Practicable Power Curve Approximation for Bioequivalence with Unequal Variances

Two-group (bio)equivalence tests assess whether two drug formulations provide similar therapeutic effects. These studies are often conducted using two one-sided t-tests, where the test statistics jointly follow a bivariate t-distribution with singular covariance matrix. Unless the two groups of data are assumed to have equal variances, the degrees of freedom for this bivariate t-distribution are noninteger and unknown a priori. This makes it difficult to analytically find sample sizes that yield desired power for the study using an automated process. Popular free software for bioequivalence study design does not accommodate the comparison of two groups with unequal variances, and certain paid software solutions that make this accommodation produce unstable results. We propose a novel simulation-based method that uses Sobol' sequences and root-finding algorithms to quickly and accurately approximate the power curve for two-group bioequivalence tests with unequal variances. We also illustrate that caution should be exercised when assuming automated methods for power estimation are robust to arbitrary bioequivalence designs. Our methods for sample size determination mitigate this lack of robustness and are widely applicable to equivalence and noninferiority tests facilitated via parallel and crossover designs. All methods proposed in this work can be implemented using the dent package in R.