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

Abstract

Measurements of both continuous and discrete outcomes are encountered in many statistical problems. Here we consider the particular context of teratology 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 will introduce two different joint marginal mean models for outcomes of a mixed nature. First, we propose the Plackett-Dale approach, where for each binary outcome it is assumed that there exists an underlying latent variable. The latent malformation outcomes are then assumed to follow a Plackett distribution. The second approach we consider is a probit approach. Here it is assumed that there exists an underlying continuous variable for each binary outcome, so the joint distribution for weight and malformation can be assumed to follow a multivariate normal distribution. In both cases, specification of the full distribution will be avoided using pseudolikelihood and generalized estimating equations methodology, respectively. Quantitative risk assessment is illustrated using data from two developmental toxicology experiments.