A Max 0-1 Weighted Log-Rank Test for Time-to-Event Data With Random Delayed Treatment Effect

In a cancer clinical trial with an immunotherapy, the treatment often becomes effective after a certain delay time. It is well known that traditional log-rank test no longer provides optimal power in this case. There has been a great interest to search for a more powerful test to detect a truly effective immunotherapy treatment. In this paper, we propose a new testing method based on the maximum value of a set of 0-1 weighted log-rank test statistics and establish useful theoretical results of the relevant test statistics. Extensive simulation studies are conducted to examine the empirical performance of the proposed method. An analysis of the real data from a non-small-cell lung cancer clinical trial is also carried out to further demonstrate the usefulness of the proposed test method. Trial Registration: ClinicalTrials.gov ID: NCT01903993, NCT02008227.