Model selection in toxicity studies

In toxicity studies, model mis-specification could lead to serious bias or faulty conclusions. As a prelude to subsequent statistical inference, model selection plays a key role in toxicological studies. It is well known that the Bayes factor and the cross-validation method are useful tools for model selection. However, exact computation of the Bayes factor is usually difficult and sometimes impossible and this may hinder its application. In this paper, we recommend to utilize the simple Schwarz criterion to approximate the Bayes factor for the sake of computational simplicity. To illustrate the importance of model selection in toxicity studies, we consider two real data sets. The first data set comes from a study of dietary fortification with carbonyl iron in which the Bayes factor and the cross-validation are used to determine the number of sub-populations in a mixture normal model. The second example involves a developmental toxicity study in which the selection of dose-response functions in a beta-binomial model is explored.