Evaluation of Incidence Rates in Pre-Clinical Studies Using a Williams-Type Procedure

Abstract

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.

Absence of modulatory action on haptic height perception with musical pitch

“…In the case of sphericity violations the Greenhouse-Geisser corrected p -value was selected 6 . We analyzed the data with three different alpha levels using Bonferroni algorithm in order to provide a broader view of our results, ranging from the less to the more conservative: 0.05 (no adjustment), 0.05/3, and 0.05/6 (Wright, 1992 ; Bender and Lange, 2001 ). In the second case, the three global ANOVAs on haptic estimations (or verbal estimations) were corrected separately, while in the third case all six global ANOVAs belonged to a single family.…”

Comparisons of proportions in k dose groups against a negative control assuming order restriction: Williams-type test vs. closed test procedures

“…For example, the comparison of the overall response rates of three doses of oral liarozole with placebo in a randomized dose-finding trial for the treatment of psoriasis was performed by the approach [13] without using order restriction [2]. Comparisons of multiple dose groups with a control group assuming a monotonic dose-response relationship are frequently performed by means of the Williams trend test [18] where a modification for risk differences (of proportions) is available [8].…”

Similarity of multiple dose-response curves in interlaboratory studies in regulatory toxicology

“…In regulatory toxicology not only the difference of means is relevant as effect size [23], such as proportions or counts. Therefore, the Williams test is available for difference [10], risk ratio or odds ratio of proportions [9], ratio-to-control estimates [11], the nonparametric relative effect sizes [14], hazard rates [7], multiple endpoints [6], heteroscedastic error terms [8] and poly-k-adjusted tumor rates [20]).…”