Combining binomial data using the logistic normal model

Abstract

Combining binomial data from multiple sources has often been done using normal linear mixed effect models. In this paper we propose to combine binomial data using a two-stage logistic normal model. This model formulation will allow coherent interpretation of parameter estimates and homogeneity tests. We discuss parameter estimation for the proposed model using the approximate maximum likelihood method with Gauss quadrature points and the penalized quasi-likelihood approach. We also describe several tests for the homogeneity of studies to be combined. Simulation results demonstrate that the penalized quasi-likelihood approach is preferred because it provide better parameter estimates and coverage probabilities.

Keywords:

• Variance components
• Penalized quasi-likelihood
• Homogeneity test

Acknowledgements

This research was supported in part by NIH grant R01 AG15813.