Joint Modeling of Longitudinal and Survival Data: New Models, Computing Techniques and Applications

Open Access
Author:
Liu, Xiaoyu
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
September 30, 2014
Committee Members:
  • Runze Li, Dissertation Advisor
  • Runze Li, Committee Chair
  • David Russell Hunter, Committee Member
  • Zhibiao Zhao, Committee Member
  • Stephanie Trea Lanza, Committee Member
Keywords:
  • Joint modeling
  • Longitudinal Study
  • Survival Analysis
  • EM-algorithm
  • Nonparametric
Abstract:
Motivated from an empirical analysis of data collected by a smoking cessation study, this dissertation studies the methodology, computation and application of joint modeling of longitudinal and survival data, and extends the existing modeling framework to several new settings. Firstly, we propose a joint model (JM) of survival data and multiple continuous longitudinal covariates, develop an estimation procedure using likelihood-based approach, and further establish the consistency and asymptotic normality of the resulting estimate. Computation for the proposed likelihood-based approach in the joint modeling framework is particularly challenging since the estimation procedure involves numerical integration over multi-dimensional space for the random effects. Existing numerical integration methods become ineffective or infeasible for JM. We introduce a numerical integration method based on computer experimental design for JM. We conduct Monte Carlo simulations to examine the finite sample performance of the proposed procedure and compare the new numerical integration method with the existing ones. We further illustrate the proposed procedure via an empirical study of smoking cessation data. Secondly, we propose a general nonparametric JM to incorporate both the time-varying survival coefficients and the longitudinal process with an irregular trajectory. Such a model is more flexible than the existing parametric joint models, and requires more powerful computational capability. We employ B-splines to approximate the functional parameters and use a maximum joint likelihood approach for parameter estimation. The estimates are calculated by the newly introduced computing algorithm, the EM-DoIt algorithm, and simulation studies are conducted to demonstrate the feasibility of the proposed estimation and computing procedures. The proposed model is applied to a smoking cessation study to explore the dynamic structure of the longitudinal process and the possible time-varying relationships between the negative affect and time to lapse. Finally, we propose a JM with discrete longitudinal covariates, which can also be fitted using the maximum joint likelihood approach, and implemented via the EM-DoIt algorithm. We conduct a few numerical studies to test the capability of the proposed approach in handling some specific types of longitudinal covariates, such as binary, count, and zero inflated discrete covariates.