Equivalence tests for the difference of two survival functions under the class of Box–Cox transformation model

Establishing equivalence of two treatments has received a lot attention in the pharmaceutical industry. For assessing equivalence of two survival curves, an elegant test is proposed by Wellek (Biometrics 49:877–881, 1993) under the Cox proportional hazards (PH) model. An alternative test based on the proportional odds (PO) model was proposed by Martinez et al. (Stat Methods Med Res 26:75–87, 2017). Recently, Shen (J Biopharm Stat 31:79–90, 2021) proposed a test for equivalence based on a semiparametric log transformation model, which can be used if neither the PH nor the PO assumptions hold. In this article, under the class of Box–Cox transformation models (BCTM), we propose an equivalence test for the difference of two survival functions. Under the class of BCTM, we show that the hypothesis of equivalence of two survival functions can be formulated as a two-sided test which involves only the treatment effect parameter. Simulation results show that the proposed test has satisfactory size and adequate power for finite sample.