Empirical bayes estimation and inference for the random effects model with binary response

Waclawiw and Liang introduced an estimating function‐based approach for estimating the parameters of the classical two‐stage random effects model for longitudinal data. In the present paper, the authors conduct a case study of the general approach for the binary response setting, where the fully specified parametric two‐stage model with fixed and univariate random effects has an analytically intractable likelihood. With successful convergence of the algorithm, the authors propose a fully parametric bootstrapping method for deriving empirical Bayes confidence intervals for all model parameters. The bootstrapping approach is a blend of the estimating function technique with the developments of Laird and Louis. The estimating function approach to estimation and inference provides a general framework for the analytis of a wide variety of medical data, including the setting of small and varying numbers of discrete repeated observations. An application of the methdology to the analysis of binary responses in a crossover clinical trial is presented.