A Geometric Mean Approach to Sampling Size Determination for the Equivalence Hypothesis

Equivalence hypothesis is the correct hypothesis to confirm whether the newly developed product conforms to the current standard product. It has great applications to evaluation of generic drug products and other new clinical modalities. Two one-sided tests (TOST) procedure was proposed to test the equivalence hypothesis for two treatments. When the difference in population means between two treatments is not 0, the power function is not symmetric, hence only approximate formulas are proposed to determine the sample size for the equivalence hypothesis. The resulting sample sizes may provide either insufficient power or unnecessarily high power. We suggest geometric mean approaches to determination of the sample size for equivalence hypothesis. A numerical study was conducted to compare the performance of our proposed method with other current methods. Numerical examples illustrate the applications to bioequivalence on the logarithmic scale and to clinical equivalence on the original scale. Remarks on the usage of different methods for sample size determination for equivalence hypothesis are made.