Testing equivalence of survival before but not after end of follow-up

Equivalence tests before end of follow-up under the class of log transformation model

One important topic in clinical trials is to show that the effects of new and standard treatments are equivalent in terms of clinical relevance. In literature, many equivalence tests based on the maximal difference between two survival functions for the two treatments over the whole time axis have been proposed. However, since survival times can only be observed until the end of follow-up, an equivalence test should be based on a comparison only in the observed time-window dictated by the end of follow-up. In this article, under the class of log transformation model, we propose an asymptotical α-level equivalence test for the difference between two survival functions that only addresses equivalence until the end of follow-up. We demonstrate that the hypothesis of equivalence of two survival functions before the end of follow-up can be formulated as interval-based hypothesis testing which involves the treatment effect parameter. Simulation results indicate that when sample size is sufficiently large the proposed test controls the type I error effectively and performs well at detecting the equivalence. The proposed test is applied to a dataset from veteran's administration lung cancer trial.

Equivalence tests under the Cox-Aalen model and the partly Aalen model

For the equivalence trial with survivor outcomes from two treatment groups, the most popular testing procedure is the test proposed by under the proportional hazards (PH) model. In this article, when the treatment effect is time invariant, we demonstrate that the result under the PH model can be extended to the Cox-Aalen model. When the treatment effect is time-variant, we propose an equivalent test for the differences of two cumulative hazard functions under the partly Aalen model. Simulation studies show that the proposed tests perform well in finite samples. We illustrate the proposed tests using bladder cancer data and the primary biliary cirrhosis (PBC) data.