An extension of Welch's approximate t-solution to comparative bioequivalence trials

SUMMARY We consider the problem of proving statistically the equivalence of two treatments with normally distributed observations. The size and the power of the commonly-used test procedures which assume equality of the variances are investigated when this assumption is violated. On the one hand the preassigned level is considerably exceeded, and on the other hand the power if no treatment difference exists drops heavily for differing sample sizes. We propose an extension of Welch's approximate t-solution for the Behrens-Fisher problem in bioequivalence assessment, which is asymptotically optimal in a certain subclass of tests. The behaviour of the proposed test is investigated in various finite sample situations. The results show that the extension of Welch's approximate t-solution should be preferred for testing bioequivalence of two treatments whenever the population variances cannot be assumed equal and the sample sizes are different. Sometimes the experimenter knows which sample has the larger variance. In this case, the larger sample size should always be assigned to that group with the larger variance in order to optimize the actual level and power of the test.