Random Effects Copula Models for Clustered Mixed Outcomes

• Activity Number: 27
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Alexander de Leon*+
• Companies: University of Calgary
• Keywords: Joint analysis ; Gaussian copula ; Correlated robit-normal model ; Mixed binary-continuous

Abstract

We consider clustered data with mixed bivariate responses, i.e., where each member of the cluster has a binary and a continuous outcome, and propose a copula-based random effects model that accounts for associations between binary and/or continuous outcomes within and between clusters, including the intrinsic association between the binary and continuous outcomes within the same subject. Our approach yields regression parameters in models for both outcomes that are marginally meaningful; in addition, by assuming a latent variable framework to describe binary outcomes, the copula used still uniquely determines the joint distribution. We implement maximum likelihood estimation of our model parameters using readily available software (e.g., PROC NLMIXED in SAS), and report results of simulations concerning the bias and efficiency of our estimates. We illustrate our methodology by analyzing a developmental toxicity study of ethylene glycol in mice.