Bayesian predictive inference for a binary random variable: Estimating quality of care and risk-adjusted assessments of medical outcomes

Given binary data from a two stage cluster sample, we outline and apply a method to do Bayesian predictive inference for a finite population proportion, P. The probabilistic specification yields simple analytical expressions for the moments of the prior and posterior distributions. To facilitate routine analysis of survey data, we investigate approximations for the posterior distribution of P. We contrast our inferences with those based on empirical Bayes techniques and design-based methods. We apply this methodology to a survey whose objective is to investigate the quality of care that cancer patients receive.; We also examine models and methodologies that are commonly used for 'provider profiling,' and evaluation of the quality of health care. The conventional approach to computing these provider assessments is to use a likelihood-based frequentist methodology. The use of locally uniform prior distributions allows direct comparison between the likelihood-based and Bayesian methods. We compare the frequentist and Bayesian results for each of three models. The models are applied to the data used by the New York State Department of Health for its annually released reports that profile hospitals permitted to perform coronary artery bypass graft surgery. With the advances of Markov Chain Monte Carlo methods, Bayesian methods are easily implemented and are preferable to standard frequentist methods for models with a binary dependent variable since the latter always rely on asymptotic approximations.; One of the three types of models presented assumes exchangeability amongst hospitals. The results from fitting these exchangeable models, either frequentist or Bayesian, exhibit the phenomenon of shrinkage. In addition to comparisons between the frequentist and Bayesian shrinkage methods, we compare results from the non-shrinkage and shrinkage methods using data from the DOH CABG reports. Additionally, data sets with known outliers are constructed to summarize what effect application of shrinkage methods would have on the detection of outliers compared with methods that are currently considered standard practice.