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This study addresses the significant problem of patient no-shows in healthcare by proposing and evaluating a novel decision analysis framework using machine learning. The primary objective is to accurately predict no-shows, particularly in the context of imbalanced datasets where actual no-shows are relatively rare. The research introduces Symbolic Regression (SR), an algorithm that discovers mathematical formulas from data, as a classification method, and Instance Hardness Threshold (IHT), a technique that balances datasets by removing hard-to-classify majority instances, as a resampling method. These are benchmarked against established algorithms like K-Nearest Neighbors (KNN) and Support Vector Machine (SVM), and other resampling techniques such as SMOTE and Random UnderSampling.
A key methodological innovation is a comprehensive six-step analytical framework that includes a rigorous dual z-fold cross-validation process. This involves splitting the data for model training and testing in two nested stages, resulting in 100 independent simulation runs for each model configuration. This approach is designed to ensure robust assessment of model generalization (ability to perform on new data) and stability, which is often a challenge with imbalanced data. The framework was validated using two distinct datasets from Brazilian hospitals with no-show rates of 6.65% and 19.03%.
The findings indicate that the novel techniques, particularly IHT, demonstrated superior performance. When combined with various classification algorithms (including SR, KNN, and SVM), IHT consistently led to high sensitivity (the proportion of actual no-shows correctly identified) and Area Under the Curve (AUC, a measure of overall model performance), with sensitivity values exceeding 0.94 for SR/IHT combinations on the validation portions of both datasets. This high sensitivity is crucial for healthcare applications, as it helps minimize false negatives (failing to predict a no-show), thereby enabling more effective targeted interventions like patient reminders or optimized overbooking strategies.
The study concludes that SR and IHT are promising methods for no-show prediction and emphasizes the critical importance of robust validation strategies, like the proposed dual cross-validation, when dealing with imbalanced datasets. Relying on few validation runs can lead to biased results and an inadequate understanding of model reliability. The research provides both theoretical contributions through its novel framework and techniques, and practical implications for improving healthcare resource management and patient care.
This research makes a significant contribution by proposing a methodologically robust framework for predicting patient no-shows, a persistent challenge in healthcare. The introduction of Symbolic Regression (SR) as a classification algorithm and Instance Hardness Threshold (IHT) as a resampling technique, both novel in this context, demonstrates considerable promise. The study's emphasis on a dual z-fold cross-validation process, yielding 100 simulation runs, sets a high standard for evaluating model performance and stability, particularly crucial when dealing with imbalanced datasets where no-shows are the minority.
The findings indicate that the IHT technique, which selectively removes hard-to-classify majority instances to improve class separation, consistently enhanced model performance across different algorithms, notably achieving high sensitivity (the ability to correctly identify patients who will not show up, e.g., >0.94 for SR/IHT on validation sets). This is practically vital as minimizing missed no-shows allows for more effective resource allocation and targeted interventions. The SR algorithm, which evolves mathematical models from data, also performed well, suggesting its utility for uncovering complex patterns in patient behavior.
However, while the paper demonstrates superior observed performance for SR and IHT combinations through extensive simulations, it's important to note that these claims of superiority are based on descriptive outcomes from the 100 replicates rather than formal statistical significance testing between methods. This is a limitation in the current analysis that tempers the certainty of comparative conclusions. The study design is a rigorous comparative evaluation of algorithmic performance within a novel framework using historical data, not an experimental trial assessing real-world impact. Therefore, its primary strength lies in advancing methodological best practices for no-show prediction and highlighting the potential of SR and IHT. Future research should incorporate formal statistical comparisons and prospective validation in clinical settings to confirm the practical efficacy and cost-effectiveness of these models.
Ultimately, the paper successfully underscores the pitfalls of relying on limited validation runs for imbalanced datasets and provides a valuable, adaptable framework for developing more reliable predictive models. This can empower healthcare managers to make more informed decisions, potentially leading to improved operational efficiency, reduced costs, and better patient access to care. The key takeaway is the critical need for methodological rigor in this domain and the promising avenues opened by the novel techniques explored.
The abstract effectively communicates the significance of the no-show problem and the practical benefits of using machine learning for prediction, immediately establishing the research's importance and relevance to healthcare service improvement.
The abstract clearly articulates the novel academic contributions of the study, specifically positioning it as the first to introduce Symbolic Regression (SR) and Instance Hardness Threshold (IHT) for predicting patient no-shows. This directness is crucial for highlighting its unique place in the literature.
The results are summarized succinctly, emphasizing the superior performance of the proposed techniques (SR and IHT) and the high sensitivity achieved (above 0.94). This provides a clear and impactful takeaway of the study's empirical outcomes.
The conclusion provides a valuable and broadly applicable caution regarding the validation of machine learning models, especially when dealing with imbalanced datasets. This highlights a commitment to methodological rigor and contributes to best practices in the field.
The abstract mentions improved model robustness and generalization in the Methods section and discusses generalization in the Conclusion. However, the Conclusion could more directly attribute the framework's specific design feature (i.e., dual z-fold cross-validation) to achieving better generalization and stability, reinforcing this as a key strength and practical outcome of the proposed methodology. This would be a medium-impact clarification, enhancing the takeaway message about the framework's utility for producing reliable models. It fits well within the abstract's concluding remarks, as it summarizes a core benefit of the methodological innovation.
Implementation: Modify the conclusion to explicitly link the dual z-fold cross-validation to its intended benefits. For instance, after '...the first to propose performing z-fold cross-validation twice,' consider adding a phrase like 'a robust validation strategy designed to enhance the generalization and stability of predictive models, especially crucial for imbalanced datasets.' Then continue with 'Our study highlights...'
The introduction thoroughly defines the no-show problem, detailing its multifaceted negative impacts on both healthcare systems (e.g., resource inefficiency, increased costs) and patients (e.g., discontinuity of care, worsened outcomes), effectively establishing the research's significance and the urgency for solutions.
The paper explicitly states the gap in current research by identifying Symbolic Regression (SR) and Instance Hardness Threshold (IHT) as unexplored methods in the context of no-show prediction. This clear identification of novelty effectively positions the paper's unique contributions to the field.
The research objectives are clearly and concisely stated, providing a distinct roadmap for the study's aims and methodologies. This clarity helps the reader understand the specific goals the paper intends to achieve regarding both framework development and empirical testing of novel techniques.
The introduction provides a solid rationale for the methodological choices, such as the exploration of new methods (SR and IHT) and the strategic use of two distinct datasets. This justification underscores the pursuit of robust, generalizable models capable of handling diverse real-world scenarios.
The authors clearly delineate both the theoretical contributions (e.g., a novel analytical framework, dual z-fold cross-validation, exploration of SR/IHT) and the practical implications (e.g., enhanced healthcare quality, targeted interventions, improved overbooking strategies) of their work, effectively highlighting its overall value.
The introduction describes Symbolic Regression (SR) and Instance Hardness Threshold (IHT) and notes their novelty in this context. However, it could more explicitly connect the specific advantages of these techniques to the inherent challenges of no-show prediction data, such as complex non-linear relationships potentially discoverable by SR, and the class imbalance and noisy data that IHT is designed to handle. This would be a medium-impact clarification, strengthening the motivation for choosing these novel methods beyond their unexplored status and better preparing the reader for why these methods might outperform others. This enhancement would fit well within the paragraph introducing SR and IHT (page 2).
Implementation: After describing SR's ability to infer mathematical structure, consider adding a sentence like: "This inherent flexibility of SR is particularly promising for no-show prediction, where the underlying factors influencing patient behavior can be multifaceted and non-linear, potentially eluding traditional models with predefined structures." Similarly, after explaining IHT's filtering mechanism, add: "Given that no-show datasets are typically imbalanced and may contain noisy or borderline instances, IHT's targeted approach to data balancing by identifying and removing such challenging majority class samples is hypothesized to be particularly effective in clarifying class distinctions for the learning algorithm."
The paper outlines a clear, comprehensive, and logically sequenced six-step predictive framework (Fig. 1), which enhances the reproducibility and understanding of the complex analytical process involved in predicting no-shows.
The study significantly contributes to the field by being the first to apply Instance Hardness Threshold (IHT) as a resampling technique and Symbolic Regression (SR) as a classification algorithm in the context of no-show prediction, addressing gaps in the existing literature.
The dual z-fold cross-validation approach (Z1=10 for calibration/validation split, Z2=10 for train/test split within calibration) is a rigorous method for assessing model performance and stability, leading to 100 evaluation runs.
The parameters for the novel Symbolic Regression (SR) algorithm are explicitly detailed (mathematical functions, population size, generations, crossover/mutation probabilities), which is crucial for transparency and reproducibility of this less common technique.
The authors provide clear justifications for key methodological decisions, such as the choice of resampling techniques (IHT for novelty), feature selection method (wrapper for performance despite computational cost), and the prioritization of the F1-score and sensitivity as performance metrics.
The use of two distinct datasets with different characteristics (one unpublished, one open-access, with varying no-show rates) strengthens the study's claims about the robustness and adaptability of the proposed framework.
While the paper mentions that for Instance Hardness Threshold (IHT), the function h (used to calculate instance hardness) is determined by a learning algorithm, defaulting to Random Forest in Python's Imbalanced-learn, the Method section could briefly state if the default parameters of this Random Forest were used or if any specific configurations were applied. This would provide a slightly more complete picture for precise replication of the IHT process. This is a low-impact suggestion, as stating the default is informative, but confirming its use or detailing minor adjustments would enhance methodological transparency.
Implementation: After stating that the default for function h in Imbalanced-learn is the random forest algorithm, add a sentence clarifying the parameterization. For example: "For this study, the default Random Forest classifier within the Imbalanced-learn library was utilized with its standard parameters to derive the instance hardness values." Or, if specific parameters were set for this internal Random Forest, they should be briefly mentioned.
The paper acknowledges the computational intensity of wrapper methods and the parameter search for SVM. Given the extensive nature of the six-step framework, particularly the 10x10 cross-validation loops combined with wrapper feature selection, a brief discussion on the overall computational resources or time involved would be beneficial. This information would provide practical context for researchers aiming to replicate or adapt this thorough methodology. This is a medium-impact suggestion that would improve the practical reproducibility aspect of the Method section.
Implementation: Consider adding a short paragraph or a few sentences towards the end of the 'Method' section (e.g., before 'Performance metrics' or as a concluding remark within the methodology description) addressing computational considerations. For instance: "The comprehensive nature of the proposed framework, particularly the dual cross-validation and wrapper-based feature selection, entails significant computational effort. Analyses were conducted using [mention type of computing resources, if possible, e.g., high-performance computing cluster or standard desktop specifications], with total run times varying based on the specific algorithm and dataset. Future implementations might explore parallelization or other optimization strategies to manage these demands."
The results are presented in well-structured tables (Tables 1 and 2 for Dataset 1; Tables 3 and 4 mentioned for Dataset 2) that clearly display multiple performance metrics for each combination of resampling technique and classification algorithm. This allows for a comprehensive comparison and easy identification of top-performing models, with best results highlighted in bold.
The paper effectively justifies the emphasis on sensitivity and AUC, linking these metrics directly to the practical implications of no-show prediction in healthcare, particularly the higher cost of false negatives. This provides a strong rationale for evaluating models based on their ability to correctly identify no-shows.
The results for Dataset 2 are presented following the same structure as Dataset 1, facilitating a consistent comparison of model performance across different data contexts. This consistency strengthens the overall findings regarding the effectiveness of techniques like IHT and SR.
The use of boxplots (Fig. 2 for Dataset 1, Fig. 4 mentioned for Dataset 2) to illustrate the stability of sensitivity results across 100 replicates is a significant strength. This provides insights into the variability and reliability of the prediction models beyond just average performance metrics.
While Tables 1 and 2 clearly show IHT's strong performance for Dataset 1, the main text could more explicitly synthesize the observation that IHT consistently elevates performance (especially sensitivity and AUC) across all three classification algorithms (KNN, SVM, SR). A similar summary for Dataset 2 would also be beneficial. This would be a medium-impact clarification, reinforcing the robustness of IHT as a resampling technique within this section's narrative summary of findings, rather than relying solely on the reader to synthesize this from the tables. This fits well when discussing the overall performance of IHT.
Implementation: After presenting the general success of IHT for a dataset, add a sentence summarizing its broad applicability. For instance, after '...confirming its suitability for highly imbalanced datasets,' for Dataset 1, add something like: 'Notably, the IHT technique demonstrated a consistent advantage, improving key metrics such as sensitivity and AUC not only for SR but also when paired with KNN and SVM, as evidenced in Table 1.' A similar statement could be made for Dataset 2 results.
The results highlight IHT's superior performance, especially for sensitivity. To further emphasize this, the text could briefly quantify the general magnitude of improvement in sensitivity achieved by IHT combinations compared to other resampling techniques (SMOTE, RUS, NM) for both datasets. This would be a medium-impact addition, providing a more concrete sense of IHT's practical advantage directly within the Results narrative, complementing the tabular data. This enhancement would fit well when discussing the best sensitivity scores achieved with IHT.
Implementation: When discussing the best sensitivity scores achieved with IHT (e.g., for SR/IHT in Dataset 1's validation set), add a comparative statement. For example: 'The combination of SR and IHT yielded the best sensitivity score (0.9537)... This represents a substantial improvement over combinations using SMOTE, RUS, or NM techniques, which generally yielded sensitivities often below 0.83 (Table 2) for Dataset 1's validation set.'
Fig. 2 Boxplot of sensitivity results in the validation set for all prediction models
Fig. 3 Features selected by top models, occurrence frequency in 100 test set replicates
Table 1 Average predictive performance and standard deviations obtained from 100 replicates of dataset 1's test portion
Table 2 Average predictive performance and standard deviations obtained from 100 replicates of dataset 1's validation portion
Table 3 Average predictive performance and standard deviations obtained from 100 replicates of dataset 2's test portion
Table 4 Average predictive performance and standard deviations obtained from 100 replicates of dataset 2's validation portion
Fig. 4 Boxplot of sensitivity results in the validation set for all prediction models
The paper provides a robust justification for its extensive cross-validation strategy (100 simulations across two stages), effectively contrasting it with the limitations of approaches with fewer validation runs commonly found in the literature, thereby highlighting the methodological rigor of the study in assessing model generalization and stability.
The discussion effectively links the use of resampling techniques to tangible improvements in sensitivity, a critical metric for no-show prediction. It clearly articulates why this is important in the healthcare context (minimizing false negatives) and positions the proposed framework favorably.
The paper offers a plausible and insightful explanation for the superior performance of the Instance Hardness Threshold (IHT) technique, attributing its success to its ability to identify and remove challenging majority class instances, which improves class separation and classification accuracy.
The discussion on significant predictors is well-balanced, acknowledging consistency with existing literature while also highlighting the dataset-specific nature of predictors and the variability based on the algorithm used. This nuanced perspective adds credibility to the findings.
The practical implications are clearly articulated, demonstrating how the study's findings can translate into actionable strategies for healthcare managers, such as targeted patient reminders and optimized overbooking, to mitigate the negative impacts of no-shows.
This is a high-impact suggestion. The Discussion section is the appropriate place to acknowledge methodological limitations and suggest avenues for future research that would bolster the current findings. While the paper claims 'most favorable outcomes' for IHT and SR combinations, this assertion lacks formal statistical backing within the study. Performing statistical tests to compare model performances across the 100 replicates would significantly strengthen the claims of superiority for these novel techniques, moving beyond observational advantage to statistically validated evidence, thereby enhancing the overall scientific rigor and impact of the study's conclusions.
Implementation: In future work or as an addendum, incorporate appropriate non-parametric statistical tests (e.g., Wilcoxon signed-rank test or Friedman test followed by post-hoc tests) to compare the performance metrics (especially sensitivity and AUC) of the IHT/SR combinations against other models across the 100 validation replicates. The Discussion should then reflect these statistical findings, stating, for example: 'Future research should also focus on statistically validating these performance differences. While our study demonstrated consistently higher mean sensitivity for IHT/SR, formal statistical testing would confirm the significance of this advantage.'
This is a medium-impact suggestion. The Discussion is an ideal section for deeper interpretation of nuanced findings. The paper correctly notes that predictor importance varies by algorithm and cites Nasir et al. regarding 'different processing strategies.' However, a brief elaboration on how these strategies might lead to such variations would provide readers with a more profound understanding. For instance, explaining that distance-based algorithms like KNN might prioritize different features than rule-based or boundary-based algorithms like SVM or equation-evolving SR would add valuable explanatory depth, making the discussion more insightful.
Implementation: Expand the sentence following the citation of Nasir et al. [28] to briefly illustrate the concept. For example: "According to Nasir et al. [28], that is due to the different processing strategies performed by the algorithms; for instance, distance-based methods like KNN may emphasize features defining local neighborhoods, while methods like SVM focus on features that define class boundaries, and Symbolic Regression may identify complex non-linear interactions that other algorithms might overlook, leading to these observed differences in predictor importance."