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

TL;DR

This paper compares Williams-type trend tests and closed testing procedures for analyzing proportions across multiple dose groups against a control, focusing on power and simplicity in the context of order restrictions.

Contribution

It introduces and evaluates two variants of closed testing procedures as alternatives to Williams-type tests for comparing proportions with order restrictions.

Findings

Closed testing procedures show improved power over Williams-type tests.

The proposed methods are simpler to implement and interpret.

R-code for the methods is provided.

Abstract

The comparison of proportions is considered in the asymptotic generalized linear model with the odds ratio as effect size. When several doses are compared with a control assuming an order restriction, a Williams-type trend test can be used. As an alternative, two variants of the closed testing approach are considered, one using global Williams-tests in the partition hypotheses, one with pairwise contrasts. Their advantages in terms of power and simplicity are demonstrated. Related R-code is provided.