A Bayesian Logistic-mixture of Normal Distributions Hierarchical Model for Hospital Mortality

• Activity Number: 194
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Health Policy Statistics
• Author(s): Peter Austin*+
• Companies: Institute for Clinical Evaluative Sciences
• Keywords: Hospital report cards ; provider profiling ; hierarchical regression models ; Bayesian methods ; Bayes factors ; mixture models

Abstract

Hierarchical regression models are being used increasingly to examine variations in outcomes following the provision of medical care across providers. These models frequently assume a normal distribution for the provider-specific random effects. To explicitly examine the parametric form of the distribution of random effects, we used Bayes factors to compare hierarchical logistic regression models in which the provider-specific random effects follow normal, t, and a mixture of normal distributions. There was strong evidence that the distribution of hospital-specific log-odds of mortality was not normal, but rather a mixture of either two or three normal distributions. The resultant distribution had heavier tails than a normal distribution. The hospital-specific posterior tail probabilities of unacceptably high mortality were biased downward when a logistic-normal model was fit compared to when a logistic-mixture of normal distributions model was fit. These findings have important consequences for those who use hierarchical models to examine variations in outcomes of medical care across providers.