Doctoral Dissertation Defense: Shijun Zhu

We study statistical methods for joint modeling that accommodates the correlations among multiple longitudinal outcomes and the time to recurrent events. We first propose the multivariate latent growth curve modeling with conditional indirect effects under the structural equation modeling framework to assess the longitudinal moderated mediation effects. We conduct an extensive simulation study to evaluate the statistical performance of the complex model in terms of bias and coverage probability of parameter estimation, and statistical power with regard to R2, effect sizes of mediation effects and moderated mediation effects, sample size, and number of measurement occasions.  We apply this model to analyze real data.  

In the second topic, we develop another joint modeling to analyze two longitudinal outcomes and time to recurrent events data. We combine the bivariate normal mixed effect model and the frailty model by including the multivariate normal random variables, which account for the dependence among the repeated measures and the dependence between longitudinal outcome and recurrent events. We use nonparametric maximum likelihood estimation (NPMLE) to estimate the parameters.  The numerical algorithm of expectation-maximization (EM) algorithm was used to compute the NPMLEs and their variance estimators. The results from the simulation study show that the NPMLEs are noticeably unbiased and the standard error estimators well reflect the true variations of the proposed estimators. The coverage probabilities are in the reasonable range. We further extend the joint model to address the dependence between the recurrent events with each individual by including an additional random effect to model the correlations. We use the similar NPMLE approach to estimate the parameters via EM algorithm.  Simulation study shows NPMLE and variance estimation are unbiased even with the higher dimensional random effects included in the model.  The joint model is applied to real data—Urea Cycle Disorders study.