Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials.
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ABSTRACT:
SUBMITTER: Lu Y
PROVIDER: S-EPMC8078843 | biostudies-literature |
REPOSITORIES: biostudies-literature
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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.
| S-EPMC5891397 | biostudies-literature
Project description:BackgroundRestricted mean survival time methods compare the areas under the Kaplan-Meier curves up to a time τ for the control and experimental treatments. Extraordinary claims have been made about the benefits (in terms of dramatically smaller required sample sizes) when using restricted mean survival time methods as compared to proportional hazards methods for analyzing noninferiority trials, even when the true survival distributions satisfy proportional hazardss.MethodsThrough some limited simulations and asymptotic power calculations, the authors compare the operating characteristics of restricted mean survival time and proportional hazards methods for analyzing both noninferiority and superiority trials under proportional hazardss to understand what relative power benefits there are when using restricted mean survival time methods for noninferiority testing.ResultsIn the setting of low-event rates, very large targeted noninferiority margins, and limited follow-up past τ, restricted mean survival time methods have more power than proportional hazards methods. For superiority testing, proportional hazards methods have more power. This is not a small-sample phenomenon but requires a low-event rate and a large noninferiority margin.ConclusionAlthough there are special settings where restricted mean survival time methods have a power advantage over proportional hazards methods for testing noninferiority, the larger issue in these settings is defining appropriate noninferiority margins. We find the restricted mean survival time methods lacking in these regards.
| S-EPMC8329935 | biostudies-literature
Project description:Meta-analysis of time-to-event outcomes using the hazard ratio as a treatment effect measure has an underlying assumption that hazards are proportional. The between-arm difference in the restricted mean survival time is a measure that avoids this assumption and allows the treatment effect to vary with time. We describe and evaluate meta-analysis based on the restricted mean survival time for dealing with non-proportional hazards and present a diagnostic method for the overall proportional hazards assumption. The methods are illustrated with the application to two individual participant meta-analyses in cancer. The examples were chosen because they differ in disease severity and the patterns of follow-up, in order to understand the potential impacts on the hazards and the overall effect estimates. We further investigate the estimation methods for restricted mean survival time by a simulation study.
| S-EPMC5695659 | biostudies-literature
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.
| S-EPMC6503508 | biostudies-literature
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.
| S-EPMC6133762 | biostudies-literature
Project description:For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal, stochastic profile of this outcome variable. The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or noninferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.
| S-EPMC5114026 | biostudies-literature
Project description:In clinical or epidemiological follow-up studies, methods based on time scale indicators such as the restricted mean survival time (RMST) have been developed to some extent. Compared with traditional hazard rate indicator system methods, the RMST is easier to interpret and does not require the proportional hazard assumption. To date, regression models based on the RMST are indirect or direct models of the RMST and baseline covariates. However, time-dependent covariates are becoming increasingly common in follow-up studies. Based on the inverse probability of censoring weighting (IPCW) method, we developed a regression model of the RMST and time-dependent covariates. Through Monte Carlo simulation, we verified the estimation performance of the regression parameters of the proposed model. Compared with the time-dependent Cox model and the fixed (baseline) covariate RMST model, the time-dependent RMST model has a better prediction ability. Finally, an example of heart transplantation was used to verify the above conclusions.
| S-EPMC9545070 | biostudies-literature
Project description:IntroductionEstimating treatment effects as time savings in disease progression may be more easily interpretable than assessing the absolute difference or a percentage reduction. In this study, we investigate the statistical considerations of the existing method for estimating time savings and propose alternative complementary methods.MethodsWe propose five alternative methods to estimate the time savings from different perspectives. These methods are applied to simulated clinical trial data that mimic or modify the Clinical Dementia Rating Sum of Boxes progression trajectories observed in the Clarity AD lecanemab trial.ResultsOur study demonstrates that the proposed methods can generate more precise estimates by considering two crucial factors: (1) the absolute difference between treatment arms, and (2) the observed progression rate in the treatment arm.DiscussionQuantifying treatment effects as time savings in disease progression offers distinct advantages. To provide comprehensive estimations, it is important to use various methods.HighlightsWe explore the statistical considerations of the current method for estimating time savings. We proposed alternative methods that provide time savings estimations based on the observed absolute differences. By using various methods, a more comprehensive estimation of time savings can be achieved.
| S-EPMC11350030 | biostudies-literature
Project description:Restricted mean survival time (RMST) is often of great clinical interest in practice. Several existing methods involve explicitly projecting out patient-specific survival curves using parameters estimated through Cox regression. However, it would often be preferable to directly model the restricted mean for convenience and to yield more directly interpretable covariate effects. We propose generalized estimating equation methods to model RMST as a function of baseline covariates. The proposed methods avoid potentially problematic distributional assumptions pertaining to restricted survival time. Unlike existing methods, we allow censoring to depend on both baseline and time-dependent factors. Large sample properties of the proposed estimators are derived and simulation studies are conducted to assess their finite sample performance. We apply the proposed methods to model RMST in the absence of liver transplantation among end-stage liver disease patients. This analysis requires accommodation for dependent censoring since pre-transplant mortality is dependently censored by the receipt of a liver transplant.
| S-EPMC5565738 | biostudies-literature
Project description:In clinical studies with time-to-event outcomes, the restricted mean survival time (RMST) has attracted substantial attention as a summary measurement for its straightforward clinical interpretation. When the data are subject to length-biased sampling, which is frequently encountered in observational cohort studies, existing methods to estimate the RMST are not applicable. In this article, we consider nonparametric and semiparametric regression methods to estimate the RMST under the setting of length-biased sampling. To assess the covariate effects on the RMST, a semiparametric regression model that directly relates the covariates and the RMST is assumed. Based on the model, we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias. Stochastic process theories are used to establish the asymptotic properties of the proposed estimators. We investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in Canada.
| S-EPMC5843504 | biostudies-literature