A permutation test based on the restricted mean survival time for comparison of net survival distributions in non-proportional excess hazard settings

2019 ◽  
Vol 29 (6) ◽  
pp. 1612-1623
Author(s):  
Anna Wolski ◽  
Nathalie Grafféo ◽  
Roch Giorgi ◽  
Keyword(s):  
Survival Time ◽  
Proportional Hazards ◽  
Permutation Test ◽  
Survival Times ◽  
Test Statistic ◽  
Specific Test ◽  
Net Survival ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time ◽  
Type Test

Net survival is used in epidemiological studies to assess excess mortality due to a given disease when causes of death are unreliable. By correcting for the general population mortality, it allows comparisons between regions or periods and thus evaluation of health policies. The Pohar-Perme non-parametric estimator of net survival has been recently proposed, soon followed by an appropriate log-rank-type test. However, log-rank tests are known to be under-optimal in non-proportional settings (e.g. crossing of the hazard functions). In classical survival analysis, one solution is to compare the restricted mean survival times. A difference in restricted mean survival time represents a life benefit or loss over the studied period. In the present article the restricted mean net survival time was used to derive a specific test statistic to compare net survivals in proportional and non-proportional hazards settings. The new test was generalized to more than two groups and to stratified analysis. The test performance was assessed on simulation study, compared to the log-rank-type test, and its use illustrated on a population-based colorectal cancer registry. The new test for net survival comparisons proved robust to non-proportionality and well-performing in proportional hazards situations. Furthermore, it is also suited to the classical survival framework.

scholarly journals A Brief Overview of Restricted Mean Survival Time Estimators and Associated Variances

Stats ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 107-119 ◽  
Author(s):  
Szilárd Nemes ◽  
Erik Bülow ◽  
Andreas Gustavsson
Keyword(s):  
Survival Time ◽  
Survival Data ◽  
Proportional Hazards ◽  
Survival Times ◽  
Mean Survival Time ◽  
Model Free ◽  
Kaplan Meier ◽  
Restricted Mean Survival Time ◽  
Parametric Survival ◽  
Method Analysis

Restricted Mean Survival Time ( R M S T ) experiences a renaissance and is advocated as a model-free, easy to interpret alternative to proportional hazards regression and hazard rates with implication in causal inference. Estimation of R M S T and associated variance is mainly done by numerical integration of Kaplan–Meier curves. In this paper we briefly review the two main alternatives to the Kaplan–Meier method; analysis based on pseudo-observations, and the flexible parametric survival method. Using computer simulations, we assess the efficacy of the three methods compared to a fully parametric approach where the distribution of survival times is known. Thereafter, the three methods are directly compared without any distributional assumption for the survival data. Generally, flexible parametric survival methods outperform both competitors, however the differences are small.

OP236 Evidence Synthesis Of Time-To-Event Outcomes In The Presence Of Non-Proportional Hazards

2021 ◽  
Vol 37 (S1) ◽  
pp. 8-8
Author(s):  
Suzanne Freeman ◽  
Nicola Cooper ◽  
Alex Sutton ◽  
Michael Crowther ◽  
James Carpenter ◽  
...  
Keyword(s):  
Survival Time ◽  
Simulation Study ◽  
Proportional Hazards ◽  
Evidence Synthesis ◽  
Meta Analysis ◽  
Clinical Effectiveness ◽  
Time To Event ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

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.

scholarly journals Are restricted mean survival time methods especially useful for noninferiority trials?

2021 ◽  
pp. 174077452097657
Author(s):  
Boris Freidlin ◽  
Chen Hu ◽  
Edward L Korn
Keyword(s):  
Survival Time ◽  
Proportional Hazards ◽  
Small Sample ◽  
Operating Characteristics ◽  
Mean Survival Time ◽  
Kaplan Meier ◽  
Noninferiority Trials ◽  
Restricted Mean Survival Time ◽  
Experimental Treatments ◽  
Event Rates

Background: Restricted mean survival time methods compare the areas under the Kaplan–Meier curves up to a time [Formula: see text] 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. Methods: Through 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. Results: In the setting of low-event rates, very large targeted noninferiority margins, and limited follow-up past [Formula: see text], 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. Conclusion: Although 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.

scholarly journals Restricted mean survival time: Does covariate adjustment improve precision in randomized clinical trials?

2018 ◽  
Vol 15 (2) ◽  
pp. 178-188 ◽  
Author(s):  
Theodore Karrison ◽  
Masha Kocherginsky
Keyword(s):  
Clinical Trial ◽  
Clinical Trials ◽  
Survival Time ◽  
Treatment Effect ◽  
Randomized Clinical Trials ◽  
Linear Models ◽  
Covariate Adjustment ◽  
Survival Times ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

Background: Restricted 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. Methods: This 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. Results: We 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. Conclusion: When comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.

scholarly journals Time-dependent treatment effects of metronomic chemotherapy in unfit AML patients: a secondary analysis of a randomised controlled trial

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Phichayut Phinyo ◽  
Jayanton Patumanond ◽  
Saranya Pongudom
Keyword(s):  
Survival Time ◽  
Palliative Treatment ◽  
Proportional Hazards ◽  
Controlled Trial ◽  
Tertiary Care ◽  
Secondary Analysis ◽  
Metronomic Chemotherapy ◽  
Time Dependent ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

Abstract Objectives To examine the presence of the time-dependent effect of metronomic chemotherapy for the treatment of older patients with acute myeloid leukemia (AML) who were unfit for standard chemotherapy and to reanalyze the data using an appropriate statistical approach in the presence of non-proportional hazards, the restricted mean survival time (RMST). Results This was a secondary analysis of a multi-center, open-label, randomized controlled trial, which was conducted in seven tertiary care hospitals across Thailand. A total of 81 unfit AML patients were randomized into two treatment groups, metronomic chemotherapy and palliative treatment. The hazard ratio of metronomic chemotherapy over palliative treatment was time-dependent. At three landmark time points of 90, 180, 365 days, the restricted mean survival time differences were 13.3 (95% CI 1.9–24.7) days, 28.9 (95% CI 3.3–54.4) days, and 40.4 (95% CI − 1.3 to 82.0) days, respectively. With non-proportional hazards modeling and RMST analysis, we were able to conclude that metronomic chemotherapy is a potentially effective alternative treatment for elderly AML patients who were medically unfit for intensive chemotherapy. In the future clinical trials, non-proportional hazards should be carefully inspected and properly handled with appropriate statistical methods. Trial registration Randomized clinical trial TCTR20150918001; registration date: 15/09/2015. Retrospectively registered

Estimation on conditional restricted mean survival time with counting process

2020 ◽  
pp. 1-15
Author(s):  
Junshan Qiu ◽  
Dali Zhou ◽  
H.M. Jim Hung ◽  
John Lawrence ◽  
Steven Bai
Keyword(s):  
Survival Time ◽  
Counting Process ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

A Model-Independent Method to Determine Restricted Mean Survival Time in the Analysis of Survival Curves

2019 ◽  
Vol 2 (1) ◽  
pp. 66-68 ◽  
Author(s):  
Andrea Messori ◽  
Vera Damuzzo ◽  
Laura Agnoletto ◽  
Luca Leonardi ◽  
Marco Chiumente ◽  
...  
Keyword(s):  
Survival Time ◽  
Independent Method ◽  
Survival Curves ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time ◽  
Model Independent

scholarly journals Extrapolating Parametric Survival Models in Health Technology Assessment Using Model Averaging: A Simulation Study

2021 ◽  
Vol 41 (4) ◽  
pp. 476-484
Author(s):  
Daniel Gallacher ◽  
Peter Kimani ◽  
Nigel Stallard
Keyword(s):  
Survival Time ◽  
Survival Data ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Information Criterion ◽  
Health Technology ◽  
Weighted Averaging ◽  
Health Technologies ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

Previous work examined the suitability of relying on routine methods of model selection when extrapolating survival data in a health technology appraisal setting. Here we explore solutions to improve reliability of restricted mean survival time (RMST) estimates from trial data by assessing model plausibility and implementing model averaging. We compare our previous methods of selecting a model for extrapolation using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Our methods of model averaging include using equal weighting across models falling within established threshold ranges for AIC and BIC and using BIC-based weighted averages. We apply our plausibility assessment and implement model averaging to the output of our previous simulations, where 10,000 runs of 12 trial-based scenarios were examined. We demonstrate that removing implausible models from consideration reduces the mean squared error associated with the restricted mean survival time (RMST) estimate from each selection method and increases the percentage of RMST estimates that were within 10% of the RMST from the parameters of the sampling distribution. The methods of averaging were superior to selecting a single optimal extrapolation, aside from some of the exponential scenarios where BIC already selected the exponential model. The averaging methods with wide criterion-based thresholds outperformed BIC-weighted averaging in the majority of scenarios. We conclude that model averaging approaches should feature more widely in the appraisal of health technologies where extrapolation is influential and considerable uncertainty is present. Where data demonstrate complicated underlying hazard rates, funders should account for the additional uncertainty associated with these extrapolations in their decision making. Extended follow-up from trials should be encouraged and used to review prices of therapies to ensure a fair price is paid.

Sign in / Sign up

Export Citation Format

Share Document