In this thesis, we explore different estimation methods for longitudinal data with binary responses and drop-outs. We also study the effect of incorrectly specifying the dependence structure or the drop-out mechanism. Although highly efficient, the traditional maximum likelihood (ML) method becomes complex when the number of responses increases, requiring intensive computation. Alternative methods such as generalized estimating equations (GEE) and weighted GEE had been proposed in the literature to overcome the limitation of the ML method. However, both estimators are known to be biased under non-ignorable drop-out mechanisms. The bivariate maximum pseudo likelihood is a pseudo likelihood method that takes into account the correlation between the current and baseline responses. Originally developed for non-monotone missing data, it was modified to be adapted for monotone drop-outs. We conduct a simlation study to assess the sensitivity of each method to model misspecifications in which a non-ignorable drop-out mechanism is our primary interest.