Exact Properties of Some Heteroscedastic TOST Alternatives for Bioequivalence

The two one-sided tests (TOST) procedure is the common method for assessing bioequivalence between two different drugs or formulations of the same drug. Several solutions to Behrens-Fisher problem have been extended to establish statistical equivalence under variance heterogeneity. Unlike other existing studies that rely exclusively on simulation results, the analytical formulas of power and Type I error rate are derived. Exact numerical investigations were conducted to evaluate the behavior of the Welch–Satterthwaite, Cochran–Cox, and Banerjee–McCullough TOST methods. The results show that the Type I error rates of the Cochran–Cox and Banerjee–McCullough tests never exceed the nominal significance level. The Banerjee–McCullough technique is actually more conservative than the Cochran–Cox procedure. The extended Welch–Satterthwaite approach maintains closest to the preassigned significance level and is almost equal to the target error probability. The exact power levels of the Cochran–Cox and Banerjee–McCullough tests are completely or nearly identical, and are always less than that of the Welch–Satterthwaite method. On the basis of excellent control of Type I error and greater power performance, the extended Welch–Satterthwaite procedure is recommended over the other two heteroscedastic TOST methods. These findings provide an update of previous studies that endorse the somehow inferior Banerjee–McCullough method.