Statistical Methods for Analyzing Bivariate Mixed Outcomes

Multivariate outcomes are ubiquitous. Joint analysis of multivariate outcomes provides several benfits over separate analysis of each outcome. However, joint analysis of multivariate outcomes that are mixed, i.e., not on the same scale of measurement, can be challenging. This dissertation provides novel methods to analyze bivariate mixed outcomes, where we have exactly one continuous outcome and one binary outcome. A penalized generalized estimating equations framework to perform simultaneous estimation and variable selection for bivaraite mixed outcomes in the presence of a large number of covariates is provided. Next, fully Bayesian and empirical Bayes approaches to estimating the association between the two outcomes using a copula-based model are provided. Finally, methods for estimating and testing genomic effects in bivariate mixed secondary outcome models under case-control designs are presented