Analysis of Multiple Ordinal Outcomes in Developmental Toxicity Studies

Abstract

In a typical developmental toxicity or teratology study, each pregnant dam and offspring are assessed for a variety of adverse outcomes, yielding a vector of correlated responses on each animal. In this paper, we consider a heatshock study conducted to assess the effects of in vitro exposure of mouse embryos to various levels and durations of heat stress, where the outcomes of interest consist of a series of ordinally classified morphological parameters. Several approaches in the area of developmental toxicity have been suggested for the assessment of multiple binary or continuous developmental outcomes; however, such a strategy has not been well-developed for multiple ordinal outcomes. We present a marginal modeling framework appropriate for correlated ordinal responses which specifies univariate cumulative probabilities for each outcome along with pairwise and higher-order associations. Maximum likelihood and quasi-likelihood approaches for estimating parameters of interest are described, and their relative merits and limitations are discussed in the context of the heatshock study. Although the particular exposure setting of the heatshock studies reduces the need to incorporate litter effects, possible extensions of this methodology to account for the clustering induced by littermates are also considered.