Regression models incorporating random effects are being used with increasing frequency 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. However, the validity of this assumption is rarely explicitly tested.
This study used Monte Carlo simulation methods to examine the impact of mis-specifying the distribution of the random effects in hierarchical logistic regression models. The researchers demonstrated that estimation and inferences concerning the fixed effects was insensitive to mis-specification of the distribution of the random effects. However, estimation and inferences concerning the provider-specific random effects was affected by model mis-specification. In particular, estimation of cluster-specific random effects and the coverage of the associated 95% confidence intervals were particularly poor for individual random effects that came from the extreme tails of t-distributions with low degrees of freedom.
These findings have important implications for those using hierarchical logistic regression models to identify health care providers with either exceptionally high or low rates of an outcome.