Sample size calculations for hierarchical Poisson and zero-inflated Poisson regression models

Abstract

In biomedical research there is a growing interest in the use of hierarchical Poisson regression models. Although sample size calculations for testing parameters in a Poisson regression model with prespecified power and size have been previously done, very little attention has been paid to this problem for the hierarchical model. We propose to use Monte Carlo simulations to calculate the sample size necessary to perform the Wald tests when the number of clusters is fixed in advance, but the cluster size is variable. The effect of the number of clusters and the covariance structure of the fixed effects is also studied. The method and the simulation study are also extended to the case of the hierarchical zero-inflated Poisson regression model in order to obtain analogous results there. The method is also illustrated on an interesting real dataset.

Keywords:

• Wald test
• Score function
• Information matrix
• Hierarchical generalized linear models
• Intraclass correlation
• Monte Carlo simulations

Acknowledgments

This work was supported by the NSERC Discovery Grants of the second and third authors. All three authors would like to thank the referees for their helpful comments which improved the original manuscript.