Evaluation of incidence rates in pre-clinical studies using a Williams-type procedure

The analysis of dose-response relationships is a common problem in pre-clinical studies. For example, proportions such as mortality rates and histopathological findings are of particular interest in repeated toxicity studies. Commonly applied designs consist of an untreated control group and several, possibly unequally spaced, dosage groups. The Williams test can be formulated as a multiple contrast test and is a powerful option to evaluate such data. In this paper, we consider simultaneous inference for Williams-type multiple contrasts when the response variable is binomial and sample sizes are only moderate. Approximate simultaneous confidence limits can be constructed using the quantiles of a multivariate normal distribution taking the correlation into account. Alternatively, multiplicity-adjusted p-values can be calculated as well. A simulation study shows that a simple correction based on adding pseudo observations leads to acceptable performance for moderate sample sizes, such as 40 per group. In addition, the calculation of adjusted p-values and approximate power is presented. Finally, the proposed methods are applied to example data from two toxicological studies; the methods are available in an R-package.