In this thesis, we explore semiparametric marginal models for binary longitudinal data with dropouts. We are specifically interested in the joint estimation of the marginal mean parameters and association parameters by second order generalized estimating equations when the marginal mean response model is partially linear.
First, we propose and explore a set of weighted generalized estimating equations (GEEs) 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 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.
We also developed a semiparametric approach to analyzing longitudinal binary data. We applied second order GEE approach to analyze longitudinal binary responses under partially linear single-index
models. We use the local polynomial smoothing technique to estimate the single-index parameters. We study the empirical properties of the proposed method in simulations. Our simulation study demonstrates that if the true underlying model is partially linear, then our proposed method generally provides unbiased and efficient estimators. The proposed method is also applied to some real data sets obtained from two longitudinal studies.
Next, we propose a weighted local linear kernel method and a weighted second order GEE approach for simultaneous estimation of the single-index, regression
and association parameters in partially linear single-index models with dropouts. Finally, the proposed methods are applied to some clinical data obtained from a Genetic and Inflammatory Marker of Sepsis (GenIMS) study. The estimates of the single-index showed strong evidence of nonlinear trend in the mean response function. It is evident from this application that our proposed methods can be used to improve the efficiency of the estimates obtained from an ordinary GEE model for binary longitudinal data with dropouts.