Multi-Arm Superiority Testing in Cluster-Randomized Designs

This technical report details the methodology for computing power and sample size for multi-arm superiority by a margin tests in cluster-randomized designs. It outlines how these tests compare treatment proportions against a single control proportion, emphasizing the unique considerations of cluster-randomized designs where entire groups are randomized rather than individual subjects. The report explains the implications of using such designs, including the potential loss of efficiency and the necessity for larger sample sizes compared to individual randomization. It also discusses the statistical hypotheses involved in testing the effectiveness of new treatments against a control, including the formulation of superiority margins. The document provides technical details on test statistics, including Z-tests and Chi-square tests, and discusses the importance of multiplicity adjustments when multiple comparisons are made. The report serves as a comprehensive guide for researchers conducting superiority tests in clinical trials using cluster-randomized methodologies.