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.

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