Missing data are common in many clinical studies. In this thesis, we review methods for analyzing incomplete data using generalized linear mixed models (GLMMs). GLMMs are widely used in clustered and longitudinal data analyses, where random effects are used to model subject or cluster specific effects. We review algorithms for finding the ML estimators in GLMMs with nonignorable missing responses. We present an application of the GLMM using actual data from a clinical study. We also conduct a simulation study to assess the performance of the ML method in the presence of nonignorable missing responses. The simulation results indicate that under misspecified missing data models one can observe systemic bias in the regression estimators and also poor coverage probabilities from the confidence intervals. We conclude that when analyzing incomplete data with nonignorable missing responses, it is necessary to incorporate a suitable missing data model into the observed data likelihood function in order to obtain unbiased and efficient estimators of the model parameters.