Are (the log-odds of) hospital mortality rates normally distributed? Implications for studying variations in outcomes of medical care

Rationale — Hierarchical regression models are increasingly being 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. The appropriateness of this assumption for examining variations in healthcare outcomes has never been explicitly tested.

Aims and Objectives — To compare hierarchical logistic regression models in which the provider-specific random effects were either a normal distribution or a mixture of three normal distributions.

Methods — We used data on 18 825 patients admitted to 109 hospitals in Ontario with a diagnosis of acute myocardial infarction. We used the Deviance Information Criterion, Bayes factors and predictive distributions to compare the evidence between the two competing models.

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, the hospital-specific posterior tail probabilities of unacceptably high mortality were lower when a logistic-normal model was fit compared to when a logistic-mixture of normal distributions model was fit. Additionally, in these same scenarios, fewer hospitals were classified as having higher than acceptable mortality when the logistic-mixture of three normal distributions was used.

Conclusions — These findings have important consequences for those who use hierarchical models to examine variations in outcomes of medical care across providers since the mixture of three normal distributions model indicated that variations in outcomes across providers was greater than indicated by the logistic-normal model.