A Bayesian Framework for Ranking Healthcare Facilities Under Uncertainty

Medicare’s VBP Program has fundamentally reshaped hospital reimbursement by linking payments to multidimensional quality metrics. However, several empirical studies highlight its inability to consistently incentivize improvement and identify substantial limitations in its performance evaluation framework, most notably the neglect of statistical uncertainty in composite scores used for hospital ranking. This paper proposes a Bayesian methodology that models hospital performance measures—specifically, the PaCE score derived from the HCAHPS survey—as probabilistic quantities with credible intervals rather than fixed values. Using publicly available CMS data from the 2023 performance period, we apply Beta-binomial modeling and Monte Carlo approximation to characterize posterior distributions of relevant quality indicators. Hospitals are ranked according to the lower bound of the 90% central credible interval, emphasizing the most conservative plausible performance and directly penalizing facilities with higher uncertainty due to limited survey data. Experimental results demonstrate that nearly half of the top 50 hospitals undergo a change of at least five positions when uncertainty is taken into account, suggesting tangible real-world consequences for resource allocation and reputation. In addition to producing fairer and more informative rankings, the proposed approach generates natural incentives for hospitals to improve data quality and survey participation, and is generalizable to other domains within pay-for-performance schemes.