Gaussian Copula Mixed Models for Clustered Mixed Outcomes, With Application in Developmental Toxicology


DOI: 10.1007/s13253-013-0155-9

Cite this article as:
Wu, B. & de Leon, A.R. JABES (2014) 19: 39. doi:10.1007/s13253-013-0155-9


This paper is concerned with the analysis of clustered data from developmental toxicity studies with mixed responses, i.e., where each member of the cluster has binary and continuous outcomes. A copula-based random effects model is proposed that accounts for associations between binary and/or continuous outcomes within clusters, including the intrinsic association between the mixed outcomes for the same subject. The approach allows the adoption of flexible distributions for the mixed outcomes as well as for the random effects. The model includes the correlated probit model of Gueorguieva and Agresti (2001) and the generalized linear mixed models of Faes et al. (2008), and Faes, Geys, and Catalano (2009) as special cases. Maximum likelihood estimation of our model parameters is implemented using standard software such as PROC NLMIXED in SAS. The proposed methodology is motivated by and illustrated using a developmental toxicity study of ethylene glycol in mice. This article has supplementary material online.

Key Words

Biserial correlation Generalized linear mixed models Latent variables Logit-normal Gaussian copula mixed model Mixed binary-continuous data Robit-t Gaussian copula mixed model Tetrachoric correlation 

Supplementary material

13253_2013_155_MOESM1_ESM.pdf (215 kb)
(PDF 215 kB)

Copyright information

© International Biometric Society 2013

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.PAREXELBillericaUSA

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