Bayesian and Frequentist Predictive Inference for the Patterns of Care Studies

TLDR

Patterns of Care Studies assess the quality of care for cancer patients receiving radiation therapy. This article proposes and evaluates models that enable Bayesian and frequentist predictive inference for finite population parameters. The authors employ hierarchical Bayesian and frequentist mixed linear models, using transformed random variables, to generate predictions and compare the three approaches on survey data. All three methods yield the same finite population mean, but empirical Bayes and frequentist variability estimates are markedly smaller than the Bayesian estimates, which incorporate uncertainty in scale parameters.

Abstract

Abstract 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.