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

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 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/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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Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome

BMC Medical Research Methodology ◽

10.1186/1471-2288-13-152 ◽

2013 ◽

Vol 13 (1) ◽

Cited By ~ 216

Author(s):

Patrick Royston ◽

Mahesh KB Parmar

Keyword(s):

Survival Time ◽

Randomized Trials ◽

Hazard Ratio ◽

Time To Event ◽

Mean Survival Time ◽

Restricted Mean Survival Time

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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 Novel Method to Calculate Mean Survival Time for Time-to-Event Data

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2011.598996 ◽

2012 ◽

Vol 41 (5) ◽

pp. 611-620 ◽

Cited By ~ 2

Author(s):

Zheng Su ◽

Liang Fang

Keyword(s):

Survival Time ◽

Event Data ◽

Time To Event ◽

Mean Survival Time ◽

Time To Event Data ◽

Novel Method

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Comparison of the restricted mean survival time with the hazard ratio in superiority trials with a time-to-event end point

Pharmaceutical Statistics ◽

10.1002/pst.1846 ◽

2017 ◽

Vol 17 (3) ◽

pp. 202-213 ◽

Cited By ~ 24

Author(s):

Bo Huang ◽

Pei-Fen Kuan

Keyword(s):

Survival Time ◽

Hazard Ratio ◽

Time To Event ◽

Mean Survival Time ◽

End Point ◽

Restricted Mean Survival Time ◽

Superiority Trials

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

Pharmaceutical Statistics ◽

10.1002/pst.2004 ◽

2020 ◽

Vol 19 (4) ◽

pp. 436-453 ◽

Cited By ~ 4

Author(s):

Takahiro Hasegawa ◽

Saori Misawa ◽

Shintaro Nakagawa ◽

Shinichi Tanaka ◽

Takanori Tanase ◽

...

Keyword(s):

Survival Time ◽

Time To Event ◽

Summary Measure ◽

Mean Survival Time ◽

Restricted Mean Survival Time

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Restricted Mean Survival Time: An Obligatory End Point for Time-to-Event Analysis in Cancer Trials?

Journal of Clinical Oncology ◽

10.1200/jco.2016.67.8045 ◽

2016 ◽

Vol 34 (28) ◽

pp. 3474-3476 ◽

Cited By ~ 58

Author(s):

Roger P. A’Hern

Keyword(s):

Survival Time ◽

Event Analysis ◽

Time To Event ◽

Mean Survival Time ◽

End Point ◽

Restricted Mean Survival Time ◽

Cancer Trials

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Assessing Clinical Equivalence in Oncology Biosimilar Trials With Time-to-Event Outcomes

JNCI Cancer Spectrum ◽

10.1093/jncics/pkz058 ◽

2019 ◽

Vol 3 (4) ◽

Cited By ~ 2

Author(s):

Hajime Uno ◽

Deborah Schrag ◽

Dae Hyun Kim ◽

Dejun Tang ◽

Lu Tian ◽

...

Keyword(s):

Overall Survival ◽

Survival Time ◽

Primary Endpoint ◽

Reference Product ◽

Survival Curve ◽

Treatment Decision ◽

Hazard Ratio ◽

Treatment Decision Making ◽

Mean Survival Time ◽

Restricted Mean Survival Time

Abstract A typical biosimilar study in oncology uses the overall response evaluated at a specific time point as the primary endpoint, which is generally acceptable regulatorily, to assess clinical equivalence between a biosimilar and its reference product. The standard primary endpoint for evaluating an anticancer therapy, progression-free or overall survival would be a secondary endpoint in a biosimilar trial. With a conventional analytic procedure via, for example, hazard ratio to quantify the group difference, it is difficult and challenging to assess clinical equivalence with respect to progression-free or overall survival because the study generally has a limited number of clinical events observed in the study. In this article, we show that an alternative procedure based on the restricted mean survival time, which has been discussed extensively for design and analysis of a general equivalence study, is readily applicable to a biosimilar trial. Unlike the hazard ratio, this procedure provides a clinically interpretable estimate for assessing equivalence. Using the restricted mean survival time as a summary measure of the survival curve will enhance better treatment decision making in adopting a biosimilar product over the reference product.

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