Topics in analyzing longitudinal data

We propose methods for analyzing longitudinal data, obtained in clinical trials and other applications with repeated measures of responses taken over time. Common characteristics of longitudinal studies are correlated responses and observations taken at unequal points in time. The first part of this dissertation examines the justification of a block bootstrap procedure for the repeated measurement designs, which takes into account the dependence structure of the data by resampling blocks of adjacent observations rather than individual data points. In the case of dependent stationary data, under regular conditions, the approximately studentized or standardized block bootstrap possesses a higher order of accuracy. With longitudinal data, the second part of this dissertation shows that the diagonal optimal weights for unbalanced designs can be made to improve the efficiency of the estimators in terms of mean squared error criterion. Simulation study is conducted for each of the longitudinal designs. We will also analyze repeated measurement data set concerning nursing home residents with multiple sclerosis, which is obtained from a large database termed the minimum data set (MDS).