Robustness of the Exact t Method for a Three-arm Clinical Endpoint Bioequivalence Study under Non-normality

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).Chang et al. [1] 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 (we call this a Z-ChiSquare method). Previously, we proposed 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 (we call this an Exact-t method) for a clinical endpoint BE study with two superiority tests and one equivalence test. Yang and Sun showed that the Exact-t method is computationally more efficient and more accurate when sample size is small as compared to the Z-ChiSquare method. These methods, however, were generally verified by simulation under thenormality assumption. In reality, data can deviate from normality (e.g., be skewed). In this paper, we test the robustness of the Exact-t method and the Z-ChiSquare method when data is mildly or severely skewed. It turns out that both methods remain accurate even when data is severely skewed as long as the mean and variance of the data are correctly specified. One thing to note is that when data is more skewed, the required sample size to attain a desired power is larger. Therefore, the Exact-t method is recommended when calculating power and determining sample size for a three-arm clinical endpoint study.