Extension of Williams’ multiple comparison test for paired data

Abstract

Multiple comparison methods such as the Williams’ test are used to adjust for multiplicity of multiple doses in many confirmatory pharmacology studies. The existing Williams test is not suitable for paired data such as experiments using human cells. We constructed a test statistic of the Williams’ test that can be applied to individual-paired data, following the method of constructing the test statistic of existing Williams’ test and using the unbiased estimator of the error variance and the degrees of freedom in the ANOVA table for a two-factor linear model. Critical values were obtained by evaluating the distribution of the test statistic under the null hypothesis. Simulation studies confirmed the validity of the critical value and that the actual significance level were maintained at the nominal level. Furthermore, the Williams’ test extended for paired data, was found to have higher power than the Dunnett’s test and the fixed sequence test in the mid-saturation dose-response relationship often seen in confirmatory pharmacology studies. And it was shown that the analysis extended for paired data is necessary when analyze the paired data. Thus, the Williams’ test extended to paired data is appropriate and is superior to other multiple comparison methods in terms of power.