"A Copula-based Method For Analyzing Bivariate Binary Longitudinal Data"
Dissertation Defense: Seunghee Baek, Ph.D. Candidate, Division of Biostatistics
November 11, 2010 @ 10:00am – 12:00pm
Location: 701 Blockley Hall
Biostatistics
"A Copula-based
Method For Analyzing Bivariate Binary Longitudinal Data"
Thesis supervisors: Scarlett
Bellamy, ScD & Andrea Troxel, ScD
Abstract: The methods developed in this dissertation are motivated by a clinical trial for HIV serodiscordant couples. Specifically, the Multisite HIV/STD Prevention Trial for African American Couples is a behavioral modification trial for African American, heterosexual, HIV discordant couples. In this trial, investigators developed and evaluated a couple-based behavioral intervention for reducing risky shared sexual behaviors and collected retrospective self-reported outcomes from both partners at baseline and at 3 follow-up assessments to evaluate the efficacy of the intervention. Couples' responses for shared sexual behaviors are expected to be correlated. Thus, modeling couple responses in this context should account for multiple sources of correlation: within-individual over time as well as within-couple both at the same measurement time and at different times. This dissertation offers novel applications and extensions of the copula approach to modeling dyadic, longitudinal data to estimate reliability and efficacy.
Copulas have been popular analytic tools for modeling multivariate outcomes. I selected a mixture of max-infinitely divisible (max-id) copula because of its desirable properties for modeling multivariate discrete data. Max-id copulas are attractive because of their flexible positive dependence structures and closed form cumulative distribution functions. In Chapter 2, I propose a copula-based approach to estimating the reliability of self-reported couples' outcomes, adjusting for key couple-level baseline covariates. Practically, reliable assessments of HIV sexual risk behaviors are critical to supporting the validity of any observed treatment effects. In Chapter 3, I extend the max-id copula approach to incorporate longitudinal (baseline and one follow-up) binary couples data. A complex correlation structure, described above, is accommodated by employing a copula-based model that allows flexible dependence structures among outcomes using several copula parameters. Chapter 4 extends the copula-based model, proposed in Chapter 3, for bivariate longitudinal binary data, enabling modeling of such data with more than two repeated measures. The joint distribution of the current observation of each bivariate outcome is modeled conditional on the previously observed bivariate outcomes. These conditional distributions are constructed using a max-id copula. The suggested model is illustrated by examining the factors that are potentially associated with two different measures of depression in a study based in a primary care clinical setting.
The copula-based modeling approach presented in this dissertation provides a useful tool for investigating complex dependence structures among multivariate outcomes as well as the covariate effect on each marginal model of the outcomes, and can be easily applied to other studies that involve multivariate outcomes (e.g., dyads) measured repeatedly.
