Likelihood Models for Clustered Binary and Continuous Out comes: Application to Developmental Toxicology

Abstract

In developmental toxicology, methods based on dose response modeling and quantitative risk assessment are being actively pursued. Among live fetuses, the presence of malformations and reduction in fetal weight are of primary interest, but ordinarily, the dose-response relationships are characterized in each of the outcomes separately while appropriately accounting for clustering within litters. Jointly modeling the outcomes, allowing different relationships with dose while incorporating the correlation between the fetuses and the outcomes, may be more appropriate. We propose a likelihood-based model that is an extension of a correlated probit model to incorporate continuous outcomes. Our model maintains a marginal dose-response interpretation for the individual outcomes while taking into account both the correlations between outcomes on an individual fetus and those due to clustering. The joint risk of malformation and low birth weight can then be estimated directly. This approach is particularly well suited to estimating safe dose levels as part of quantitative risk assessment.

Semiparametric latent variable transformation models for multiple mixed outcomes

“…For example, the related literature has focused primarily on joint models for binary and continuous outcomes in a joint normal framework (Catalano and Ryan, 1992;Cox and Wermuth, 1992;Fitzmaurice and Laird, 1995;Sammel et al, 1997;Regan and Catalano, 1999;Dunson, 2000;Roy and Lin, 2000;and Gueorguieva and Agresti, 2001;Song et al, 2009), and in a generalized linear model setting (GLLVM, Moustaki, 1996;Sammel, Ryan, and Legler, 1997;Bartholomew and Knott, 1999;Moustaki and Knott, 2000;Dunson, 2003;Huber et al, 2004;Zhu, Eickhoff and Yan, 2005).…”

A copula‐based model for multivariate non‐normal longitudinal data: analysis of a dose titration safety study on a new antidepressant

“…Regan and Catalano [15] showed how to build a joint model for clustered binary and continuous outcomes with an application to developmental toxicology. They use an extension of the correlated probit model [16] to obtain a joint distribution for the binary and the continuous responses.…”

On the Multivariate Probit Model for Exchangeable Binary Data with Covariates

“…This is also possible via an extension of the multivariate latent variable approach. We will not discuss this further here -see Regan and Catalano (1999) and Geys et al (2001) who use likelihood methods, and the comment in the next section.…”

“…This is an important consideration when clusters are of varying sizes -the interpretability assumption as discussed by Stefanescu and Turnbull (2003). Finally, due to the underlying threshold approach, the multivariate probit model extends to analysis of clustered mixed binary and continuous data, or of multivariate binary data (Regan and Catalano, 1999;Geys et al, 2001). An extension to multiple thresholds leads to a model for clustered ordinal data (Sorensen et al, 1995).…”