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.