Multi-Arm Equivalence Tests for Survival Curves

This technical report details a procedure for calculating power and sample size for testing the equivalence of multiple treatment hazard rates against a common control hazard rate using Cox’s proportional hazards regression in a cluster-randomized design. It explains that survival times are not normally distributed and may be censored, making Cox proportional-hazards regression a suitable method for analysis. The report outlines the equivalence hypothesis, which establishes that the ratio of two hazard rates must fall within a clinically insignificant margin from one. It also discusses the Bonferroni adjustment for type I error rates when multiple comparisons are tested. The report provides technical details on the Cox regression model, the test statistic, and the design effect in cluster-randomized trials. Additionally, it includes an example demonstrating how to find the sample size needed for an equivalence trial, highlighting the importance of adjusting for the control group size and the number of clusters used in the design.