Bias in Penalized Quasi-Likelihood Estimation in Random Effects Logistic Regression Models When the Random Effects Are not Normally Distributed

ABSTRACT

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 on 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.

Keywords:

• Bias
• Estimation
• Penalized quasi-likelihood
• Random effects models

Mathematics Subject Classification:

• 62F
• 62J
• 62P

Acknowledgments

The Institute for Clinical Evaluative Sciences (ICES) is supported in part by a grant from the Ontario Ministry of Health and Long Term Care. The opinions, results and conclusions are those of the author and no endorsement by the Ministry of Health and Long-Term Care or by the Institute for Clinical Evaluative Sciences is intended or should be inferred. Dr. Austin is supported in part by a New Investigator award from the Canadian Institutes of Health Research (CIHR).

Notes

Note: Each cell contains the p-value associated with the significance of the Type III sum of squares for the associated factor in the ANOVA model.