Energy Distance and Kernel Mean Embeddings for Two-sample Survival Testing with Application in Immunotherapy Clinical Trial

Accepted - June 2024

Abstract

We study the comparison problem of distribution equality between two random samples under a random censoring scheme. We design a series of tests based on energy distance and kernel mean embeddings to address this problem. We calibrate our tests using permutation methods and prove that they are consistent against all fixed continuous alternatives. To evaluate our proposed tests in real-world clinical scenarios, we simulate survival curves from immunotherapy clinical trials published in the most important medical journals. Additionally, we provide practitioners with recommendations on selecting parameters/distances for the crossing survival curves problem that appear in the real data analyzed. Based on the method for parameter tunning that we propose, we show that our tests demonstrate a considerable gain of statistical power against classical survival tests. In addition, as our test depends on the semi-metric or kernel selected can be adapted to another clinical settings or survival analysis problems.