Log-Rank Test vs MaxCombo and Difference in Restricted Mean Survival Time Tests for Comparing Survival Under Nonproportional Hazards in Immuno-oncology Trials
Authors: Mukhopadhyay Pralay , Ye Jiabu , Anderson Keaven M. , Roychoudhury Satrajit , Rubin Eric H. , Halabi Susan , Chappell Richard J. 
Published: July 2022

ImportanceThe log-rank test is considered the criterion standard for comparing 2 survival curves in pivotal registrational trials. However, with novel immunotherapies that often violate the proportional hazards assumptions over time, log-rank can lose power and may fail to detect treatment benefit. The MaxCombo test, a combination of weighted log-rank tests, retains power under different types of nonproportional hazards. The difference in restricted mean survival time (dRMST) test is frequently proposed as an alternative to the log-rank under nonproportional hazard scenarios.ObjectiveTo compare the log-rank with the MaxCombo and dRMST in immuno-oncology trials to evaluate their performance in practice.Data SourcesComprehensive literature review using Google Scholar, PubMed, and other sources for randomized clinical trials published in peer-reviewed journals or presented at major clinical conferences before December 2019 assessing efficacy of anti-programmed cell death protein-1 or anti-programmed death/ligand 1 monoclonal antibodies.Study SelectionPivotal studies with overall survival or progression-free survival as the primary or key secondary end point with a planned statistical comparison in the protocol. Sixty-three studies on anti-programmed cell death protein-1 or anti-programmed death/ligand 1 monoclonal antibodies used as monotherapy or in combination with other agents in 35 902 patients across multiple solid tumor types were identified.Data Extraction and SynthesisStatistical comparisons (n = 150) were made between the 3 tests using the analysis populations as defined in the original protocol of each trial.Main Outcomes and MeasuresNominal significance based on a 2-sided .05-level test was used to evaluate concordance. Case studies featuring different types of nonproportional hazards were used to discuss more robust ways of characterizing treatment benefit instead of sole reliance on hazard ratios.ResultsIn this systematic review and meta-analysis of 63 studies including 35 902 patients, between the log-rank and MaxCombo, 135 of 150 comparisons (90%) were concordant; MaxCombo achieved nominal significance in 15 of 15 discordant cases, while log-rank did not. Several cases appeared to have clinically meaningful benefits that would not have been detected using log-rank. Between the log-rank and dRMST tests, 137 of 150 comparisons (91%) were concordant; log-rank was nominally significant in 5 of 13 cases, while dRMST was significant in 8 of 13. Among all 3 tests, 127 comparisons (85%) were concordant.Conclusions and RelevanceThe findings of this review show that MaxCombo may provide a pragmatic alternative to log-rank when departure from proportional hazards is anticipated. Both tests resulted in the same statistical decision in most comparisons. Discordant studies had modest to meaningful improvements in treatment effect. The dRMST test provided no added sensitivity for detecting treatment differences over log-rank.