Joint Modeling of Longitudinal Binary and Continuous Responses: New Models, Statistical Procedures and Applications

Open Access
Author:
Kurum, Esra
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 11, 2012
Committee Members:
  • Runze Li, Dissertation Advisor
  • Naomi S Altman, Committee Member
  • Zhibiao Zhao, Committee Member
  • Stephanie Trea Lanza, Special Member
Keywords:
  • Joint Modeling
  • Longitudinal data analysis
  • Varying coefficient models
  • Partially linear models
Abstract:
Longitudinal data of mixed (e.g., binary and continuous) type are now very common. In this dissertation, we propose two classes of joint modeling procedures for studying the time-varying association between two intensively measured longitudinal responses: a continuous one and a binary one. Since it is well-established that varying-coefficient models increase the flexibility of parametric models and may reduce the modeling bias, our first procedure is based on time-varying coefficient models. However, it is known that semiparametric models represent an appealing compromise between parametric models and nonparametric models, retaining the explanatory power of parametric models while offering the flexibility of nonparametric models. Hence, in the second part of this dissertation, we propose a semiparametric approach, namely, partially linear models. A major challenge in jointly modeling binary and continuous responses is the lack of a multivariate distribution. We suggest introducing a normal latent variable underlying the binary response and factorizing the model into two components: a marginal model for the continuous response, and a conditional model for the binary response given the continuous response. For both techniques, we develop a two-stage estimation procedure and establish the asymptotic normality of the resulting estimators. We also derive the standard error formulas for the estimated coefficients. In each part we conduct a Monte Carlo simulation study to assess the finite sample performance of our procedures. The proposed nonparametric method is illustrated by an empirical analysis of smoking cessation data \citep{Shiffman:1996fk}, in which we investigate the association between urge to smoke, the continuous response, and the status of alcohol use, the binary response, and how this association varies over time. We apply our proposed semiparametric methodology to data from the Women’s Interagency HIV Study. In this analysis we examine the time-varying association between CD4 cell count, the continuous response, and smoking status, the binary response.