A Method to Assess Uncertainty in System-Level Performance Evaluation Measures and Statistical Benchmarks
Keywords: Bayesian methods; empirical distribution function; hierarchical model; histograms; performance evaluation; threshold exceedances
Performance evaluation of health care providers often includes monitoring system-wide performance and estimating statistical benchmarks to characterize excellent performance. The primary inferential target in both cases is an estimate of the histogram, or empirical distribution function (EDF), of unit-level parameters. A major limitation to using the EDF is the lack of an uncertainty statement for it. We address this limitation by developing a percentile-based histogram estimate for univariate unit-specific parameters. Our approach structures an uncertainty assessment within a Bayesian hierarchical modeling framework and provides an alternative approach to moment-based estimation. We employ a fully Bayesian approach, simulating posterior distributions of model parameters using Markov Chain Monte Carlo (MCMC). Our approach relies on computing order statistics of MCMC samples drawn from the posterior distribution of the unit-specific parameters to obtain the relevant uncertainty assessment of the histogram estimate itself and features of it. We illustrate our method with a motivating example from the Medicare End Stage Renal Disease (ESRD) Program, a health insurance program in the United States for people with irreversible kidney failure and discuss the implications of our method for evaluating the performance of healthcare providers.