Fertility-sparing surgery vs standard surgery for early-stage cervical cancer: difference in 5-year life expectancy by tumor size.

BACKGROUND: Cervical cancer incidence among premenopausal women is rising, and fertility-sparing surgery serves as an important option for this young population. There is a lack of evidence on what tumor size cutoff should be used to define candidacy for fertility-sparing surgery. OBJECTIVE: We sought to describe how the association between fertility-sparing surgery (compared with standard surgery) and life expectancy varies by tumor size among patients with cervical cancers measuring ≤4 cm in largest diameter. Our secondary objective was to quantify the probability of undergoing adjuvant radiotherapy among patients who underwent fertility-sparing surgery as a function of tumor size. STUDY DESIGN: We identified patients in the National Cancer Database aged ≤45 years, diagnosed with stage I cervical cancer with tumors ≤4 cm between 2006 and 2018, who received no preoperative radiation or chemotherapy, and who underwent either fertility-sparing surgery (cone or trachelectomy, either simple or radical) or standard surgery (simple or radical hysterectomy) as their primary treatment. Propensity-score matching was performed to compare patients who underwent fertility-sparing surgery with those who underwent standard surgery. A flexible parametric model was employed to quantify the difference in life expectancy within 5 years of diagnosis (restricted mean survival time) based on tumor size among patients who underwent fertility-sparing and those who underwent standard surgery. In addition, among those who underwent fertility-sparing surgery, a logistic regression model was used to explore the relationship between tumor size and the probability of receiving adjuvant radiation. RESULTS: A total of 11,946 patients met the inclusion criteria of whom 904 (7.6%) underwent fertility-sparing surgery. After propensity-score matching, 897 patients who underwent fertility-sparing surgery were matched 1:1 with those who underwent standard surgery. Although the 5-year life expectancy was similar among patients who had fertility sparing surgery and those who had standard surgery regardless of tumor sizes, the estimates of life-expectancy differences associated with fertility-sparing surgery were more precise among patients with smaller tumors (1-cm tumor: restricted mean survival time difference, -0.10 months; 95% confidence interval, -0.67 to 0.47) than among those with larger tumors (4-cm tumor: restricted mean survival time difference, -0.11 months; 95% confidence interval, -3.79 to 3.57). The probability of receiving adjuvant radiation increased with tumor size, ranging from 5.6% (95% confidence interval, 3.9-7.9) for a 1-cm tumor to 37% (95% confidence interval, 24.3-51.8) for a 4-cm tumor. CONCLUSION: Within 5 years of diagnosis, young patients with stage I cancers measuring ≤4 cm had similar survival outcomes after either fertility-sparing surgery or standard surgery. However, because few patients with tumors >2 cm underwent fertility-sparing surgery, a clinically important survival difference could not be excluded in this population.

RMST-based multiple contrast tests in general factorial designs.

Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

Comparison between asymptotic and re-randomisation tests under non-proportional hazards in a randomised controlled trial using the minimisation method.

BACKGROUND: Pocock-Simon's minimisation method has been widely used to balance treatment assignments across prognostic factors in randomised controlled trials (RCTs). Previous studies focusing on the survival outcomes have demonstrated that the conservativeness of asymptotic tests without adjusting for stratification factors, as well as the inflated type I error rate of adjusted asymptotic tests conducted in a small sample of patients, can be relaxed using re-randomisation tests. Although several RCTs using minimisation have suggested the presence of non-proportional hazards (non-PH) effects, the application of re-randomisation tests has been limited to the log-rank test and Cox PH models, which may result in diminished statistical power when confronted with non-PH scenarios. To address this issue, we proposed two re-randomisation tests based on a maximum combination of weighted log-rank tests (MaxCombo test) and the difference in restricted mean survival time (dRMST) up to a fixed time point τ , both of which can be extended to adjust for randomisation stratification factors. METHODS: We compared the performance of asymptotic and re-randomisation tests using the MaxCombo test, dRMST, log-rank test, and Cox PH models, assuming various non-PH situations for RCTs using minimisation, with total sample sizes of 50, 100, and 500 at a 1:1 allocation ratio. We mainly considered null, and alternative scenarios featuring delayed, crossing, and diminishing treatment effects. RESULTS: Across all examined null scenarios, re-randomisation tests maintained the type I error rates at the nominal level. Conversely, unadjusted asymptotic tests indicated excessive conservatism, while adjusted asymptotic tests in both the Cox PH models and dRMST indicated inflated type I error rates for total sample sizes of 50. The stratified MaxCombo-based re-randomisation test consistently exhibited robust power across all examined scenarios. CONCLUSIONS: The re-randomisation test is a useful alternative in non-PH situations for RCTs with minimisation using the stratified MaxCombo test, suggesting its robust power in various scenarios.

Effect of complete mesocolic excision (cme) on long-term survival after right colectomy for cancer: multivariate meta-analysis and restricted mean survival time estimation.

INTRODUCTION: Debate exists concerning the impact of complete mesocolic excision (CME) on long-term oncological outcomes. The aim of this review was to condense the updated literature and assess the effect of CME on long-term survival after right colectomy for cancer. METHODS: PubMed, MEDLINE, Scopus, and Web of Science were searched through July 2023. The included studies evaluated the effect of CME on survival. The primary outcome was long-term overall survival. Restricted mean survival time difference (RMSTD), hazard ratio (HR), and 95% confidence intervals (CI) were used as pooled effect size measures. GRADE methodology was used to summarize the certainty of evidence. RESULTS: Ten studies (3665 patients) were included. Overall, 1443 (39.4%) underwent CME. The RMSTD analysis shows that at 60-month follow-up, stage I-III CME patients lived 2.5 months (95% CI 1.1-4.1) more on average compared with noCME patients. Similarly, stage III patients that underwent CME lived longer compared to noCME patients at 55-month follow-up (6.1 months; 95% CI 3.4-8.5). The time-dependent HRs analysis for CME vs. noCME (stage I-III disease) shows a higher mortality hazard in patients with noCME at 6 months (HR 0.46, 95% CI 0.29-0.71), 12 months (HR 0.57, 95% CI 0.43-0.73), and 24 months (HR 0.73, 95% CI 0.57-0.92) up to 27 months. CONCLUSIONS: This study suggests that CME is associated with unclear OS benefit in stage I-III disease. Caution is recommended to avoid overestimation of the effect of CME in stage III disease since the marginal benefit of a more extended resection may have been influenced by tumor biology/molecular profile and multimodal adjuvant treatments.

Dissecting the restricted mean time in favor of treatment.

The restricted mean time in favor (RMT-IF) summarizes the treatment effect on a hierarchical composite endpoint with mortality at the top. Its crude decomposition into "stage-wise effects," i.e., the net average time gained by the treatment prior to each component event, does not reveal the patient state in which the extra time is spent. To obtain this information, we break each stage-wise effect into subcomponents according to the specific state to which the reference condition is improved. After re-expressing the subcomponents as functionals of the marginal survival functions of outcome events, we estimate them conveniently by plugging in the Kaplan -- Meier estimators. Their robust variance matrices allow us to construct joint tests on the decomposed units, which are particularly powerful against component-wise differential treatment effects. By reanalyzing a cancer trial and a cardiovascular trial, we acquire new insights into the quality and composition of the extra survival times, as well as the extra time with fewer hospitalizations, gained by the treatment in question. The proposed methods are implemented in the rmt package freely available on the Comprehensive R Archive Network (CRAN).

Effectiveness of pembrolizumab in trial-ineligible patients with metastatic urothelial carcinoma.

BACKGROUND: The KEYNOTE-045 trial showed that pembrolizumab therapy improved the survival of patients with advanced urothelial carcinoma (UC). However, its effectiveness in trial-ineligible patients remains unclear. MATERIALS AND METHODS: We conducted a multicenter retrospective study to evaluate the effectiveness of pembrolizumab in patients with metastatic UC who were trial-ineligible. The data of 164 consecutive patients with platinum-treated metastatic UC who received pembrolizumab as second-line therapy were analyzed. Trial eligibility was assessed using the KEYNOTE-045 criteria. Inverse probability of treatment weighting (IPTW) was used to balance patient characteristics. Overall survival (OS) and progression-free survival (PFS) were examined using the IPTW-adjusted Kaplan-Meier method. IPTW-adjusted restricted mean survival times (RMSTs) were compared between ineligible and eligible patients. RESULTS: Seventy-five patients (45.7%) were classified as ineligible based on the KEYNOTE-045 criteria. Baseline hemoglobin concentration of less than 9.0 g/dL was the most common reason for trial protocol violation (N = 23 [14.0%]). An IPTW-adjusted logistic regression model showed that the trial-eligibility was not significantly associated with objective response (OR: 0.65, 95% CI: 0.32 to 1.29, P = 0.22). Ineligible patients had similar RMST for PFS (difference: 3.8 months, 95% CI: -1.6 to 9.3, P = 0.17) and RMST for OS (difference: 1.4 months, 95% CI: -5.4 to 8.2, P = 0.93) compared with eligible patients. CONCLUSIONS: This study suggests that the effectiveness of pembrolizumab may be retained in ineligible patients with platinum-treated metastatic UC. Expanding trial eligibility criteria for these patients may be beneficial.

Nonparametric inference of general while-alive estimands for recurrent events.

Measuring the treatment effect on recurrent events like hospitalization in the presence of death has long challenged statisticians and clinicians alike. Traditional inference on the cumulative frequency unjustly penalizes survivorship as longer survivors also tend to experience more adverse events. Expanding a recently suggested idea of the "while-alive" event rate, we consider a general class of such estimands that adjust for the length of survival without losing causal interpretation. Given a user-specified loss function that allows for arbitrary weighting, we define as estimand the average loss experienced per unit time alive within a target period and use the ratio of this loss rate to measure the effect size. Scaling the loss rate by the width of the corresponding time window gives us an alternative, and sometimes more photogenic, way of showing the data. To make inferences, we construct a nonparametric estimator for the loss rate through the cumulative loss and the restricted mean survival time and derive its influence function in closed form for variance estimation and testing. As simulations and analysis of real data from a heart failure trial both show, the while-alive approach corrects for the false attenuation of treatment effect due to patients living longer under treatment, with increased statistical power as a result. The proposed methods are implemented in the R-package WA, which is publicly available from the Comprehensive R Archive Network (CRAN).

On restricted mean time in favor of treatment.

The restricted mean time in favor (RMT-IF) of treatment is a nonparametric effect size for complex life history data. It is defined as the net average time the treated spend in a more favorable state than the untreated over a prespecified time window. It generalizes the familiar restricted mean survival time (RMST) from the two-state life-death model to account for intermediate stages in disease progression. The overall estimand can be additively decomposed into stage-wise effects, with the standard RMST as a component. Alternate expressions of the overall and stage-wise estimands as integrals of the marginal survival functions for a sequence of landmark transitioning events allow them to be easily estimated by plug-in Kaplan-Meier estimators. The dynamic profile of the estimated treatment effects as a function of follow-up time can be visualized using a multilayer, cone-shaped "bouquet plot." Simulation studies under realistic settings show that the RMT-IF meaningfully and accurately quantifies the treatment effect and outperforms traditional tests on time to the first event in statistical efficiency thanks to its fuller utilization of patient data. The new methods are illustrated on a colon cancer trial with relapse and death as outcomes and a cardiovascular trial with recurrent hospitalizations and death as outcomes. The R-package rmt implements the proposed methodology and is publicly available from the Comprehensive R Archive Network (CRAN).

Analysis of dynamic restricted mean survival time based on pseudo-observations.

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

Designing superiority trials with window mean survival time as a primary endpoint.

Window mean survival time (WMST), a simple extension of restricted mean survival time (RMST), allows for clinicians to evaluate the mean survival difference between treatment groups in specific windows of time during the follow-up period of a trial. The advantages of WMST are numerous. Not only does it produce estimates of treatment effect that can be meaningfully interpreted, but also has power advantages over competing methods when hazards are non-proportional (NPH). WMST, like RMST, is currently underutilized due to clinicians' lack of familiarity with tests comparing mean survival times and the lack of tools to facilitate trial design with this endpoint. The aim of this article is to provide investigators with insights and software to design trials with WMST as the primary endpoint. Functions for performing power and sample size calculations are provided in the survWMST package in R available on GitHub.

A nonparametric simultaneous confidence band for biomarker effect on the restricted mean survival time.

Study of prognostic and predictive biomarkers plays an important role in the design and analysis of clinical trials. The Cox proportional hazards model is often used to study the biomarker main effect and the treatment-biomarker interaction effect for survival data. The estimated effects can be biased if the proportional hazards assumption is violated. The restricted mean survival time is becoming popular in clinical studies for having a clear intuitive interpretation. In this article, we first propose nonparametric methods to make statistical inference for the one-sample problem of the biomarker effect on the restricted mean survival time; we then extend the methods to the two-sample problem for studying the difference in the biomarker effects between treatment groups in clinical trials. For a given biomarker, the restricted mean survival time is estimated by kernel smoothing methods with the inverse probability of censoring weights. We prove the consistency for the estimates and develop simultaneous confidence bands for the biomarker effects on the restricted mean survival time. The simultaneous confidence bands are evaluated in extensive simulation studies and are found to have good finite sample performance. We then apply the proposed methods to a breast cancer study conducted by the Breast International Group (BIG) to illustrate how the Ki67 biomarker, a protein marker of cell proliferation, affects the survival time of patients, compared between the treatment groups.

Ratio and difference of average hazard with survival weight: New measures to quantify survival benefit of new therapy.

The hazard ratio (HR) has been the most popular measure to quantify the magnitude of treatment effect on time-to-event outcomes in clinical research. However, the traditional Cox's HR approach has several drawbacks. One major issue is that there is no clear interpretation when the proportional hazards (PH) assumption does not hold, because the estimated HR is affected by study-specific censoring time distribution in non-PH cases. Another major issue is that the lack of a group-specific absolute hazard value in each group obscures the clinical significance of the magnitude of the treatment effect. Given these, we propose average hazard with survival weight (AH-SW) as a summary metric of event time distribution and will use difference in AH-SW (DAH-SW) or ratio of AH-SW (RAH-SW) to quantify the treatment effect magnitude. The AH-SW is interpreted as a person-time incidence rate that does not depend on random censoring. It is defined as the ratio of cumulative incidence probability and restricted mean survival time (RMST), which can be estimated non-parametrically. Numerical studies demonstrate that DAH-SW and RAH-SW offer almost identical power to Cox's HR-based tests under PH scenarios and can be more powerful for delayed-difference patterns often seen in immunotherapy trials. Like median and RMST differences, the proposed approach is a good model-free alternative to the HR-based approach for evaluating the treatment effect magnitude. Such a model-free measure will increase the likelihood that results from clinical studies are correctly interpreted and generalized to future populations.

Studentized permutation method for comparing two restricted mean survival times with small sample from randomized trials.

Recent observations, especially in cancer immunotherapy clinical trials with time-to-event outcomes, show that the commonly used proportional hazard assumption is often not justifiable, hampering an appropriate analysis of the data by hazard ratios. An attractive alternative advocated is given by the restricted mean survival time (RMST), which does not rely on any model assumption and can always be interpreted intuitively. Since methods for the RMST based on asymptotic theory suffer from inflated type-I error under small sample sizes, a permutation test was proposed recently leading to more convincing results in simulations. However, classical permutation strategies require an exchangeable data setup between comparison groups which may be limiting in practice. Besides, it is not possible to invert related testing procedures to obtain valid confidence intervals, which can provide more in-depth information. In this paper, we address these limitations by proposing a studentized permutation test as well as respective permutation-based confidence intervals. In an extensive simulation study, we demonstrate the advantage of our new method, especially in situations with relatively small sample sizes and unbalanced groups. Finally, we illustrate the application of the proposed method by re-analyzing data from a recent lung cancer clinical trial.

Semiparametric estimation of restricted mean survival time as a function of restriction time.

The restricted mean survival time (RMST) is an appealing measurement in clinical or epidemiological studies with censored survival outcome and receives a lot of attention in the past decades. It provides a useful alternative to the Cox model for evaluating the covariate effect on survival time. The covariate effect on RMST usually varies with the restriction time. However, existing methods cannot address this problem properly. In this article, we propose a semiparametric framework that directly models RMST as a function of the restriction time. Our proposed model adopts a widely-used proportional form, enabling the estimation of RMST predictions across an interval using a unified model. Furthermore, the covariate effect for multiple restriction time points can be derived simultaneously. We develop estimators based on estimating equations theories and establish the asymptotic properties of the proposed estimators. The finite sample properties of the estimators are evaluated through extensive simulation studies. We further illustrate the application of our proposed method through the analysis of two real data examples. Supplementary Material are available online.

Prognosis of Patients With Heart Failure Receiving Autologous Myoblast Patches　- Comparison of Single-Arm Trial Data to Registry Data.

BACKGROUND: Clinical studies in regenerative medicine remain insufficient in Japan due to ethical concerns regarding the control group and a lack of statistical methodology to evaluate efficacy in a small treatment group. This study evaluated the efficacy of autologous myoblast patch (AMP) treatment for heart failure using restricted mean survival time (RMST) analysis by comparing data from a small single-arm trial to epidemiological data from a registry.Methods and Results: The clinical trial arm included 55 patients with advanced ischemic cardiomyopathy who received an AMP between 2010 and 2020. The registry-based control group comprised 937 participants with severely impaired left ventricular function who were hospitalized for heart failure during the study period. Due to the limited number of patients, RMST analysis was used to compare survival between the 2 groups. Cox regression analyses revealed non-significant differences in survival between the groups at 3, 3.5, and 4 years. In contrast, RMST analyses revealed significant differences in survival at 3 years (P=0.008) and 3.5 (P=0.024) years, but not at 4 years. CONCLUSIONS: This small single-arm trial using RMST analyses was able to detect the efficacy of AMP transplantation for advanced heart failure (compared with a registry-based control group), with better survival until 3.5 years. This approach may be useful for efficacy analyses in regenerative medicine, where traditional clinical trials are difficult.

A comparison of different population-level summary measures for randomised trials with time-to-event outcomes, with a focus on non-inferiority trials.

BACKGROUND: The population-level summary measure is a key component of the estimand for clinical trials with time-to-event outcomes. This is particularly the case for non-inferiority trials, because different summary measures imply different null hypotheses. Most trials are designed using the hazard ratio as summary measure, but recent studies suggested that the difference in restricted mean survival time might be more powerful, at least in certain situations. In a recent letter, we conjectured that differences between summary measures can be explained using the concept of the non-inferiority frontier and that for a fair simulation comparison of summary measures, the same analysis methods, making the same assumptions, should be used to estimate different summary measures. The aim of this article is to make such a comparison between three commonly used summary measures: hazard ratio, difference in restricted mean survival time and difference in survival at a fixed time point. In addition, we aim to investigate the impact of using an analysis method that assumes proportional hazards on the operating characteristics of a trial designed with any of the three summary measures. METHODS: We conduct a simulation study in the proportional hazards setting. We estimate difference in restricted mean survival time and difference in survival non-parametrically, without assuming proportional hazards. We also estimate all three measures parametrically, using flexible survival regression, under the proportional hazards assumption. RESULTS: Comparing the hazard ratio assuming proportional hazards with the other summary measures not assuming proportional hazards, relative performance varies substantially depending on the specific scenario. Fixing the summary measure, assuming proportional hazards always leads to substantial power gains compared to using non-parametric methods. Fixing the modelling approach to flexible parametric regression assuming proportional hazards, difference in restricted mean survival time is most often the most powerful summary measure among those considered. CONCLUSION: When the hazards are likely to be approximately proportional, reflecting this in the analysis can lead to large gains in power for difference in restricted mean survival time and difference in survival. The choice of summary measure for a non-inferiority trial with time-to-event outcomes should be made on clinical grounds; when any of the three summary measures discussed here is equally justifiable, difference in restricted mean survival time is most often associated with the most powerful test, on the condition that it is estimated under proportional hazards.

Treatment effect measures under nonproportional hazards.

In a clinical trial with a time-to-event endpoint the treatment effect can be measured in various ways. Under proportional hazards all reasonable measures (such as the hazard ratio and the difference in restricted mean survival time) are consistent in the following sense: Take any control group survival distribution such that the hazard rate remains above zero; if there is no benefit by any measure there is no benefit by all measures, and as the magnitude of treatment benefit increases by any measure it increases by all measures. Under nonproportional hazards, however, survival curves can cross, and the direction of the effect for any pair of measures can be inconsistent. In this paper we critically evaluate a variety of treatment effect measures in common use and identify flaws with them. In particular, we demonstrate that a treatment's benefit has two distinct and independent dimensions which can be measured by the difference in the survival rate at the end of follow-up and the difference in restricted mean survival time, and that commonly used measures do not adequately capture both dimensions. We demonstrate that a generalized hazard difference, which can be estimated by the difference in exposure-adjusted subject incidence rates, captures both dimensions, and that its inverse, the number of patient-years of follow-up that results in one fewer event (the NYNT), is an easily interpretable measure of the magnitude of clinical benefit.

Two-sample inference procedures under nonproportional hazards.

We introduce a new two-sample inference procedure to assess the relative performance of two groups over time. Our model-free method does not assume proportional hazards, making it suitable for scenarios where nonproportional hazards may exist. Our procedure includes a diagnostic tau plot to identify changes in hazard timing and a formal inference procedure. The tau-based measures we develop are clinically meaningful and provide interpretable estimands to summarize the treatment effect over time. Our proposed statistic is a U-statistic and exhibits a martingale structure, allowing us to construct confidence intervals and perform hypothesis testing. Our approach is robust with respect to the censoring distribution. We also demonstrate how our method can be applied for sensitivity analysis in scenarios with missing tail information due to insufficient follow-up. Without censoring, Kendall's tau estimator we propose reduces to the Wilcoxon-Mann-Whitney statistic. We evaluate our method using simulations to compare its performance with the restricted mean survival time and log-rank statistics. We also apply our approach to data from several published oncology clinical trials where nonproportional hazards may exist.

Fast approximations of pseudo-observations in the context of right censoring and interval censoring.

In the context of right-censored and interval-censored data, we develop asymptotic formulas to compute pseudo-observations for the survival function and the restricted mean survival time (RMST). These formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right-censored data, Von Mises expansions of the Kaplan-Meier estimator are used to derive the pseudo-observations. For interval-censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo-observations is derived involving the Hessian matrix and the score vector. Theoretical results that justify the use of pseudo-observations in regression are also derived. The formula is illustrated on the piecewise-constant-hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated by Monte Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for a large dataset.

Restricted mean survival time as a function of restriction time.

Restricted mean survival time (RMST) is a clinically interpretable and meaningful survival metric that has gained popularity in recent years. Several methods are available for regression modeling of RMST, most based on pseudo-observations or what is essentially an inverse-weighted complete-case analysis. No existing RMST regression method allows for the covariate effects to be expressed as functions over time. This is a considerable limitation, in light of the many hazard regression methods that do accommodate such effects. To address this void in the literature, we propose RMST methods that permit estimating time-varying effects. In particular, we propose an inference framework for directly modeling RMST as a continuous function of L. Large-sample properties are derived. Simulation studies are performed to evaluate the performance of the methods in finite sample sizes. The proposed framework is applied to kidney transplant data obtained from the Scientific Registry of Transplant Recipients.