Longitudinal designs are common in epidemiology and other areas of the biomedical sciences because they allow characterization of health status over time and determinants of any changes. The analysis of longitudinal studies present some unique problems especially when subjects have incomplete observations. This proposal address these problems. The first goal is to develop a semiparametric estimator that is an extension of the generalized estimating equations (GEE) estimator of Liang and Zeger (1986), and that results in valid inferences when the data are missing at random as defined by Rubin (1976). The current GEE makes the stronger assumption of data missing completely at random. The likelihood approach is another procedure for analyzing longitudinal studies with data missing at random. However this approach is non-robust to misspecification of the joint distribution of the outcomes. When non- response depends on the unobserved outcome the likelihood approach proceeds by maximizing the likelihood of the joint distribution of the outcomes and an assumed non-response model. No adjustment to the GEE exist when a non-response model is known. The second goal is to develop adjustments to the GEE when the data are not missing at random and to compare the bias of likelihood-based estimators with the proposed semiparametric estimators under violations of the assumptions under which both estimators are consistent. The proposed semiparametric approach, although simple to implement, may be less efficient than the likelihood approach. Our third goal is to study the relative efficiency comparing the estimators given by the two approaches under a variety of missing data scenarios and covariate design structures. The fourth goal is to develop semiparametric estimators that are consistent when the data are not missing at random but data from subsamples of the non-respondents are obtained at each occasion. These methods will allow the probability of selection in the subsample to depend on past data values. Methods are available for adjusting for mismeasured covariates using validation samples in cross-sectional designs. None exist for longitudinal designs. The final objective is to develop semiparametric methods for analyzing longitudinal studies in the presence of covariate measurement error when error-free measurements are obtained on a subsample at each occasion.
