Statistical model for fetal death, fetal weight, and malformation in developmental toxicity studies

The purpose of this paper is to present a statistical model for analyzing the joint effects of exposure on fetal death, fetal weight, and malformation in a developmental toxicity study. In addition to allowing for the usual litter effect, the model allows for correlations between different outcomes measured on the same fetus. Fitting the model requires first focusing on non‐live outcomes by modeling the probability of fetal death or resorption as a function of dose. Then outcomes among live fetuses are modeled using a two‐stage regression approach. The first stage models fetal weight as a function of dose and the second stage models fetal malformation as a function of dose, as well as residuals from the weight model. The regression coefficients from the malformation model have intuitive interpretations in terms of correlations between littermates and between different outcomes measured within the same fetus. Not only does the approach provide a useful way to investigate the relationship between adverse fetal outcomes, it also yields a natural framework for conducting quantitative risk assessment. A procedure is proposed for quantifying overall risk by incorporating the three outcomes in order to estimate safe dose levels and corresponding lower confidence limits. The method is illustrated using data from an experiment in mice conducted through the National Toxicology Program. © 1993 Wiley‐Liss, Inc.