly identifies which color corresponds to which classifier (Logistic Regression, Random Forest, Catboost), making it easy to distinguish the bars within each group.
  • ✅ Concise title and informative caption: The title 'AUCs for Non-newborns' is concise and accurately reflects the content of the chart. The caption further clarifies that it depicts data from Table 10.
  • ✅ Effectively communicates relative model performance: The chart effectively visualizes the superior performance of Random Forest and Catboost over Logistic Regression across all class scenarios. It also allows for easy comparison of performance across different classes for each model.
  • ✅ Appropriate level of detail (no data labels on bars): The exact numerical AUC values are not displayed on the bars themselves, which is acceptable as the primary purpose is visual comparison and the exact values are in Table 10. Adding data labels could clutter the chart.
Fig. 25 A bar chart that depicts the data in Table 11
Figure/Table Image (Page 23)
Fig. 25 A bar chart that depicts the data in Table 11
First Reference in Text
Not explicitly referenced in main text
Description
  • Chart Type and Purpose: Figure 25 is a grouped bar chart that visually represents the Area Under the ROC Curve (AUC) scores from Table 11. These scores are for three different classifiers—Logistic Regression, Random Forest, and Catboost—when applied to data specifically for newborn patients. The AUC score is a measure of a classifier's ability to distinguish between classes, where a higher AUC indicates better performance.
  • Axes Description: The y-axis represents the AUC score, scaled from 0 to 1.2 (though AUC values do not exceed 1.0). The x-axis has five categories, each corresponding to a 'one-vs-rest' evaluation scenario for a specific class of Length of Stay (LoS): 'One vs. rest for class 0', 'One vs. rest for class 1', 'One vs. rest for class 2', 'One vs. rest for class 3', and 'One vs. rest for class 4'.
  • Bar Grouping and Legend: For each of the five x-axis categories, a group of three bars is presented. Each bar in the group represents one of the classifiers, differentiated by color as per the legend: Blue bars for 'Logistic Regression'. Orange bars for 'Random Forest'. Green bars for 'Catboost'. The height of each bar indicates the AUC score achieved by that classifier for that specific 'one-vs-rest' class scenario with newborn data.
  • Logistic Regression Performance Visualization: Across all five class scenarios, the blue bars (Logistic Regression) are consistently the shortest, indicating the lowest AUC scores among the three models. These scores are generally around 0.4 to 0.65.
  • Random Forest and Catboost Performance Visualization: The orange bars (Random Forest) and green bars (Catboost) are consistently taller than the blue bars, signifying better performance. Their heights are often very similar to each other. For example, for 'One vs. rest for class 0', Random Forest AUC is ~0.59 and Catboost is ~0.66. For 'One vs. rest for class 3', both Random Forest and Catboost show AUCs around 0.67.
  • Performance for 'Class 4': A striking feature is the performance for 'One vs. rest for class 4', where both Random Forest and Catboost achieve very high AUC scores, appearing to be above 0.95. Logistic Regression also performs its best for this class, with an AUC around 0.64.
  • Overall Comparative Performance Visualization: The chart visually confirms that for the newborn dataset, Random Forest and Catboost generally outperform Logistic Regression. The performance difference between Random Forest and Catboost appears to be relatively small for most classes, with Catboost often having a slight edge, except for 'One vs. rest for class 1' where Random Forest appears slightly better.
Scientific Validity
  • ✅ Appropriate visualization technique: A grouped bar chart is an appropriate and standard visualization for comparing performance metrics (like AUC) of multiple models across several distinct categories or scenarios.
  • ✅ Accurate representation of Table 11 data: The figure accurately reflects the AUC data presented in Table 11 for newborns. The visual heights of the bars correspond directly to the numerical AUC values in that table.
  • ✅ Effectively highlights key comparative findings: The chart effectively highlights the key findings concerning classifier performance on the newborn dataset: the superior performance of Random Forest and Catboost over Logistic Regression, the particularly strong performance for Class 4, and the similar performance levels of Random Forest and Catboost for most classes.
  • ✅ Supports discussion of classifier performance for newborns: This visualization supports the discussion of classifier performance for newborns by providing an accessible graphical summary of the data in Table 11, making trends and comparisons easier to grasp than from the table alone.
  • 💡 Relies on external context for class definitions: The definitions of 'class 0' through 'class 4' (the specific LoS bins for newborns) are not directly provided in this figure. For a full interpretation of which LoS distinctions are being made, reference to other parts of the paper (e.g., Figure 13 which defines bins as 1, 2, 3, 4-6, >6 days) or the source Table 11 is necessary.
  • 💡 Minor y-axis scaling quirk: The y-axis extending to 1.2 while AUC scores are capped at 1.0 is a minor visual quirk but does not detract from the scientific validity of the comparisons shown within the 0-1 range.
Communication
  • ✅ Effective chart type for comparison: The grouped bar chart is an effective and standard way to visually compare the AUC scores of the three classifiers across the five different 'one-vs-rest' class scenarios for newborns.
  • ✅ Clear axis labels and appropriate scale: The y-axis (AUC score, scaled 0 to 1.2) and x-axis (labeling the five 'One vs. rest for class X' scenarios) are clearly labeled. The y-axis maximum of 1.2 is slightly unusual given AUC scores max out at 1.0, but it doesn't impede interpretation.
  • ✅ Clear and effective legend: The legend clearly distinguishes the three classifiers (Logistic Regression, Random Forest, Catboost) by color, facilitating easy identification of each model's performance within each group.
  • ✅ Concise title and informative caption: The title 'AUCs for Newborns' is concise and accurately describes the chart's content. The caption further clarifies that it visualizes data from Table 11.
  • ✅ Effectively communicates relative model performance: The chart effectively communicates the relative performance of the models. It clearly shows that Random Forest and Catboost generally outperform Logistic Regression, and that performance for all models is exceptionally high for 'Class 4'.
  • ✅ Supports textual observations about specific class performance: The visual comparison makes it easy to see that for 'Class 3', the performance of Random Forest and Catboost is very similar, as noted in the text discussing Table 13.

Conclusion

Key Aspects

Strengths

Suggestions for Improvement