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Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials.

ABSTRACT: In this paper, we illustrate the method of designing a group-sequential randomized clinical trial based on the difference in restricted mean survival time (RMST). The procedure is based on theoretical formulations of Murray and Tsiatis (1999). We also present a numerical example in designing a cardiology surgical trial. Various practical considerations are discussed. R codes are provided in the Supplementary Materials. We conclude that the group-sequential design for RMST is a viable option in practice. A simulation study is performed to compare the proposed method to the Max-Combo and conventional log-rank tests. The simulation result shows that when there is a delayed treatment benefit and the proportional hazards assumption is untrue, the sequential design based on the RMST can be more efficient than that based on the log-rank test but less efficient than that based on the Max-Combo test. Compared with Max-Combo test, the RMST-based study design yield coherent estimand, statistical inference and result interpretation.

SUBMITTER: Lu Y

PROVIDER: S-EPMC8078843 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials.

Lu Ying Y Tian Lu L

Statistics in biopharmaceutical research 20201009 2

In this paper, we illustrate the method of designing a group-sequential randomized clinical trial based on the difference in restricted mean survival time (RMST). The procedure is based on theoretical formulations of Murray and Tsiatis (1999). We also present a numerical example in designing a cardiology surgical trial. Various practical considerations are discussed. R codes are provided in the Supplementary Materials. We conclude that the group-sequential design for RMST is a viable option in p ...[more]

PMID: 33927801

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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:BackgroundRestricted mean survival time is the expected duration of survival up to a chosen time of restriction τ. For comparison studies, the difference in restricted mean survival times between two groups provides a summary measure of the treatment effect that is free of assumptions regarding the relative shape of the two survival curves, such as proportional hazards. However, it can be difficult to judge the magnitude of the effect from a comparison of restricted means due to the truncation of observation at time τ.MethodsIn this article, we describe additional ways of expressing the treatment effect based on restricted means that can be helpful in this regard. These include the ratio of restricted means, the ratio of life-years (or time) lost, and the average integrated difference between the survival curves, equal to the difference in restricted means divided by τ. These alternative metrics are straightforward to calculate and provide a means for scaling the effect size as an aid to interpretation. Examples from two randomized, multicenter clinical trials in prostate cancer, NRG/RTOG 0521 and NRG/RTOG 0534, with primary endpoints of overall survival and biochemical/radiological progression-free survival, respectively, are presented to illustrate the ideas.ResultsThe four effect measures (restricted mean survival time difference, restricted mean survival time ratio, time lost ratio, and average survival rate difference) were 0.45 years, 1.05, 0.81, and 0.038 for RTOG 0521 and 1.36 years, 1.17, 0.56, and 0.12 for RTOG 0534 with τ = 12 and 11 years, respectively. Thus, for example, the 0.45-year difference in the first trial translates into a 19% reduction in time lost and a 3.8% average absolute difference between the survival curves over the 12-year horizon, a modest effect size, whereas the 1.36-year difference in the second trial corresponds to a 44% reduction in time lost and a 12% absolute survival difference, a rather large effect.ConclusionsIn addition to the difference in restricted mean survival times, these alternative measures can be helpful in determining whether the magnitude of the treatment effect is clinically meaningful.

Project description:ImportanceImmune checkpoint inhibitors (ICIs) have unique patterns of response and survival that differ from conventional chemotherapies. Novel intermediate end points are urgently required to detect the early signals of ICI activity.ObjectiveTo evaluate milestone rate (Kaplan-Meier estimates of survival probabilities at given time points) and milestone restricted mean survival time (RMST, the area under survival curves up to given time points) as potential intermediate end points for ICI trials.Data sourcesElectronic databases (pre-MEDLINE, MEDLINE, Embase, and the Cochrane Central Register of Controlled Trials) were searched for randomized clinical trials published between January 1, 2000, and December 31, 2017.Study selectionPhase 2 and phase 3 randomized clinical trials evaluating ICIs in advanced solid tumors.Data extraction and synthesisTwo investigators extracted the data and reconstructed individual patient data to estimate the milestone rate or milestone RMST from the published Kaplan-Meier curves.Main outcomes and measuresTrial-level milestone rates or milestone RMSTs were estimated for 6-month and 9-month progression-free survival (PFS) and 9-month and 12-month overall survival (OS). A weighted linear regression model evaluated the correlations of ratios of milestone rates or milestone RMSTs with OS hazard ratios (HRs).ResultsTwenty-six trials examining 8 different tumor types were identified, including 12 892 patients. Overall survival HR was correlated with the ratio of 9-month OS milestone rate (R2 = 0.45; 95% CI, 0.27-0.74), and with the ratio of 12-month OS milestone rate (R2 = 0.40; 95% CI, 0.22-0.70). The ratio of 9-month OS milestone RMST (R2 = 0.60; 95% CI, 0.28-0.74) and ratio of 12-month OS milestone RMST were correlated with OS HR (R2 = 0.64; 95% CI, 0.42-0.78). No correlations were observed between OS HR and the ratio of 6-month or 9-month PFS milestone rates or milestone RMSTs.Conclusions and relevanceRatios of OS milestone RMSTs had a stronger correlation with OS HRs than ratios of OS milestone rates, whereas ratios of PFS milestone rates and ratios of PFS milestone RMSTs were not correlated with OS HRs. The OS milestone RMST could be further studied as an intermediate end point in future ICI trials.

Project description: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.

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Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials.

Publications

Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials.

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