Multi-Arm Superiority by a Margin Tests for Treatment Means

This technical report details the computation of power and sample size for multiple superiority by a margin tests in a cluster-randomized design. It addresses the challenges of estimating sample sizes in such designs, where entire clusters are randomized rather than individual subjects. The report discusses the implications of using cluster-randomized designs, including the potential for increased sample size requirements due to loss of efficiency. It outlines the hypotheses for superiority by a margin tests, including scenarios where higher or lower values are considered better. The report also covers power calculations and the importance of multiplicity adjustments, such as the Bonferroni adjustment, when conducting multiple comparisons. Additionally, it provides an example of finding the sample size for a four-arm study, specifying parameters for the analysis. The document serves as a guide for researchers aiming to implement these statistical methods effectively in their studies.