OPTIMUM ALLOCATION OF TREATMENTS FOR WELCHS TEST IN EQUIVALENCE ASSESSMENT

As an extension of Welch's test to equivalence trials in a matched pai r design, we determine the sample sizes n(1) and n(2) that maximize th e 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 2 5. For convenience, we provide tables containing the optimal combinati ons for the bioequivalence problem as well as for the problem of testi ng a clinically relevant difference. Results indicate that for small s ample sizes, the optimum allocations of the treatments differ signific antly in both testing problems, although they are asymptotically ident ical. 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.