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Design of non-inferiority randomized trials using the difference in restricted mean survival times.

ABSTRACT: Background/aims Non-inferiority trials with time-to-event outcomes are becoming increasingly common. Designing non-inferiority trials is challenging, in particular, they require very large sample sizes. We hypothesized that the difference in restricted mean survival time, an alternative to the hazard ratio, could lead to smaller required sample sizes. Methods We show how to convert a margin for the hazard ratio into a margin for the difference in restricted mean survival time and how to calculate the required sample size under a Weibull survival distribution. We systematically selected non-inferiority trials published between 2013 and 2016 in seven major journals. Based on the protocol and article of each trial, we determined the clinically relevant time horizon of interest. We reconstructed individual patient data for the primary outcome and fit a Weibull distribution to the comparator arm. We converted the margin for the hazard ratio into the margin for the difference in restricted mean survival time. We tested for non-inferiority using the difference in restricted mean survival time and hazard ratio. We determined the required sample size based on both measures, using the type I error risk and power from the original trial design. Results We included 35 trials. We found evidence of non-proportional hazards in five (14%) trials. The hazard ratio and the difference in restricted mean survival time were consistent regarding non-inferiority testing, except in one trial where the difference in restricted mean survival time led to evidence of non-inferiority while the hazard ratio did not. The median hazard ratio margin was 1.43 (Q1-Q3, 1.29-1.75). The median of the corresponding margins for the difference in restricted mean survival time was -21?days (Q1-Q3, -36 to -8) for a median time horizon of 2.0?years (Q1-Q3, 1-3?years). The required sample size according to the difference in restricted mean survival time was smaller in 71% of trials, with a median relative decrease of 8.5% (Q1-Q3, 0.4%-38.0%). Across all 35 trials, about 25,000 participants would have been spared from enrollment using the difference in restricted mean survival time compared to hazard ratio for trial design. Conclusion The margins for the hazard ratio may seem large but translate to relatively small differences in restricted mean survival time. The difference in restricted mean survival time offers meaningful interpretation and can result in considerable reductions in sample size. Restricted mean survival time-based measures should be considered more widely in the design and analysis of non-inferiority trials with time-to-event outcomes.

SUBMITTER: Weir IR

PROVIDER: S-EPMC6133762 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature

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Design of non-inferiority randomized trials using the difference in restricted mean survival times.

Weir Isabelle R IR Trinquart Ludovic L

Clinical trials (London, England) 20180803 5

Background/aims Non-inferiority trials with time-to-event outcomes are becoming increasingly common. Designing non-inferiority trials is challenging, in particular, they require very large sample sizes. We hypothesized that the difference in restricted mean survival time, an alternative to the hazard ratio, could lead to smaller required sample sizes. Methods We show how to convert a margin for the hazard ratio into a margin for the difference in restricted mean survival time and how to calculat ...[more]

PMID: 30074407

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Project description:BackgroundRestricted mean survival time is a measure of average survival time up to a specified time point. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves.MethodsThis article addresses the question of whether covariate adjustment in randomized clinical trials that compare restricted mean survival times improves precision of the estimated treatment effect (difference in restricted mean survival times between treatment arms). Although precision generally increases in linear models when prognostic covariates are added, this is not necessarily the case in non-linear models. For example, in logistic and Cox regression, the standard error of the estimated treatment effect does not decrease when prognostic covariates are added, although the situation is complicated in those settings because the estimand changes as well. Because estimation of restricted mean survival time in the manner described in this article is also based on a model that is non-linear in the covariates, we investigate whether the comparison of restricted mean survival times with adjustment for covariates leads to a reduction in the standard error of the estimated treatment effect relative to the unadjusted estimator or whether covariate adjustment provides no improvement in precision. Chen and Tsiatis suggest that precision will increase if covariates are chosen judiciously. We present results of simulation studies that compare unadjusted versus adjusted comparisons of restricted mean survival time between treatment arms in randomized clinical trials.ResultsWe find that for comparison of restricted means in a randomized clinical trial, adjusting for covariates that are associated with survival increases precision and therefore statistical power, relative to the unadjusted estimator. Omitting important covariates results in less precision but estimates remain unbiased.ConclusionWhen comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.

Project description: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.

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Design of non-inferiority randomized trials using the difference in restricted mean survival times.

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Design of non-inferiority randomized trials using the difference in restricted mean survival times.

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