Analysis Of Longitudinal Studies With General Linear Models And Generalized Linear Models

The defining characteristic of longitudinal data is that individuals are measured repeatedly through time. An observed sequence is obtained for each individual. Longitudinal data often occur in medical researches and clinical trials. If we adopt the cross-sectional methods, such as t-test, analysis of variance, to analyze longitudinal data, we may lost some information. And more important, ignoring the possible existed correlation between repeated measures would make inaccurate estimation for parameters and even draw wrong conclusions.For longitudinal studies, many methods, especially concerned with generalized linear models, are still at the stage of exploration, complete theoretical system has not been formed. However, longitudinal studies considered sufficiently the mutual dependence between repeated measures. Typically it has two important advantages, that is, increasing power and robustness to model selection. So more and more interests have been aroused in this area. At present the general appoaches for analyzing longitudinal data are to fit linear models and generalized linear models. The central problem is how to cope with the correlation between repeated measures.In this thesis we fitted linear models for normal responses. The general method for analyzing continuous longitudinal data was given. We fitted generalized linear models for binary data and count data, and put forward Markov model for clinical follow-up data.1. We developed general linear models for normal longitudinal data, in which the inferences about regression parameters recognize the likely correlation structure in the data. We formulated the linear models by time-plots of observed averages within treatment groups. Sample variogram plots were used to formulate covariance structure. Weighted least-squares and...