Predicting the restricted mean event time with the subject's baseline covariates in survival analysis.
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ABSTRACT:
SUBMITTER: Tian L
PROVIDER: S-EPMC3944973 | biostudies-literature |
REPOSITORIES: biostudies-literature
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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.
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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.
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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.
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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.
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Project description:ObjectivesTo use restricted mean survival time, which summarizes treatment effects in terms of event-free time over a fixed time period, to evaluate the benefit of pravastatin therapy for primary prevention of cardiovascular disease in older adults.DesignSecondary analysis of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial-Lipid-Lowering Trial (ALLHAT-LLT).SettingAmbulatory setting.ParticipantsIndividuals aged 65 and older (mean aged 71, 49% female) free of cardiovascular disease (N=2,867).InterventionPravastatin 40 mg/d (n=1,467) versus usual care (n=1,400).MeasurementsWe estimated the difference in RMST for total and coronary heart disease (CHD)-free survival between the pravastatin and usual care groups over the 6-year trial period and used parametric survival models to estimate RMST differences projected over 10 years.ResultsOver 6 years, individuals treated with pravastatin lived (RMST 2,008.1 days), on average, 33.7 fewer days than those receiving usual care (RMST 2,041.8 days) (difference -33.7 days, 95% confidence interval (CI)=-67.0 to -0.5 days, p=.047). Pravastatin-treated individuals lived RMST 2,088.1 days), on average, 18.7 more days free of CHD over 6 years than those receiving usual care (RMST 2,069.4 days), but this difference was not statistically significant (difference 18.7 days, 95% CI=-10.4-47.8 days, p=.21). The 10-year projection showed that pravastatin-treated individuals would live 108.1 fewer days (95% CI=-204.5 to -14.1, p=.03) than those receiving usual care, although treated individuals would gain 77.9 days (95% CI=3.8-159.6, p=.046) of CHD-free survival.ConclusionRMST provides an intuitive and explicit way to express the effect of pravastatin therapy on CHD-free and overall survival in older adults free of cardiovascular disease. This measure allows a more personalized interpretation than hazard ratios of the benefits and risks of a medical intervention for decision-making.
| S-EPMC6181782 | 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:Estimation and prediction of heterogeneous restricted mean survival time (hRMST) is of great clinical importance, which can provide an easily interpretable and clinically meaningful summary of the survival function in the presence of censoring and individual covariates. The existing methods for the modeling of hRMST rely on proportional hazards or other parametric assumptions on the survival distribution. In this paper, we propose a random forest based estimation of hRMST for right-censored survival data with covariates and prove a central limit theorem for the resulting estimator. In addition, we present a computationally efficient construction for the confidence interval of hRMST. Our simulations show that the resulting confidence intervals have the correct coverage probability of the hRMST, and the random forest based estimate of hRMST has smaller prediction errors than the parametric models when the models are mis-specified. We apply the method to the ovarian cancer data set from The Cancer Genome Atlas (TCGA) project to predict hRMST and show an improved prediction performance over the existing methods. A software implementation, srf using R and C++, is available at https://github.com/lmy1019/SRF.
| S-EPMC7873855 | biostudies-literature
Project description:Although recurrent event data analysis is a rapidly evolving area of research, rigorous studies on estimation of the effects of intermittently observed time-varying covariates on the risk of recurrent events have been lacking. Existing methods for analyzing recurrent event data usually require that the covariate processes are observed throughout the entire follow-up period. However, covariates are often observed periodically rather than continuously. We propose a novel semiparametric estimator for the regression parameters in the popular proportional rate model. The proposed estimator is based on an estimated score function where we kernel smooth the mean covariate process. We show that the proposed semiparametric estimator is asymptotically unbiased, normally distributed, and derives the asymptotic variance. Simulation studies are conducted to compare the performance of the proposed estimator and the simple methods carrying forward the last covariates. The different methods are applied to an observational study designed to assess the effect of group A streptococcus on pharyngitis among school children in India. Copyright © 2016 John Wiley & Sons, Ltd.
| S-EPMC4935555 | biostudies-other
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:Background/objectivesRestricted mean survival time (RMST) summarizes treatment effect in terms of a gain or loss in the event-free days. It remains uncertain whether communicating treatment benefit and harm using RMST-based summary is more effective than conventional summary based on absolute and relative risk reduction. We compared the effect of RMST-based approach and conventional approach on decisional conflict using an example of intensive versus standard blood pressure-lowering strategies.DesignOn-line survey.SettingA convenience sample of patients in the United States.ParticipantsTwo hundred adults aged 65 and older with hypertension requiring anti-hypertensive treatment (response rate 85.5%).InterventionsParticipants were randomly assigned to either RMST-based summary or conventional summary about the benefit and harm of blood pressure-lowering strategies.MeasurementsDecisional Conflict Scale (DCS), ranging from 0 (no conflict) to 100 (high conflict), and preference for intensive blood pressure-lowering strategy.ResultsParticipants assigned to RMST-based approach (n = 100) and conventional approach (n = 100) had similar age (mean [standard deviation, SD]: 72.3 [5.6] vs 72.8 [5.5] years) and proportions of female (50 [50.0%] vs 61 [61.0%]) and white race (92 [92.0%] vs 92 [92.0%]). The mean (SD) DCS score was 25.2 (15.0) for RMST-based approach and 25.6 (14.1) for conventional approach (p = 0.84). The number (%) of participants who preferred intensive strategy was 10 (10.0%) for RMST-based approach and 14 (14.0%) for conventional approach (p = 0.52). The results were consistent in subgroups defined by age, sex, education level, cardiovascular disease status, and predicted mortality risk categories.ConclusionIn a sample of relatively healthy older adults with hypertension, RMST-based approach was as effective as conventional approach on decisional conflict about choosing a blood pressure-lowering strategy. This study provides proof-of-concept evidence that RMST-based approach can be used in conjunction with absolute and relative risk reduction for communicating treatment benefit and harm in a decision aid.
| S-EPMC8373742 | biostudies-literature