A Bayesian analysis of quantal bioassay experiments incorporating historical controls via Bayes factors

This paper addresses model-based Bayesian inference in the analysis of data arising from bioassay experiments. In such experiments, increasing doses of a chemical substance are given to treatment groups (usually rats or mice) for a fixed period of time (usually 2 years). The goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect (usually presence of adenoma or carcinoma). The data consists of dosage, survival time, and the occurrence of the adverse event for each unit in the study. To determine whether such relationship exists, this paper proposes using Bayes factors to compare two probit models, the model that assumes increasing dose effects and the model that assumes no dose effect. These models account for the survival time of each unit through a Poly-k type correction. In order to increase statistical power, the proposed approach allows the incorporation of information from control groups from previous studies. The proposed method is able to handle data with very few occurrences of the adverse event. The proposed method is compared with a variation of the Peddada test via simulation and is shown to have higher power. We demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors. Copyright © 2017 John Wiley & Sons, Ltd.