Bias in penalized quasi-likelihood estimation in random effects logistic regression models when the random effects are not normally distributed

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. We used Monte Carlo simulation methods to examine the impact of misspecifying the distribution of the random effects oil estimation of and inference about both the fixed effects and the random effects in hierarchical logistic regression models. We demonstrated that estimation and inferences concerning the fixed effects was insensitive to misspecification of the distribution of the random effects. However, estimation and inferences concerning the provider-specific random effects was affected by model misspecification. 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.