PhD Candidate, University of Georgia Department of Statistics
Semiparametric regression models have been wildly applied into the longitudinal data. In this dissertation, we model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ration (GQLR) test procedure to test if these functions are the same. We first consider an estimation approach for our semiparametric regression model based on profile estimation equations combined with local linear smoothers. Next, we describe the proposed GQLR test procedure and study the asymptotic null distribution of test statistics. We find that the much celebrated Wilks phenomenon which is well established for independent data still holds for longitudinal data if variance is estimated consistently, even though the working correlation structure is misspecified. However, this property does not hold in general, especially when the wrong working variance function is assumed. As for the power of the proposed GQLR test, our empirical study shows that incorporating correlation into the GQLR test does not necessarily improve the power of the test. A more extensive simulation study is conducted in which the Wilks Phenomenon is investigated under both Gaussian and Non-Gaussian longitudinal data and a wider variety of scenarios. The proposed methods are also illustrated with two real applications from AIDS clinical trial and opioid agonist treatment.