Date of Award

Spring 2020

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Hrishikesh Chakraborty

Abstract

The joint modeling of longitudinal and time-to-event data is an active area of statistical research that has received a lot of attention. The standard joint models, referred to as univariate joint models, allow simultaneous modeling of a single longitudinal outcome and a single time-to-event under an assumption of independent censoring. The majority of the joint modeling research in the last two decades has focused on extending and improving the univariate joint models. While many of the practical applications involve data on multivariate longitudinal outcomes and multiple timeto- events possibly informatively censored by some other terminal time-to-event, the developments of joint models to analyze such complex data structure have not received deserved attention. One other area of statistical joint modeling methods that remained understudied is the joint analysis of multivariate longitudinal outcomes and multiple ordered time-to-events. The joint models for recurrent events in existing literature can be applied to analyze ordered time-to-events of the same type under an assumption that all occurrences of the time-to-event are homogeneously influenced by the covariates. However, in problems of ordered time-to-events of different types or of the same kind where different occurrences may be impacted differently by the covariates, the current methods may not be applied. Given the limitations in the existing body of joint modeling literature, this research work aims to present joint modeling extensions with the potentials of filling in the noted literature gaps.

In Chapter 2 of this dissertation, we presented a shared parameters Bayesian latent trait joint frailty model for analyzing multivariate longitudinal outcomes and multiple unordered non-terminal time-to-events in the presence of a terminal event inducing dependent right censoring. We adopted a semiparametric latent trait generalized mixed-effects approach to define the longitudinal submodel. Semiparametric hazard regression models are used to model the non-terminal and terminal time-to-event risks with multivariate non-terminal event frailties to account for the inter-event associations. Chapter 4 introduces an extension of the joint model presented in Chapter 2 for multivariate longitudinal outcomes and multiple ordered time-to-events. For both the proposed models, Bayesian approaches of parameter estimation are discussed, and Bayesian Monte Carlo Markov Chain (MCMC) dynamic prediction algorithms for longitudinal outcomes and time-to-event risks are outlined. The finite sample performances of the parameter estimation methods and dynamic prediction algorithms are studied through statistical simulations for both the proposed models.

Before presenting the joint frailty model for multiple ordered time-to-events in Chapter 4, we revisited a long-studied problem of estimating the survival functions for multiple ordered time-to-events in Chapter 3. Given the complexities and unbecomingness under certain assumptions of the current methods, we discussed two straightforward and easy to compute approaches of estimating survival functions of multiple ordered time-to-events. The first approach is non-parametric, based on Kaplan-Meier survival estimates, and assumes independence between the consecutive event times to estimate the marginal survival curves. The second approach is fully parametric, assumes the consecutive event gap times to be log-normally distributed, and estimates the marginal and conditional survival functions when the consecutive event times may not be expected to be independent. Simulations studies were performed to evaluate the finite sample properties of both the non-parametric and parametric approaches at different sample sizes and censoring rates. In addition to the extensive simulation studies, we have demonstrated applications of all the proposed joint models, and survival function estimation approaches using statewide surveillance data from South Carolina (SC) HIV/AIDS patients.

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