Models and analysis for longitudinal binary data

In longitudinal studies, repeated observations of a response variable and a set of covariates are made on individuals over time. Repeated observations made on the same individual will be correlated, and this dependence must be taken into account in order to obtain appropriate standard errors and make valid inferences.; Risk factors, if differently distributed in different people, can introduce heterogeneity in the risk of disease. Usual regression methods are inadequate if the groups of observations are not homogeneous. Testing for heterogeneity in groups of observations is important; since it might indicate familial aggregation of a disease or presence of unmeasured risk factors.; In this thesis, we develop a score statistic to test for heterogeneity in binary data. The score statistic is based on the logistic regression model with random effects. It is powerful in detecting the presence of unexplained variability and makes no assumptions about the distribution of the random effect.; We study marginal models, joint estimation models, and random effect models for the analyses of longitudinal binary data. These methods and models are applied to study the Left Ventricular Hypertrophy (LVH) data set from the Multiple Risk Factor Intervention Trial.