Modelling overdispersion in toxicological mortality data grouped over time

Toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment. Both survival analysis and generalized linear models have been proposed for analyzing this type of data. Whatever the approach taken, the model should allow for the presence of extra-multinomial variation arising from the use of groups of animals rather than individuals as the experimental units. We consider a number of models for overdispersion that can be incorporated into the generalized linear model framework for multinomial data. These models are extensions of ones proposed for binomial data by Williams (1982, Applied Statistics 31, 144-148) and Moore (1986, Biometrika 73, 583-588; 1987, Applied Statistics 36, 8-14). In addition, we examine robust asymptotic covariance matrix estimators for regression parameters, similar to those given in Liang and Zeger (1986, Biometrika 73, 13-22) and Zeger and Liang (1986, Biometrics 42, 121-130), and compare them to the model-based asymptotic estimators. Recommendations for analysis are given.