An Exact Method for Power Calculation for a Three-arm Clinical Endpoint Bioequivalence Study

Abstract

A clinical endpoint bioequivalence (BE) study aims to establish BE between a generic drug (TEST) and an innovator drug (REF). A placebo (PLB) is usually included to demonstrate the sensitivity of the study. BE is established if TEST is shown to be superior to PLB, REF superior to PLB, and TEST equivalent to REF. Therefore, an overall BE test for a clinical endpoint BE study is composed of two superiority tests (TEST vs. PLB and REF vs. PLB) and one equivalence test (TEST vs. REF).
 Previously, Chang et al (2014) calculated the sample size and power for an overall BE test based on one superiority test (TEST vs. PLB) and an equivalence test (TEST vs. REF) using the joint distribution of sample means and sample variances because ’it is not easy to derive the sample size based on the multivariate t-distribution’ (we call this a ZChiSquare method). In this paper, we propose an exact method to calculate the power and sample size for an overall BE test based on two superiority tests (TEST vs. PLB, REF vs. PLB) and one equivalence test (TEST vs. REF) using a multivariate non-central t distribution directly, which we call an Exact-t method. We also extended the Z-ChiSquare method to an overall BE test with two superiority tests and one equivalence test, rather than one superiority and one equivalence test as in Chang et al’s paper.
 Simulation shows that our proposed Exact-t method is computationally more efficient than the Z-ChiSquare method without self-writing codes to numerically calculate the conditional expectation of a multivariate normal distribution conditional upon a truncated Chi-Square distribution. When sample size is small, the Exact-t method generates more accurate results than the Z-ChiSquare method.
 The Exact-t method is recommended when calculating power and determining sample size for a three-arm clinical endpoint BE study.