Log-Rank Test vs MaxCombo and Difference in Restricted Mean Survival Time Tests for Comparing Survival Under Nonproportional Hazards in Immuno-oncology Trials: A Systematic Review and Meta-analysis

Abstract

Importance: The 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.

Objective: To compare the log-rank with the MaxCombo and dRMST in immuno-oncology trials to evaluate their performance in practice.

Data sources: Comprehensive 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 selection: Pivotal 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 synthesis: Statistical 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 measures: Nominal 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.

Results: In 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 relevance: The 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.

Figure 1.. Overall Survival in First-line Non–Small Cell Lung Cancer in All Randomized Patients Regardless of PD-L1 Expression

Data from the Phase III Open Label First Line Therapy Study of MEDI 4736 (Durvalumab) With or Without Tremelimumab Versus SOC in Non Small-Cell Lung Cancer (NSCLC) (MYSTIC) trial. Hazard ratio (HR) and 95% CI computed from an unstratified Cox model. PD-L1 indicates programmed death/ligand 1; mS, median survival; SoC, standard of care; Trt, treatment.

Figure 2.. Overall Survival in Patients With PD-L1–Positive First-line Non–Small Cell Lung Cancer (≥1% Tumor Cell Positivity)

Data from the Study of Atezolizumab Compared With a Platinum Agent (Cisplatin or Carboplatin) + (Pemetrexed or Gemcitabine) in Participants With Stage IV Non-Squamous or Squamous Non-Small Cell Lung Cancer (Impower 110) study. Hazard ratio (HR) and 95% CI computed from an unstratified Cox model. PD-L1 indicates programmed death/ligand 1; mS, median survival; NA, not applicable; SoC, standard of care group; Trt, treatment group.