Two latent variable risk assessment approaches for mixed continuous and discrete outcomes from developmental toxicity data

Measurements of both continuous and discrete outcomes are encountered in ma ny statistical problems. Here we consider the particular context of teratol ogy studies, where quantitative risk assessment is aimed at determining the effect of dose on the probability that an individual fetus is malformed or of low birth weight, both being important measures of teratogenicity. We w ill introduce two different joint marginal mean models for outcomes of a mi xed nature. First, we propose the Plackett-Dale approach, where for each bi nary outcome it is assumed that there exists an underlying latent variable. The latent malformation outcomes are then assumed to follow a Plackett dis tribution. The second approach we consider is a probit approach. Here it is assumed that there exists an underlying continuous variable for each binar y outcome, so the joint distribution for weight and malformation can be ass umed to follow a multivariate normal distribution. In both cases, specifica tion of the full distribution will be avoided using pseudolikelihood and ge neralized estimating equations methodology, respectively. Quantitative risk assessment is illustrated using data from two developmental toxicology exp eriments.