Restricted mean survival time as a summary measure of time‐to‐event outcome

IntroductionSynthesis of clinical effectiveness is a well-established component of health technology assessment (HTA) combining data from multiple trials to obtain an overall pooled estimate of clinical effectiveness, which may inform an associated economic evaluation. Time-to-event outcomes are often synthesized using effect measures from Cox proportional hazards models assuming a constant hazard ratio over time. However, where treatment effects vary over time an assumption of proportional hazards is not always valid. Several methods have been proposed for synthesizing time-to-event outcomes in the presence of non-proportional hazards. However, guidance on choosing between these methods and the implications for HTA is lacking.MethodsWe applied five methods for estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption to a network of melanoma trials, reporting overall survival: restricted mean survival time, an accelerated failure time generalized gamma model, piecewise exponential, fractional polynomial and Royston-Parmar models. We conducted a simulation study to compare these five methods. Simulated individual patient data was generated from a mixture Weibull distribution assuming a treatment-time interaction. Each simulated meta-analysis consisted of five trials with varying numbers of patients and length of follow-up across trials. For each model fitted to each dataset, we calculated the restricted mean survival time at the end of observed follow-up and following extrapolation to a 20-year time horizon.ResultsAll models fitted the melanoma data reasonably well with some variation in the treatment rankings and differences in the survival curves. The simulation study demonstrated the potential for different conclusions from different modelling approaches.ConclusionsThe restricted mean survival time, generalized gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can all accommodate non-proportional hazards and differing lengths of trial follow-up within an evidence synthesis of time-to-event outcomes. Further work is needed in this area to extend the simulation study to the network meta-analysis setting and provide guidance on the key considerations for informing model choice for the purposes of HTA.

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Restricted mean survival time analysis in heart failure clinical trials

European Heart Journal ◽

10.1093/ehjci/ehaa946.1039 ◽

2020 ◽

Vol 41 (Supplement_2) ◽

Author(s):

C Perego ◽

M Sbolli ◽

C Specchia ◽

C Oriecuia ◽

G Peveri ◽

...

Keyword(s):

Heart Failure ◽

Clinical Trials ◽

Survival Time ◽

Treatment Effect ◽

Treatment Effects ◽

Statistical Testing ◽

Secondary Outcome ◽

Time To Event ◽

Mean Survival Time ◽

Restricted Mean Survival Time

Abstract Background The hazard ratio (HR) is the most common measure used to quantify treatment effects in heart failure (HF) clinical trials. However, the HR is only valid when the proportional hazards assumption is plausible, and the HR may be difficult to interpret for clinicians and laypeople. Restricted mean survival time (RMST), defined as the average time-to-event before a specific timepoint, is an intuitive summary of group-wise survival. The difference between two RMSTs measures treatment effects without model assumptions and may communicate more clinically interpretable results. Purpose To evaluate statistical and clinical properties of RMST-based statistics applied to clinical trial data for treatments of HF with reduced ejection fraction. Methods Patient time-to-event data was reconstructed from the published primary and secondary outcome Kaplan-Meier curves from landmark HF clinical trials. We estimated the RMST-differences between treatment groups as a measure of treatment effect with published data, and compared statistical testing results and effect size values to HR analysis results. Results We analyzed 7 HF clinical trials, including data from a total of 27,845 patients (Table 1). RMST should be interpreted as the average number of months that the outcome is avoided over the study period. As examples: On average, treatment with enalapril for 12 months extended each patient's life by 2.2 months compared to placebo, and treatment with spironolactone for 34 months extended each patient's life by 2.2 months compared to placebo. Conclusions RMST-difference test statistic has identical statistical conclusions as HRs but provided an intuitive estimate of each treatment effect. RMST-based data can potentially be used to better communicate treatment effects to patients, to assist in patient-preference discussions and shared decision-making Funding Acknowledgement Type of funding source: None

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Meta-analysis of time-to-event outcomes from randomized trials using restricted mean survival time: application to individual participant data

Statistics in Medicine ◽

10.1002/sim.6556 ◽

2015 ◽

Vol 34 (21) ◽

pp. 2881-2898 ◽

Cited By ~ 20

Author(s):

Yinghui Wei ◽

Patrick Royston ◽

Jayne F. Tierney ◽

Mahesh K. B. Parmar

Keyword(s):

Survival Time ◽

Randomized Trials ◽

Meta Analysis ◽

Individual Participant Data ◽

Time To Event ◽

Mean Survival Time ◽

Restricted Mean Survival Time ◽

Individual Participant

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

Clinical Trials ◽

10.1177/1740774518792259 ◽

2018 ◽

Vol 15 (5) ◽

pp. 499-508 ◽

Cited By ~ 7

Author(s):

Isabelle R Weir ◽

Ludovic Trinquart

Keyword(s):

Sample Size ◽

Survival Time ◽

Trial Design ◽

Time Horizon ◽

Hazard Ratio ◽

Sample Sizes ◽

Time To Event ◽

Mean Survival Time ◽

Restricted Mean Survival Time ◽

The Difference

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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A univariable and multivariable analysis of time-to-event data based on restricted mean survival time: A combination with traditional survival methods.

10.21203/rs.2.18724/v1 ◽

2019 ◽

Author(s):

Qiao Huang ◽

Jun Lyv ◽

Bing-hui Li ◽

Lin-lu Ma ◽

Tong Deng ◽

...

Keyword(s):

Survival Time ◽

Cox Regression ◽

Multivariable Analysis ◽

Hazard Ratio ◽

Event Data ◽

Time To Event ◽

Mean Survival Time ◽

Time To Event Data ◽

Effect Measure ◽

Restricted Mean Survival Time

Abstract Background Hazard ratio is considered as an appropriate effect measure of time-to-event data. However, hazard ratio is only valid when proportional hazards (PH) assumption is met. The use of the restricted mean survival time (RMST) is proposed and recommended without limitation of PH assumption. Method 4405 osteosarcomas were captured from Surveillance, Epidemiology and End Results Program Database. Traditional survival analyses and RMST-based analyses were integrated into a flowchart and applied for univariable and multivariable analyses, using hazard ratio (HR) and difference in RMST (survival time lost or gain, STL or STG) as effect measures. The relationship between difference in RMST and HR were explored when PH assumption was and was not met, respectively. Results In univariable analyses, using difference in RMST calculated by Kaplan-Meier methods as reference, pseudo-value regressions (R2=0.99) and inverse probability of censoring probability (IPCW) regressions with group-specific weights (R2=1.00) provided more consistent estimation on difference in RMST than IPCW with individual weights (R2=0.09). In multivariable analysis, age (HR:1.03, STL: 3.86 months), diagnosis in 1970~1980s (HR:1.39 STL:27.49 months), metastasis (HR:4.47, STL: 202 months), surgery (HR:0.58, SLG:35.55 months) and radiation (HR:1.46, SLT:44.65 months), met PH assumption and were main independent factors for overall survival. In both univariable and multivariable variables, a robust negative logarithmic linear relationship between HRs estimated by Cox regression and differences in RMST by pseudo-value regressions was only observed when PH assumption was hold (Difference in RMST = -109.3✕ln (HR) - 0.83, R² = 0.97, and Difference = -127.7✕ln (HR) – 9.49, R² = 0.93, respectively.) Conclusion The flowchart will be intuitive and helpful to instruct appropriate use of RMST based and traditional methods. RMST-based methods provided an absolute effect measure to inspect effects of covariates on survival time and promote evidence communication with HR. Difference in RMST should be reported with hazard ratio routinely.

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A univariable and multivariable analysis of right censored time-to-event data based on restricted mean survival time: A combination with traditional survival methods.

10.21203/rs.2.18724/v2 ◽

2020 ◽

Author(s):

Qiao Huang ◽

Jun Lyv ◽

Bing-hui Li ◽

Lin-lu Ma ◽

Tong Deng ◽

...

Keyword(s):

Survival Time ◽

Cox Regression ◽

Multivariable Analysis ◽

Hazard Ratio ◽

Event Data ◽

Time To Event ◽

Mean Survival Time ◽

Time To Event Data ◽

Effect Measure ◽

Restricted Mean Survival Time

Abstract Background Hazard ratio is considered as an appropriate effect measure of time-to-event data. However, hazard ratio is only valid when proportional hazards (PH) assumption is met. The use of the restricted mean survival time (RMST) is proposed and recommended without limitation of PH assumption. Method 4405 osteosarcomas were captured from Surveillance, Epidemiology and End Results Program Database. Traditional survival analyses and RMST-based analyses were integrated into a flowchart and applied for univariable and multivariable analyses, using hazard ratio (HR) and difference in RMST (survival time lost or gain, STL or STG) as effect measures. The relationship between difference in RMST and HR were explored when PH assumption was and was not met, respectively. Results In group comparison and univariable regressions, using difference in RMST calculated by Kaplan-Meier methods as reference, pseudo-value regressions (R2=0.99) and inverse probability of censoring probability (IPCW) regressions with group-specific weights (R2=1.00) provided more consistent estimation on difference in RMST than IPCW with individual weights (R2=0.09). In multivariable analysis, age (HR:1.03, STL: 3.86 months), diagnosis in 1970~1980s (HR:1.39 STL:27.49 months), metastasis (HR:4.47, STL: 202 months), surgery (HR:0.58, SLG:35.55 months) and radiation (HR:1.46, SLT:44.65 months) met PH assumption and were main independent factors for overall survival. In both univariable and multivariable variables, a robust negative logarithmic linear relationship between HRs estimated by Cox regression and differences in RMST by pseudo-value regressions was only observed when PH assumption was hold. Conclusion The flowchart will be intuitive and helpful to instruct appropriate use of RMST based and traditional methods. RMST-based methods provided an absolute effect measure to inspect effects of covariates on survival time and promote evidence communication with HR. Difference in RMST should be reported with hazard ratio routinely.

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A univariable and multivariable analysis of right censored time-to-event data based on restricted mean survival time: A combination with traditional survival methods.

10.21203/rs.2.18724/v3 ◽

2020 ◽

Author(s):

Qiao Huang ◽

Jun Lyv ◽

Bing-hui Li ◽

Lin-lu Ma ◽

Tong Deng ◽

...

Keyword(s):

Overall Survival ◽

Survival Time ◽

Multivariable Analysis ◽

Group Comparison ◽

Event Data ◽

Time To Event ◽

Survival Analyses ◽

Mean Survival Time ◽

Time To Event Data ◽

Restricted Mean Survival Time

Abstract Background: Many traditional survival analyses and restricted mean survival time (RMST) based analyses have been proposed for dealing with right censored time-to-event data. It is necessary to sort out the conditions and relationship among these methods for instruction. Comparison between hazard ratio (HR) and RMST in a study may promote appropriate understanding and application of the two effect measures.Method : Traditional survival analyses and RMST-based analyses were integrated into a flowchart and applied for univariable and multivariable analyses, RMST-based analyses included group comparison for difference in RMST, pseudo-value (PV) regressions, inverse probability of censoring probability (IPCW) regressions with group-specific weights and individual weights with homogeneity of censoring mechanism assumption. 4405 osteosarcomas were captured from Surveillance, Epidemiology and End Results Program Database. HR and difference in RMST (survival time lost or gain, STL or STG) were considered as effect measures and the effect of all included covariates on overall survival were reported for comparison. The relationship between difference in RMST and HR were explored when proportional hazard (PH) assumption was and was not met, respectively. Results: In group comparison and univariable regressions, using difference in RMST calculated by Kaplan-Meier methods as reference, PV regressions (R2=0.99) and IPCW regressions with group-specific weights (R2=1.00) provided more consistent estimation on difference in RMST than IPCW with individual weights (R2=0.09). In multivariable analysis, age (HR:1.03, STL: 3.86 months), diagnosis in 1970~1980s (HR:1.39 STL:27.49 months), metastasis (HR:4.47, STL: 202 months), surgery (HR:0.58, SLG:35.55 months) and radiation (HR:1.46, SLT:44.65 months) met PH assumption and were main independent factors for overall survival. In both univariable and multivariable variables, a robust negative logarithmic linear relationship between HRs estimated by Cox regression and differences in RMST by pseudo-value regressions was only observed when PH assumption was hold. Conclusion: The flowchart may be intuitive and helpful to instruct appropriate use of RMST based and traditional methods. PH assumption and homogeneity of censoring mechanism assumption will determine the appropriate selection of these method. HR and difference in RMST can be reported comprehensively.

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