Multi-Arm Non-Inferiority Tests in Cluster-Randomized Design

This document is a technical report that outlines the methodology for conducting multi-arm non-inferiority tests for the ratio of treatment and control proportions in a cluster-randomized design. It describes the computational aspects related to power and sample size estimation when binary data is collected from clusters rather than individual subjects. The report explains the implications of using a cluster-randomized design, particularly the challenges associated with contamination risks and the efficiency of sample size requirements. The document details the statistical hypotheses involved, including the application of the Bonferroni adjustment for multiple comparisons, and provides examples illustrating the design and analysis of such studies. It also discusses the importance of determining an appropriate sample size to achieve desired power levels and outlines the necessary adjustments for the control group size in relation to treatment groups. Overall, the report serves as a comprehensive guide for researchers planning to implement multi-arm non-inferiority trials in clinical settings.