Contributions to Copula Modeling of Mixed Discrete-Continuous Outcomes
Creators: name: Beilei, Wu
Publisher: name: Graduate Studies
Year: 2013
Subjects: subject: Mathematics
subject: FOS: Mathematics
subject: copula models
subject: multiple correlated discrete and continuous outcomes
subject: latent-varible approach
subject: random effects
subject: full and pairwise likelihood estimation methods
subject: "continuous-ation" approach
subject: surrogate likelihood approach
subject: multiple mixed binary and continuous co-primary endpoints
subject: calculating the sample size in clinical trials
subject: longitudinal data settings

description: This thesis includes three topics that are concerned with joint modeling and analysis of multiple correlated mixed discrete and continuous outcomes. The first topic is concerned with the analysis of multiple correlated discrete and continuous outcomes that are observed on the same subjects over time in the case of longitudinal studies, or from clustered subjects in cross-sectional settings. Joint analysis of such disparate responses (i.e., mixed discrete and continuous outcomes) is problematic in practice due mainly to the difficulty of defining or constructing a joint model. Our proposed approach is based on a new generalized linear mixed model (GLMM) that accounts for associations between the outcomes (of the same or of different types) for the same subject at the same time point, and/or at different time points for the longitudinal data, or between mixed outcomes within clusters, including the intrinsic association between the mixed outcomes for the same subject, in clustered settings. A latent-variable approach is adopted to sidestep complications of direct application of copula models to discrete data. The approach yields regression parameters that are marginally meaningful, and permits the adoption of flexible non-Gaussian distributions for the mixed outcomes as well as for the random effects. Special cases of our model include conventional GLMMs previously proposed by a number of authors, among whom are Faes (2013), Gueorguieva (2013), and Lin et al. (2010). Full and pairwise likelihood estimation methods are implemented for the model using PROC NLMIXED in SAS. The proposed methodology is illustrated using individual panel data on the wages, work hours, and union memberships, and data on fetal malformation and weight in a developmental toxicity study on mice. In the second topic, we adopt the continuous-ation" approach of Machado and Santos Silva (2005) and Denuit and Lambert (2005) to construct a Gaussian copula joint model for mixed discrete and continuous outcomes. The joint model does not require a latent variable formulation of the discrete outcomes, and does not suffer from the complications of directly using discrete margins in copula models (Genest and Neslehova, 2007). A surrogate likelihood approach to estimation is implemented for the model and empirical results concerning the relative bias and efficiency of the resulting estimates are reported. The proposed methodology is illustrated using data on burn injuries. The third and final topic concerns a methodology for calculating the sample size in clinical trials with multiple mixed binary and continuous co-primary endpoints. The Gaussian copula joint model we proposed permits the adoption of flexible marginal distributions for the mixed endpoints, and includes the conditional grouped continuous model (CGCM) - a popular model for mixed endpoints based on the multivariate Gaussian distribution - as a special case. The proposed methodology adopts a latent variable description of the binary endpoints and makes use of tests on the latent means to test for differences in the binary proportions. This approach results in a simple and streamlined methodology akin to that for multiple continuous co-primary endpoints studied in Sozu et al. (2011). In addition, our approach is more powerful than that recently proposed by Sozu et al. (2012), in that it yields smaller sample sizes at powers comparable to those considered in Sozu et al. (2012). We report the results of empirical comparisons as well as a numerical illustration of our methodology.