Are (the log-odds of) Hospital Mortality Rates Normally Distributed in Ontario? Implications for Studying Variations in Outcomes of Medical Care
Objective: Hierarchical regression models are used 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. Poincaré said, “Everyone believes in the normal law, the experimenters because they imagine it a mathematical theorem, and the mathematicians because they think it an experimental fact”. Our objective was to examine the appropriateness of this assumption when examining variations in mortality.
Study design and setting: We used Bayesian model selection methods to compare hierarchical regression models in which the provider-specific random effects were either a normal distribution or a mixture of three normal distributions. We used data on 18,825 patients admitted to 109 hospitals in Ontario with a diagnosis of acute myocardial infarction.
Results: There was strong evidence that the distribution of hospital-specific log-odds of mortality was a mixture of three normal distributions compared to the evidence that it was normal. In some scenarios, fewer hospitals were classified as having higher than acceptable mortality when the logistic-normal model was used compared to when the logistic-mixture of three normal distributions model was used.
Conclusions: Variation in outcomes across providers is greater than indicated by the conventional logistic-normal model.
Peter C. Austin. "Are (the log-odds of) Hospital Mortality Rates Normally Distributed in Ontario? Implications for Studying Variations in Outcomes of Medical Care" Journal of Evaluation in Clinical Practice 15 (2009): 514-523.