In this paper, we propose and explore a set of weighted generalized estimating equations for fitting regression models to longitudinal binary responses when there are dropouts. Under a given missing data mechanism, the proposed method provides unbiased estimators of the regression parameters and the association parameters. Simulations were carried out to study the robustness properties of the proposed method under both correctly specified and misspecified correlation structures. The method is also illustrated in an analysis of some actual incomplete longitudinal data on cigarette smoking trends, which were used to study coronary artery development in young adults.