Approximate conditional inference in mixed-effects models with binary data

1 Summary Conditional likelihood approach is a sensible choice for a hierarchical logistic regression model or other generalized regression models with binary data. However, its heavy computational burden limits its use, especially for the related mixed effects model. In this paper, we use modified profile likelihood as an accurate approximation to conditional likelihood, and then propose the use of two methods for inferences for the hierarchical generalized regression models with mixed effects. One is based on hierarchical likelihood and Laplace approximation method, and the other is based on Markov chain Monte Carlo EM algorithm. The methods are applied to a meta-analysis model for trend estimation and the model for multi-arm trials. A simulation study is conducted to illustrate the performance of the proposed methods.