Ranking USRDS Provider Specific SMRs from 1998-2001
Published In: Health Services and Outcomes Research Methodology, v. 9, no. 1, Mar. 2009, p. 22-38
Posted on RAND.org on December 31, 2008
Bayesian models coupled with optimizing a loss function provide an effective framework for computing non-standard inferences such as ranks. Inferences depend on the posterior distribution and should be guided by inferential goals. However, even optimal methods might not lead to definitive results and ranks should be accompanied by valid uncertainty assessments. The authors outline the Bayesian approach and use estimated Standardized Mortality Ratios (SMRs) in 1998-2001 from the United States Renal Data System (USRDS) as a platform to identify issues and demonstrate approaches. Our analyses extend Liu et al. (2004) by computing estimates developed by Lin et al. (2006) that minimize errors in classifying providers above or below a percentile cut-point, by combining evidence over multiple years via a first-order, autoregressive model on log (SMR), and by use of a nonparametric prior. Results show that ranks/percentiles based on maximum likelihood estimates of the SMRs and those based on testing whether an SMR = 1 substantially under-perform the optimal estimates. Combining evidence over the four years using the autoregressive model reduces uncertainty, improving performance over percentiles based on only one year. Furthermore, percentiles based on posterior probabilities of exceeding a properly chosen SMR threshold are essentially identical to those produced by minimizing classification loss. Uncertainty measures effectively calibrate performance, showing that considerable uncertainty remains even when using optimal methods. Findings highlight the importance of using loss function guided percentiles and the necessity of accompanying estimates with uncertainty assessments.