Tests for equivalence of two survival functions: alternatives to the PH and PO models

For the equivalence trial with survivor outcomes from two treatment groups, the most popular testing procedure is the extension of log-rank test under proportional hazards (PH) model. In literature, an alternative test has been proposed under the  proportional odds (PO) survival model. In practice, both PH and PO hazards assumptions can be violated. One alternative is the log transformation model other than the PH or PO models. Another alternative model is the partly Aalen's additive risk model which allows the influence of some covariates to vary over time. In this article, we propose equivalence tests for the difference of two survival functions under the class of log transformation model and that of two cumulative hazard functions under the partly Aalen's model. Simulation studies demonstrate that the proposed tests perform well in finite samples.