Two-step Estimation for a Generalized Linear Mixed Model with Auxiliary Covariates

Generalized linear mixed models (GLMM) are useful in a variety of applications. With surrogate covariate data, existing methods of inference for GLMM are usually computationally intensive. We propose a two-step inference procedure for GLMM with missing covariate data. It is shown that the proposed estimator is consistent and asymptotically normal with covariance matrix that can be easily estimated. Simulation studies show that the proposed method outperforms those ignoring random effects or only using the validation data. We illustrate the proposed method with a data set from an environmental epidemiology study on the maternal serum DDE level in relationship to male birth defects.