Robust Hospital Efficiency Ranking: A Bayesian and Machine Learning Integrated Dynamic Slacks-Based Measure DEA Approach

Hospitals are complex organizations operating in a dynamic environment, where multiple parameters vary over time. Ranking hospitals by efficiency using traditional methods often overlooks changes in effectiveness and quality. This study proposes a simulation-based Dynamic Slack-Based Measure Data Envelopment Analysis (Dynamic SBM-DEA) framework. The study is methodological and simulation-based, generated using Monte Carlo simulation methods, calibrated from real multispecialty hospital data, healthcare literature, etc. To evaluate intertemporal hospital performance, the methodology incorporates carry-over effects and unwanted outputs and uses bootstrap validation to evaluate the reliability of efficiency estimations. The persistence and transition of performance states across time are examined using Markov chain analysis, and the stability measurements that are obtained are combined with Dynamic SBM efficiency ratings to create a composite performance indicator. Additionally, the framework can capture operational stability, ranking robustness, and predicted efficiency trends inside a single evaluation model thanks to Bayesian forecasting's probabilistic estimations of future performance. The machine learning model attained a testing R² of 0.4765 and a cross-validated R² of 0.553 ± 0.048, indicating moderate predictive capability and stable performance. Sensitivity research showed that the composite ranking framework was resilient, with Kendall's tau values ranging from 0.716 to 0.926 across different weighting schemes and Spearman's rank correlations ranging from 0.881 to 0.983. The findings revealed a set of hospitals with continuously excellent efficiency, stable rankings, and promising future performance. Staffing levels, surgical activity, and clinical results are some of the most important factors influencing efficiency, according to the SHAP study. The development of an integrated Dynamic SBM-DEA, Machine Learning, and Bayesian decision-support framework that offers a transparent, stability-adjusted, and forward-looking benchmarking tool for evidence-based hospital management, resource allocation, and healthcare policy decision-making is the study's primary contribution.