Multi-Arm Equivalence Tests for Treatment Proportions

This document is a technical report that details the computation of power and sample size for multi-arm equivalence tests concerning the difference between treatment and control proportions in a cluster-randomized design. It outlines the methodology based on established research, specifically referencing works by Donner and Klar (2000) and Machin et al. (2018). The report explains the concept of cluster-randomized designs, where entire groups of subjects are randomized rather than individual subjects, which is crucial in minimizing contamination risks. It further discusses the implications of using multiple treatment groups compared to a single control group, emphasizing the necessity of comparing each treatment with a control to maintain research integrity. The document also includes technical details on statistical hypotheses, test statistics, and the importance of multiplicity adjustments in the analysis of results. Additionally, it provides examples and formulas for calculating sample sizes and power for both pooled and unpooled tests, ensuring accurate estimations in clinical trials.