Multi-Arm Equivalence Tests for Treatment Proportions

This technical report outlines the methodology for computing power and sample size for multi-arm equivalence tests of the ratio of treatment and control proportions in a cluster-randomized design. The document explains that a cluster-randomized design involves randomizing whole units or clusters of subjects rather than individual subjects, which can lead to a loss of efficiency. The report details the statistical methods used, including the TOST z-test for comparing treatment groups against a common control group. It discusses the importance of making a Bonferroni adjustment for type I error rates due to multiple comparisons. The document also provides examples of how to set up experiments, including determining sample sizes based on desired power and significance levels. Additionally, it addresses the implications of using a control group repeatedly and suggests adjustments to account for this in study design. The report is based on established statistical principles and references key literature in the field.