Optimum allocation of treatments for Welch's test in equivalence assessment

Abstract

As an extension of Welch's test to equivalence trials in a matched pair design, we determine the sample sizes n(1) and n(2) that maximize the power at given alternatives for a given total sample size n = n(1) + n(2). Although the optimal allocation is obtained asymptotically when the ratio of the standard deviations in both treatment groups equals the ratio of the sample sizes, numerical investigations show that this result does not hold for sample sizes where n less than or equal to 25. For convenience, we provide tables containing the optimal combinations for the bioequivalence problem as well as for the problem of testing a clinically relevant difference. Results indicate that for small sample sizes, the optimum allocations of the treatments differ significantly in both testing problems, although they are asymptotically identical. In addition, we provide simple approximate equations that can be used for the determination of the required sample sizes to control a preassigned probability of type II error.