On the Assessment of Average Biosimilarity Based on a Three-Arm Parallel Design

Abstract

Average biosimilarity is investigated under a three-arm parallel design: one arm corresponds to the test drug T , and the other two arms correspond to two versions of the reference drug, say R1 and R2. The hypothesis of interest is the equivalence of the population average response for T with the mean of the population average responses for R_1 and R_2. The parameter of interest is formulated as the absolute difference of the above two averages, scaled by the absolute difference between the population means corresponding to R_1 and R_2. A difference parameter is also proposed. For the ratio parameter, a test can be derived using the asymptotic normality of an appropriate test statistic; however, the test is not satisfactory in terms of type I error probabilities. Improved tests are derived by applying a bootstrap calibration, and by using the idea of a generalized pivotal quantity (gpq). The tests are developed under equal variance and unequal variance scenarios. Sample size determination is also addressed. For the difference parameter, a satisfactory test is developed using the gpq idea. The proposed methods result in tests that are satisfactory in terms of type I error performance.

Keywords

• Bootstrap calibration; equivalence testing; generalized pivotal quantity; sample size determination