Equivalence Tests Before the End of Follow-up Under Box–Cox Transformation Model

For the equivalence trial with survivor outcomes from two treatment groups, the most popular testing procedure is the extension of log-rank test proposed by Wellek (Biometrics 49:877–881, 1993) under the proportional hazards (PH) model. This test is based on extrapolation of two survival curves to the whole time axis. In practice, the information on event progression is available only up to the end of follow-up (denoted by \(\tau \) $\tau$ ). In this article, under the class of Box–Cox transformation models, which includes the PH and proportional odds models as special cases, we propose an equivalence test for the difference of two survival functions before the end of follow-up. We show that the hypothesis of equivalence of two survival functions can be formulated as the interval-based hypothesis test, which involves the treatment effect parameter. Simulation studies demonstrate that the proposed test performs well in finite samples. The proposed test is applied to a veteran’s administration lung cancer data set.