Bayesian and frequentist predictive inference for the patterns of care studies

The Patterns of Care Studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy. In this article, we propose and evaluate models which, if acceptable, permit Bayesian and frequentist model-based predictive inference for the desired finite population parameters. Using both hierarchical Bayesian and frequentist mixed linear models, we describe methodology for making the desired inferences, emphasizing the use of transformed random variables. Finally, we compare the frequentist, Bayes, and empirical Bayes approaches using data from one of the surveys. All three methods produce essentially the same value for the (finite population) mean. The standard empirical Bayes and frequentist measures of variability are very much smaller than those derived from the Bayesian approach, the latter reflecting uncertainty about the values of the scale parameters in the model.