Power and sample size computations in simultaneous tests for non-inferiority based on relative margins

Abstract

In this paper, we address the problem of calculating power and sample sizes associated with simultaneous tests for non-inferiority. We consider the case of comparing several experimental treatments with an active control. The approach is based on the ratio view, where the common non-inferiority margin is chosen to be some percentage of the mean of the control treatment. Two power definitions in multiple hypothesis testing, namely, complete power and minimal power, are used in the computations. The sample sizes associated with the ratio-based inference are also compared with that of a comparable inference based on the difference of means for various scenarios. It is found that the sample size required for ratio-based inferences is smaller than that of difference-based inferences when the relative non-inferiority margin is less than one and when large response values indicate better treatment effects. The results are illustrated with examples.

An introductory note to the CHMP guidelines: choice of the non‐inferiority margin and data monitoring committees by David Brown, Peter Volkers and Simon Day, Statistics in Medicine 2006; 25:1623–1627

“…This means that the sample size for the noninferiority testing based on the ratio E = R is smaller than based on the comparable di erence E − R , because  R ¡1. Similar results were found for multiple ratios when comparing several experimental treatments with a reference where the advantage of the ratio-based approach over the di erence-based approach increases with increasing number of comparisons [10].…”

How to deal with multiple treatment or dose groups in randomized clinical trials?

“…For the most relevant comparisons of several treatment groups against placebo, closed expressions for the power are available for hypotheses stated in terms of differences [72] of means ratios [73] and proportions [74]. For the most relevant comparisons of several treatment groups against placebo, closed expressions for the power are available for hypotheses stated in terms of differences [72] of means ratios [73] and proportions [74].…”

“…In the design phase of multi-armed trials it is important to calculate the necessary sample size on the basis of an appropriate power definition for multiple test problems. For the most relevant comparisons of several treatment groups against placebo, closed expressions for the power are available for hypotheses stated in terms of differences [72] of means ratios [73] and proportions [74].…”

A ratio‐to‐control Williams‐type test for trend

“…Moreover, Dilba et al . 12 and Laster and Johnson 13 note the power advantage of certain ratio‐based tests for non‐inferiority (or superiority).…”