Beyond Efficiency Scores: Explaining Health System Performance Using Two-Stage Bootstrap DEA and Machine Learning

Background/Objectives: Health systems involve numerous stakeholders interconnected through nonlinear relationships. While Data Envelopment Analysis (DEA) has been widely used to measure health system efficiency, conventional estimates may exhibit finite-sample bias. An important question, therefore, concerns how health system performance can be measured more reliably, and what factors explain cross-country differences in efficiency. This study introduces an integrated framework that combines Two-Stage Bootstrap DEA with machine learning to assess the performance of the health systems of 26 OECD countries using 2022 data. Methods: In the first step, technical efficiency scores are computed using an output-oriented constant returns to scale (CRS) DEA model. Subsequently, bias-corrected efficiency estimates are derived using the Bootstrap procedure proposed by Simar and Wilson. In the second step, truncated regression analysis and machine learning-based partial dependence analysis, the latter validated through leave-one-out cross-validation, are employed to investigate the determinants of efficiency. Results: The Bootstrap procedure reveals statistically significant differences from conventional DEA results, and bias-corrected results indicate that South Korea, Canada, and the United States achieve the highest efficiency levels. The findings show that tobacco use prevalence has a significantly negative association with health system efficiency and alcohol consumption exhibits a negative, threshold-type pattern, while GDP per capita and out-of-pocket health expenditure display more complex, nonlinear effects. Furthermore, the scenario analysis indicates that a 10% reduction in tobacco use yields the largest predicted single-intervention improvement, while combined interventions produce additional but sub-additive gains. Conclusions: The proposed framework presents a transparent and validated approach for assessing and explaining health system performance, generating findings relevant to the development of evidence-based health policy.