Bayes rules for optimally using Bayesian hierarchical regression models in provider profiling to identify high-mortality hospitals

We propose several families of loss functions for hospital report cards and then develop Bayes rules for these families of loss functions. The resultant Bayes rules minimize the expected loss arising from misclassifying hospital performance. We develop Bayes rules for generalized 1-0 loss functions, generalized absolute error loss functions, and for generalized squared error loss functions. We then illustrate the application of these decision rules on a sample of 19,757 patients hospitalized with an acute myocardial infarction at 163 hospitals.We found that the number of hospitals classified as having higher than acceptable mortality is affected by the relative penalty assigned to false negatives compared to false positives. However, the choice of loss function family had a lesser impact upon which hospitals were identified as having higher than acceptable mortality.The design of hospital report cards can be placed in a decision-theoretic framework. This allows researchers to minimize costs arising from the misclassification of hospitals. The choice of loss function can affect the classification of a small number of hospitals.Public reporting of comparative health care performance by hospitals is part of current public policy in a range of jurisdictions. Several jurisdictions have released public report cards comparing hospital or physician-specific outcomes. California [1], Pennsylvania [2], Scotland [3], and Ontario, Canada [4] have released hospital-specific reports for mortality following admission for acute myocardial infarction (AMI). New Jersey [5], New York [6], Pennsylvania [7], and Massachusetts [8] have published hospital and surgeon-specific mortality rates following coronary artery bypass graft (CABG) surgery, while Ontario has published hospital-specific mortality rates [9].It has been suggested that there are two main goals behind public reporting [10]. The first is providing information that can guide purchasing decisions by individual consumers or g