Comparison of two approaches to analyzing correlated binary data in developmental toxicity studies

Recently developed statistical methodology is presented for analyzing correlated developmental toxicity data where multiple measures are obtained on individual units such as rat pups. Of particular interest is the assessment of the homogeneity of effects from chemical exposure across different outcomes such as malformation types or non-ossification of forepaw digits. Such contrasts are referred to as within-cluster effects, as they represent differences between observations within a cluster (e.g., pup). Between-cluster effects correspond to comparison of observations from different clusters, e.g., pups exposed to varied doses of chemicals or carcinogens. Two classes of statistical models are available for estimation of these distinct types of effects: (1) cluster-specific models in which regression adjustments are made for cluster effects, and hence all parameters are interpreted as within-cluster effects; and (2) population-averaged models in which no explicit adjustments are made for cluster, and thus all parameters are interpreted as group differences without regard to whether they represent between- or within-cluster effects. Many models in the developmental toxicity literature are population-averaged logistic regression models ignoring variation among clusters which may be significant under strong influences of genetic and environmental factors. Under such conditions, confidence interval-based inference for effect homogeneity will depend upon the class of models. These issues are illustrated with data from two developmental toxicity studies: (1) a National Toxicology Program study of the effects of in utero exposure to di(2ethylhexyl)phthalate among three malformation outcomes in mouse pups; and (2) a study conducted by Hartsfield to investigate the effects of anticonvulsant phenytoin on the risk of non-ossification among digits of the left and right forepaws in rat pups.