Sample size calculation for mixture cure model with restricted mean survival time as a primary endpoint

It is not uncommon for a substantial proportion of patients to be cured (or survive long-term) in clinical trials with time-to-event endpoints, such as the endometrial cancer trial. When designing a clinical trial, a mixture cure model should be used to fully consider the cure fraction. Previously, mixture cure model sample size calculations were based on the proportional hazards assumption of latency distribution between groups, and the log-rank test was used for deriving sample size formulas. In real studies, the latency distributions of the two groups often do not satisfy the proportional hazards assumptions. This article has derived a sample size calculation formula for a mixture cure model with restricted mean survival time as the primary endpoint, and did simulation and example studies. The restricted mean survival time test is not subject to proportional hazards assumptions, and the difference in treatment effect obtained can be quantified as the number of years (or months) increased or decreased in survival time, making it very convenient for clinical patient-physician communication. The simulation results showed that the sample sizes estimated by the restricted mean survival time test for the mixture cure model were accurate regardless of whether the proportional hazards assumptions were satisfied and were smaller than the sample sizes estimated by the log-rank test in most cases for the scenarios in which the proportional hazards assumptions were violated.

Time-varying effect in older patients with early-stage breast cancer: a model considering the competing risks based on a time scale

Background

Patients with early-stage breast cancer may have a higher risk of dying from other diseases, making a competing risks model more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors of breast cancer may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor.

Methods

To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale.

Results

A simulation validated the accuracy of the coefficient estimates in the proposed regression. Applying this model to an older early-stage breast cancer cohort, it was found that 1) the protective effects of positive estrogen receptor and chemotherapy decreased over time; 2) the protective effect of breast-conserving surgery increased over time; and 3) the deleterious effects of stage T2, stage N2, and histologic grade II cancer increased over time. Moreover, from the view of prediction, the mean C-index in external validation reached 0.78.

Conclusion

Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist.

Design of a clinical trial using generalized pairwise comparisons to test a less intensive treatment regimen

BACKGROUND/AIMS

Showing "similar efficacy" of a less intensive treatment typically requires a non-inferiority trial. Yet such trials may be challenging to design and conduct. In acute promyelocytic leukemia, great progress has been achieved with the introduction of targeted therapies, but toxicity remains a major clinical issue. There is a pressing need to show the favorable benefit/risk of less intensive treatment regimens.

METHODS

We designed a clinical trial that uses generalized pairwise comparisons of five prioritized outcomes (alive and event-free at 2 years, grade 3/4 documented infections, differentiation syndrome, hepatotoxicity, and neuropathy) to confirm a favorable benefit/risk of a less intensive treatment regimen. We conducted simulations based on historical data and assumptions about the differences expected between the standard of care and the less intensive treatment regimen to calculate the sample size required to have high power to show a positive Net Treatment Benefit in favor of the less intensive treatment regimen.

RESULTS

Across 10,000 simulations, average sample sizes of 260 to 300 patients are required for a trial using generalized pairwise comparisons to detect typical Net Treatment Benefits of 0.19 (interquartile range 0.14-0.23 for a sample size of 280). The Net Treatment Benefit is interpreted as a difference between the probability of doing better on the less intensive treatment regimen than on the standard of care, minus the probability of the opposite situation. A Net Treatment Benefit of 0.19 translates to a number needed to treat of about 5.3 patients (1/0.19 ≃ 5.3).

CONCLUSION

Generalized pairwise comparisons allow for simultaneous assessment of efficacy and safety, with priority given to the former. The sample size required would be of the order of 300 patients, as compared with more than 700 patients for a non-inferiority trial using a margin of 4% against the less intensive treatment regimen for the absolute difference in event-free survival at 2 years, as considered here.

Regression models for average hazard

Limitations of using the traditional Cox's hazard ratio for summarizing the magnitude of the treatment effect on time-to-event outcomes have been widely discussed, and alternative measures that do not have such limitations are gaining attention. One of the alternative methods recently proposed, in a simple 2-sample comparison setting, uses the average hazard with survival weight (AH), which can be interpreted as the general censoring-free person-time incidence rate on a given time window. In this paper, we propose a new regression analysis approach for the AH with a truncation time τ. We investigate 3 versions of AH regression analysis, assuming (1) independent censoring, (2) group-specific censoring, and (3) covariate-dependent censoring. The proposed AH regression methods are closely related to robust Poisson regression. While the new approach needs to require a truncation time τ explicitly, it can be more robust than Poisson regression in the presence of censoring. With the AH regression approach, one can summarize the between-group treatment difference in both absolute difference and relative terms, adjusting for covariates that are associated with the outcome. This property will increase the likelihood that the treatment effect magnitude is correctly interpreted. The AH regression approach can be a useful alternative to the traditional Cox's hazard ratio approach for estimating and reporting the magnitude of the treatment effect on time-to-event outcomes.

The net benefit for time-to-event outcome in oncology clinical trials with treatment switching

BACKGROUND

The net benefit is an effect measure for any type of endpoint, including the time-to-event outcome, and can provide intuitive and clinically meaningful interpretation. It is defined as the probability of a randomly selected subject from the experimental arm surviving by at least a clinically relevant time longer than a randomly selected subject from the control arm. In oncology clinical trials, an intercurrent event such as treatment switching is common, which potentially causes informative censoring; nevertheless, conventional methods for the net benefit are not able to deal with it. In this study, we proposed a new estimator using the inverse probability of censoring weighting (IPCW) method and illustrated an oncology clinical trial with treatment switching (the SHIVA study) to apply the proposed method under the estimand framework.

METHODS

The net benefit can be estimated using the survival functions of each treatment group. The proposed estimator was based on the survival functions estimated by the inverse probability of the censoring weighting method that can handle covariate-dependent censoring. The simulation study was undertaken to evaluate the operating characteristics of the proposed estimator under several scenarios; we varied the shapes of the survival curves, treatment effect, covariates effect on censoring, proportion of the censoring, threshold of the net benefit, and sample size. We also applied conventional methods (the scoring rules by Péron or Gehan) and the proposed method to the SHIVA study.

RESULTS

Our simulation study showed that the proposed estimator provided less biased results under the covariate-dependent censoring than existing estimators. When applying the proposed method to the SHIVA study, we were able to estimate the net benefit by incorporating the information of the covariates with different estimand strategies to address the intercurrent event of the treatment switching. However, the estimates of the proposed method and those of the aforementioned conventional methods were similar under the hypothetical strategy.

CONCLUSIONS

We proposed a new estimator of the net benefit that can include covariates to account for the possibly informative censoring. We also provided an illustrative analysis of the proposed method for the oncology clinical trial with treatment switching using the estimand framework. Our proposed new estimator is suitable for handling the intercurrent events that can potentially cause covariate-dependent censoring.

Generalized Pairwise Comparisons to Assess Treatment Effects: JACC Review Topic of the Week

A time-to-first-event composite endpoint analysis has well-known shortcomings in evaluating a treatment effect in cardiovascular clinical trials. It does not fully describe the clinical benefit of therapy because the severity of the events, events repeated over time, and clinically relevant nonsurvival outcomes cannot be considered. The generalized pairwise comparisons (GPC) method adds flexibility in defining the primary endpoint by including any number and type of outcomes that best capture the clinical benefit of a therapy as compared with standard of care. Clinically important outcomes, including bleeding severity, number of interventions, and quality of life, can easily be integrated in a single analysis. The treatment effect in GPC can be expressed by the net treatment benefit, the success odds, or the win ratio. This review provides guidance on the use of GPC and the choice of treatment effect measures for the analysis and reporting of cardiovascular trials.

Trial Design for Cancer Immunotherapy: A Methodological Toolkit

Immunotherapy with checkpoint inhibitors (CPIs) and cell-based products has revolutionized the treatment of various solid tumors and hematologic malignancies. These agents have shown unprecedented response rates and long-term benefits in various settings. These clinical advances have also pointed to the need for new or adapted approaches to trial design and assessment of efficacy and safety, both in the early and late phases of drug development. Some of the conventional statistical methods and endpoints used in other areas of oncology appear to be less appropriate in immuno-oncology. Conversely, other methods and endpoints have emerged as alternatives. In this article, we discuss issues related to trial design in the early and late phases of drug development in immuno-oncology, with a focus on CPIs. For early trials, we review the most salient issues related to dose escalation, use and limitations of tumor response and progression criteria for immunotherapy, the role of duration of response as an endpoint in and of itself, and the need to conduct randomized trials as early as possible in the development of new therapies. For late phases, we discuss the choice of primary endpoints for randomized trials, review the current status of surrogate endpoints, and discuss specific statistical issues related to immunotherapy, including non-proportional hazards in the assessment of time-to-event endpoints, alternatives to the Cox model in these settings, and the method of generalized pairwise comparisons, which can provide a patient-centric assessment of clinical benefit and be used to design randomized trials.

On assessing survival benefit of immunotherapy using long-term restricted mean survival time

The pattern of the difference between two survival curves we often observe in randomized clinical trials for evaluating immunotherapy is not proportional hazards; the treatment effect typically appears several months after the initiation of the treatment (ie, delayed difference pattern). The commonly used logrank test and hazard ratio estimation approach will be suboptimal concerning testing and estimation for those trials. The long-term restricted mean survival time (LT-RMST) approach is a promising alternative for detecting the treatment effect that potentially appears later in the study. A challenge in employing the LT-RMST approach is that it must specify a lower end of the time window in addition to a truncation time point that the RMST requires. There are several investigations and suggestions regarding the choice of the truncation time point for the RMST. However, little has been investigated to address the choice of the lower end of the time window. In this paper, we propose a flexible LT-RMST-based test/estimation approach that does not require users to specify a lower end of the time window. Numerical studies demonstrated that the potential power loss by adopting this flexibility was minimal, compared to the standard LT-RMST approach using a prespecified lower end of the time window. The proposed method is flexible and can offer higher power than the RMST-based approach when the delayed treatment effect is expected. Also, it provides a robust estimate of the magnitude of the treatment effect and its confidence interval that corresponds to the test result.

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.

Clinical effectiveness reporting of novel cancer drugs in the context of non-proportional hazards: a review of nice single technology appraisals

OBJECTIVES

The hazard ratio (HR) is a commonly used summary statistic when comparing time to event (TTE) data between trial arms, but assumes the presence of proportional hazards (PH). Non-proportional hazards (NPH) are increasingly common in NICE technology appraisals (TAs) due to an abundance of novel cancer treatments, which have differing mechanisms of action compared with traditional chemotherapies. The goal of this study is to understand how pharmaceutical companies, evidence review groups (ERGs) and appraisal committees (ACs) test for PH and report clinical effectiveness in the context of NPH.

METHODS

A thematic analysis of NICE TAs concerning novel cancer treatments published between 1 January 2020 and 31 December 2021 was undertaken. Data on PH testing and clinical effectiveness reporting for overall survival (OS) and progression-free survival (PFS) were obtained from company submissions, ERG reports, and final appraisal determinations (FADs).

RESULTS

NPH were present for OS or PFS in 28/40 appraisals, with log-cumulative hazard plots the most common testing methodology (40/40), supplemented by Schoenfeld residuals (20/40) and/or other statistical methods (6/40). In the context of NPH, the HR was ubiquitously reported by companies, inconsistently critiqued by ERGs (10/28), and commonly reported in FADs (23/28).

CONCLUSIONS

There is inconsistency in PH testing methodology used in TAs. ERGs are inconsistent in critiquing use of the HR in the context of NPH, and even when critiqued it remains a commonly reported outcome measure in FADs. Other measures of clinical effectiveness should be considered, along with guidance on clinical effectiveness reporting when NPH are present.

Investigations of methods for multiple time-to-event endpoints: A chronic myeloid leukemia data analysis

BACKGROUND

In randomized controlled trials, multiple time-to-event endpoints are commonly used to determine treatment effects. However, choosing an appropriate method to address multiple endpoints, according to different purposes of clinical practice, is a challenge for researchers.

METHODS

We applied single endpoint, composite endpoint and win ratio analysis to chronic myeloid leukemia (CML) data to illustrate the distinctions with different multiple endpoints, including relapse, recovery and death after transplantation.

RESULTS

Regarding relapse and death, the hazard ratio in single endpoint analysis (HR_s ) were 1.281 (95% CI: 1.061-1.546) and hazard ratio in composite endpoint analysis (HR_c ) were 1.286 (95% CI: 1.112-1.486) and 1/WR (win ratio) was 1.292 (95% CI: 1.115-1.497) indicated a similar negative effect for non-prophylaxis patients. However, when considering recovery and death, the corresponding HR_s  = 1.280 (95% CI: 1.056-1.552) may not be enough to describe the effect on death with nonproportional hazards (p < 0.05), and for the composite endpoint analysis, the HR_c  = 0.828 (95% CI: 0.740-0.926) cannot quantify and interpret the clinical effect on the composite endpoint with the combination of recovery and death, while the 1/WR = 1.351 (95% CI: 1.207-1.513) showed an unfavourable effect for non-prophylaxis patients CONCLUSIONS: When dealing with multiple endpoints, single endpoints, researchers may choose single endpoints, composite endpoints and WR analysis due to different clinical applications and purposes. However, both single and composite endpoint analyses are hazard-based measures, and thus, the proportional hazards assumption should be considered. Moreover, composite endpoint analysis should be applied for endpoints with similar clinical meanings but not opposing implications. Win ratio analysis can be considered for different clinical importance of multiple endpoints, but the meaning of 'winner' needs to be specified for desired or undesired endpoints.

The case against censoring of progression-free survival in cancer clinical trials - A pandemic shutdown as an illustration

Background

Missing data may lead to loss of statistical power and introduce bias in clinical trials. The Covid-19 pandemic has had a profound impact on patient health care and on the conduct of cancer clinical trials. Although several endpoints may be affected, progression-free survival (PFS) is of major concern, given its frequent use as primary endpoint in advanced cancer and the fact that missed radiographic assessments are to be expected. The recent introduction of the estimand framework creates an opportunity to define more precisely the target of estimation and ensure alignment between the scientific question and the statistical analysis.

Methods

We used simulations to investigate the impact of two basic approaches for handling missing tumor scans due to the pandemic: a “treatment policy” strategy, which consisted in ascribing events to the time they are observed, and a “hypothetical” approach of censoring patients with events during the shutdown period at the last assessment prior to that period. We computed the power of the logrank test, estimated hazard ratios (HR) using Cox models, and estimated median PFS times without and with a hypothetical 6-month shutdown period with no patient enrollment or tumor scans being performed, varying the shutdown starting times.

Results

Compared with the results in the absence of shutdown, the “treatment policy” strategy slightly overestimated median PFS proportionally to the timing of the shutdown period, but power was not affected. Except for one specific scenario, there was no impact on the estimated HR. In general, the pandemic had a greater impact on the analyses using the “hypothetical” strategy, which led to decreased power and overestimated median PFS times to a greater extent than the “treatment policy” strategy.

Conclusion

As a rule, we suggest that the treatment policy approach, which conforms with the intent-to-treat principle, should be the primary analysis to avoid unnecessary loss of power and minimize bias in median PFS estimates.

Restricted mean survival time regression model with time-dependent covariates

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.

Versatile tests for window mean survival time

Window mean survival time (WMST) evaluates the mean survival between a lower time horizon, τ 0 $$ {\tau}_0 $$ , and an upper time horizon, τ 1 $$ {\tau}_1 $$ . As a flexible extension of restricted mean survival time, specific clinically relevant windows of time can be assessed for survival difference accompanied by a communicable interpretation of estimates and tests. In its original application, WMST required the pre-specification of a window through the selection of appropriate window bounds, τ 0 $$ {\tau}_0 $$ and τ 1 $$ {\tau}_1 $$ . In the instance of severe window misspecification of τ 0 $$ {\tau}_0 $$ and τ 1 $$ {\tau}_1 $$ , the analysis may suffer from low power and a less meaningful interpretation. In this article, we introduce versatile tests whose procedures are based on the simultaneous use of multiple WMST test statistics that are asymptotically normal under the null hypothesis of no difference between two groups. Simulations are performed to examine the power of the tests in moderate sample sizes when the data are uncensored to heavily censored with a ramp-up enrollment period. The survival scenarios chosen for simulation are intended to imitate those which are commonly encountered in oncology, especially in trials involving immunotherapies. Implementation of the procedures is discussed in two real data examples for illustration. Functions for performing versatile WMST tests are provided in the survWMST package in R.

Two-sample survival probability curves: A graphical approach for the analysis of time to event data in clinical trials

With the aim to improve the communication of trial results, we introduce a novel graphical approach that complements the analysis of time to event outcomes in two-arm randomized trials. We define the so-called two-sample survival probability curve and propose a nonparametric estimator of the curve based on a random walk using Kaplan-Meier survival estimates for the two arms. We then use the estimated curve to visualize treatment effect as well as potential effect modification of factors of interest. We also propose to estimate two-sample survival probability curves within the framework of the Cox model to graphically assess model fit. The proposed two-sample survival probability plot puts trials in a standardized [0,1] × [0,1] space, allowing for a simple visualization of the main effect, effect modification, and the adequacy of a model fit.

Comparison of radiation exposure between endoscopic ultrasound-guided drainage and transpapillary drainage by endoscopic retrograde cholangiopancreatography for pancreatobiliary diseases

OBJECTIVES

The transpapillary drainage by endoscopic retrograde cholangiopancreatography (ERCP-D) cannot be performed without fluoroscopy, and there are many situations in which fluoroscopy is required even in endoscopic ultrasound-guided drainage (EUS-D). Previous studies have compared the efficacy, but not the radiation exposure of EUS-D and ERCP-D. While radiation exposure in ERCP-D has been previously evaluated, there is a paucity of information regarding radiation doses in EUS-D. This study aimed to assess radiation exposure in EUS-D compared with that in ERCP-D.

METHODS

This retrospective single-center cohort study included consecutive patients who underwent EUS-D and ERCP-D between October 2017 and March 2019. The air kerma (AK, mGy), kerma-area product (KAP, Gycm² ), fluoroscopy time (FT, min), and procedure time (PT, min) were assessed. The invasive probability weighting method was used to qualify the comparisons.

RESULTS

We enrolled 372 and 105 patients who underwent ERCP-D and EUS-D, respectively. The mean AK, KAP, and FT in the EUS-D group were higher by 53%, 28%, and 27%, respectively, than those in the ERCP-D group, whereas PT was shorter by approximately 11% (AK, 135.0 vs. 88.4; KAP, 28.1 vs. 21.9; FT, 20.4 vs. 16.0; PT, 38.7 vs. 43.5). The sub-analysis limited to biliary drainage cases showed the same trend (AK, 128.3 vs. 90.9; KAP, 27.0 vs. 22.2; FT, 16.4 vs. 16.1; PT, 32.5 vs. 44.4).

CONCLUSIONS

This is the first study to assess radiation exposure in EUS-D compared with that in ERCP-D. Radiation exposure was significantly higher in EUS-D than in ERCP-D, despite the shorter procedure time.

Excess Body Fatness during Early to Mid-Adulthood and Survival from Colorectal and Breast Cancer: A Pooled Analysis of Five International Cohort Studies

BACKGROUND

Here, we explore the association between excess weight during early to mid-adulthood and survival in patients diagnosed with breast and colorectal cancer, using a pooled analysis of five cohort studies and study participants from 11 countries.

METHODS

Participant-level body mass index (BMI) trajectories were estimated by fitting a growth curve model using over 2 million repeated BMI measurements from close to 600,000 cohort participants. Cumulative measures of excess weight were derived. Data from over 23,000 patients with breast and colorectal cancer were subsequently analyzed using time-to-event models for death with the date of diagnosis as start of follow-up. Study-specific results were combined through a random effect meta-analysis.

RESULTS

We found a significant dose-response relationship (P trend = 0.013) between the average BMI during early and mid-adulthood and death from breast cancer, with a pooled HR of 1.31 (1.07-1.60) and the time to death shortened by 16% for average BMI above 25 kg/m2 compared with average BMI less than or equal to 22.5 kg/m2, respectively. Similar results were found for categories of cumulative time spent with excess weight. There was no association between excess body fatness during early to mid-adulthood and death in patients with colorectal cancer.

CONCLUSIONS

Excess body fatness during early to mid-adulthood is associated not only with an increased risk of developing cancer, but also with a lower survival in patients with breast cancer.

IMPACT

Our results emphasize the importance of public health policies aimed at reducing overweight during adulthood and inform future studies on the relationship between excess weight and cancer outcomes.

Restricted survival benefit with right-censored data

The hazard ratio is widely used to quantify treatment effects. However, it may be difficult to interpret for patients and practitioners, especially when the hazard ratio is not constant over time. Alternative measures of the treatment effects have been proposed such as the difference of the restricted mean survival times, the difference in survival proportions at some fixed follow-up time, or the net chance of a longer survival. In this paper, we propose the restricted survival benefit (RSB), a quantity that can incorporate multiple useful measurements of treatment effects. Hence, it provides a framework for a comprehensive assessment of the treatment effects. We provide estimation and inference procedures for the RSB that accommodate censored survival outcomes, using methods of the inverse-probability-censoring-weighted U -statistic and the jackknife empirical likelihood. We conduct extensive simulation studies to examine the numerical performance of the proposed method, and we analyze data from a randomized Phase III clinical trial (SWOG S0777) using the proposed method.

From Model Organisms to Humans, the Opportunity for More Rigor in Methodologic and Statistical Analysis, Design, and Interpretation of Aging and Senescence Research

This review identifies frequent design and analysis errors in aging and senescence research and discusses best practices in study design, statistical methods, analyses, and interpretation. Recommendations are offered for how to avoid these problems. The following issues are addressed: (a) errors in randomization, (b) errors related to testing within-group instead of between-group differences, (c) failing to account for clustering, (d) failing to consider interference effects, (e) standardizing metrics of effect size, (f) maximum life-span testing, (g) testing for effects beyond the mean, (h) tests for power and sample size, (i) compression of morbidity versus survival curve squaring, and (j) other hot topics, including modeling high-dimensional data and complex relationships and assessing model assumptions and biases. We hope that bringing increased awareness of these topics to the scientific community will emphasize the importance of employing sound statistical practices in all aspects of aging and senescence research.

A non-parametric approach for jointly combining evidence on progression free and overall survival time in network meta-analysis

Randomised controlled trials of cancer treatments typically report progression free survival (PFS) and overall survival (OS) outcomes. Existing methods to synthesise evidence on PFS and OS either rely on the proportional hazards assumption or make parametric assumptions which may not capture the diverse survival curve shapes across studies and treatments. Furthermore, PFS and OS are not independent: OS is the sum of PFS and post-progression survival (PPS). Our aim was to develop a non-parametric approach for jointly synthesising evidence from published Kaplan-Meier survival curves of PFS and OS without assuming proportional hazards. Restricted mean survival times (RMST) are estimated by the area under the survival curves (AUCs) up to a restricted follow-up time. The correlation between AUCs due to the constraint that OS>PFS is estimated using bootstrap re-sampling. Network meta-analysis models are given for RMST for PFS and PPS and ensure that OS=PFS + PPS. Both additive and multiplicative network meta-analysis models are presented to obtain relative treatment effects as either differences or ratios of RMST. The methods are illustrated with a network meta-analysis of treatments for Stage IIIA-N2 Non-Small Cell Lung Cancer. The approach has implications for health economic models of cancer treatments which require estimates of the mean time spent in the PFS and PPS health-states. The methods can be applied to a single time-to-event outcome, and so have wide applicability in any field where time-to-event outcomes are reported, the proportional hazards assumption is in doubt, and survival curve shapes differ across studies and interventions. This article is protected by copyright. All rights reserved.

Assessment of Treatment Effects and Long-term Benefits in Immune Checkpoint Inhibitor Trials Using the Flexible Parametric Cure Model: A Systematic Review

IMPORTANCE

Compared with standard cytotoxic therapies, randomized immune checkpoint inhibitor (ICI) phase 3 trials reveal delayed benefits in terms of patient survival and/or long-term response. Such outcomes generally violate the assumption of proportional hazards, and the classical Cox proportional hazards regression model is therefore unsuitable for these types of analyses.

OBJECTIVE

To evaluate the ability of the flexible parametric cure model (FPCM) to estimate treatment effects and long-term responder fractions (LRFs) independently of prespecified time points.

EVIDENCE REVIEW

This systematic review used reconstructed individual patient data from ICI advanced or metastatic melanoma and lung cancer phase 3 trials extracted from the literature. Trials published between January 1, 2010, and October 1, 2019, with long-term follow-up periods (maximum follow-up, ≥36 months in first line and ≥30 months otherwise) were selected to identify LRFs. Individual patient data for progression-free survival were reconstructed from the published randomized ICI phase 3 trial results. The FPCM was applied to estimate treatment effects on the overall population and on the following components of the population: LRF and progression-free survival in non-long-term responders. Results obtained were compared with treatment effects estimated using the Cox proportional hazards regression model.

FINDINGS

In this systematic review, among the 23 comparisons studied using the FPCM, a statistically significant association between the time-to-event component and experimental treatment was observed in the main analyses and confirmed in the sensitivity analyses of 18 comparisons. Results were discordant for 4 comparisons that were not significant by the Cox proportional hazards regression model. The LRFs varied from 1.5% to 12.7% for the control arms and from 4.6% to 38.8% for the experimental arms. Differences in LRFs varied from 2% to 29% and were significantly increased in the experimental compared with the control arms, except for 4 comparisons.

CONCLUSIONS AND RELEVANCE

This systematic review of reconstructed individual patient data found that the FPCM was a complementary approach that provided a comprehensive and pertinent evaluation of benefit and risk by assessing whether ICI treatment was associated with an increased probability of patients being long-term responders or with an improved progression-free survival in patients who were not long-term responders.

Stratified Restricted Mean Survival Time Model for Marginal Causal Effect in Observational Survival Data

Time to event outcomes is commonly encountered in epidemiologic research. Multiple papers have discussed the inadequacy of using the hazard ratio as a causal effect measure due to its noncollapsibility and the time-varying nature. In this paper, we further clarified that the hazard ratio might be used as a conditional causal effect measure, but it is generally not a valid marginal effect measure, even under randomized design. We proposed to use the restricted mean survival time (RMST) difference as a causal effect measure, since it essentially measures the mean difference over a specified time horizon and has a simple interpretation as the area under survival curves. For observational studies, propensity score adjustment can be implemented with RMST estimation to remove observed confounding bias. We proposed a propensity score stratified RMST estimation strategy, which performs well in our simulation evaluation and is relatively easy to implement for epidemiologists in practice. Our stratified RMST estimation includes two different versions of implementation, depending on whether researchers want to involve regression modeling adjustment, which provides a powerful tool to examine the marginal causal effect with observational survival data.

The asymptotic distribution of the Net Benefit estimator in presence of right-censoring

The benefit-risk balance is a critical information when evaluating a new treatment. The Net Benefit has been proposed as a metric for the benefit-risk assessment, and applied in oncology to simultaneously consider gains in survival and possible side effects of chemotherapies. With complete data, one can construct a U-statistic estimator for the Net Benefit and obtain its asymptotic distribution using standard results of the U-statistic theory. However, real data is often subject to right-censoring, e.g. patient drop-out in clinical trials. It is then possible to estimate the Net Benefit using a modified U-statistic, which involves the survival time. The latter can be seen as a nuisance parameter affecting the asymptotic distribution of the Net Benefit estimator. We present here how existing asymptotic results on U-statistics can be applied to estimate the distribution of the net benefit estimator, and assess their validity in finite samples. The methodology generalizes to other statistics obtained using generalized pairwise comparisons, such as the win ratio. It is implemented in the R package BuyseTest (version 2.3.0 and later) available on Comprehensive R Archive Network.

RELAY Subgroup Analyses by EGFR Ex19del and Ex21L858R Mutations for Ramucirumab Plus Erlotinib in Metastatic Non-Small Cell Lung Cancer

PURPOSE

In EGFR-mutated metastatic non-small cell lung cancer (NSCLC), outcomes from EGFR tyrosine kinase inhibitors have differed historically by mutation type present, with lower benefit reported in patients with ex21L858R versus ex19del mutations. We investigated if EGFR-activating mutation subtypes impact treatment outcomes in the phase III RELAY study. Associations between EGFR mutation type and preexisting co-occurring and treatment-emergent genetic alterations were also explored.

PATIENTS AND METHODS

Patients with metastatic NSCLC, an EGFR ex19del or ex21L858R mutation, and no central nervous system metastases were randomized (1:1) to erlotinib (150 mg/day) with either ramucirumab (10 mg/kg; RAM+ERL) or placebo (PBO+ERL), every 2 weeks, until RECIST v1.1-defined progression or unacceptable toxicity. The primary endpoint was progression-free survival (PFS). Secondary and exploratory endpoints included overall response rate (ORR), duration of response (DOR), PFS2, time-to-chemotherapy (TTCT), safety, and next-generation sequencing analyses.

RESULTS

Patients with ex19del and ex21L858R mutations had similar clinical characteristics and comutational profiles. One-year PFS rates for ex19del patients were 74% for RAM+ERL versus 54% for PBO+ERL; for ex21L858R rates were 70% (RAM+ERL) versus 47% (PBO+ERL). Similar treatment benefits (ORR, DOR, PFS2, and TTCT) were observed in RAM+ERL-treated patients with ex19del and ex21L858R. Baseline TP53 comutation was associated with superior outcomes for RAM+ERL in both ex19del and ex21L858R subgroups. EGFR T790M mutation rate at progression was similar between treatment arms and by mutation type.

CONCLUSIONS

RAM+ERL provided significant clinical benefit for both EGFR ex19del and ex21L858R NSCLC, supporting this regimen as suitable for patients with either of these EGFR mutation types.

Window mean survival time

We propose a class of alternative estimates and tests to restricted mean survival time (RMST) which improves power in numerous survival scenarios while maintaining a level of interpretability. The industry standards for interpretable hypothesis tests in survival analysis, RMST and logrank tests (LRTs), can suffer from low power in cases where the proportional hazards assumption fails. In particular, when late differences occur between survival curves, our proposed estimate and class of tests, window mean survival time (WMST), outperforms both RMST and LRT without sacrificing interpretability, unlike weighted rank tests (WRTs). WMST has the added advantage of maintaining high power when the proportional hazards assumption is met, while WRTs do not. With testing methods often being chosen in advance of data collection, WMST can ensure adequate power without distributional assumptions and is robust to the choice of its restriction parameters. Functions for performing WMST analysis are provided in the survWM2 package in R.

Impact of follow-up on generalized pairwise comparisons for estimating the irinotecan benefit in advanced/metastatic gastric cancer

BACKGROUND AND OBJECTIVES

The net treatment effect (∆) is a new method to assess the treatment benefit that combines multiple time-to-event, binary and continuous endpoints according to a pre-specified sequence. It represents the net probability for a random patient treated in the experimental arm to have a better overall outcome than a random patient from the control arm does. We aimed at characterizing the impact of follow-up on ∆ estimated from both time-to-event and binary toxicity endpoints, in randomized controlled trials (RCTs) of irinotecan-based regimen in advanced/metastatic gastric cancer (AGC).

STUDY DESIGN

Three RCTs are reanalysed. The net treatment effect using from one to three outcomes (i.e. overall survival, time to progression and toxicity in this order) and the hazard ratio (HR) were estimated after various cut-off dates and compared to the values obtained after complete follow-up were reported.

RESULTS

In all three RCTs (897 patients), the irinotecan-based regimen was superior to the non-irinotecan containing regimen in terms of HR and ∆. This superiority was lower when the net treatment effect also accounted for toxicity. The HR was slightly less influenced by an incomplete follow-up than ∆ was, but correction proposed by Péron to account for censored observations showed quite robust results.

CONCLUSIONS

The net treatment effect using Péron's correction can be used in case of interim analyses or high censoring rates. In addition to relative measures such as the hazard ratio, it provides a simple mean to evaluate the net treatment effect with and without toxicity outcomes.

Progression-free survival in oncological clinical studies: Assessment time bias and methods for its correction

Progression-free survival (PFS) is a frequently used endpoint in oncological clinical studies. In case of PFS, potential events are progression and death. Progressions are usually observed delayed as they can be diagnosed not before the next study visit. For this reason potential bias of treatment effect estimates for progression-free survival is a concern. In randomized trials and for relative treatment effects measures like hazard ratios, bias-correcting methods are not necessarily required or have been proposed before. However, less is known on cross-trial comparisons of absolute outcome measures like median survival times. This paper proposes a new method for correcting the assessment time bias of progression-free survival estimates to allow a fair cross-trial comparison of median PFS. Using median PFS for example, the presented method approximates the unknown posterior distribution by a Bayesian approach based on simulations. It is shown that the proposed method leads to a substantial reduction of bias as compared to estimates derived from maximum likelihood or Kaplan-Meier estimates. Bias could be reduced by more than 90% over a broad range of considered situations differing in assessment times and underlying distributions. By coverage probabilities of at least 94% based on the credibility interval of the posterior distribution the resulting parameters hold common confidence levels. In summary, the proposed approach is shown to be useful for a cross-trial comparison of median PFS.

On information fraction for Fleming-Harrington type weighted log-rank tests in a group-sequential clinical trial design

When comparing survival times of treatment and control groups under a more realistic nonproportional hazards scenario, the standard log-rank (SLR) test may be replaced by a more efficient weighted log-rank (WLR) test, such as the Fleming-Harrington (FH) test. Designing a group-sequential clinical trial with one or more interim looks during which a FH test will be performed, necessitates correctly quantifying the information fraction (IF). For SLR test, IF is defined simply as the ratio of interim to final numbers of events; but for FH test, it can deviate substantially from this ratio. In this article, we separate the effect of weight function (of FH test) alone on IF from the effect of censoring. We have shown that, without considering the effect of censoring, IF can be derived analytically for FH test using information available at the design stage and the additional effect due to censoring is relatively smaller. This article intends to serve two major purposes: first, to emphasize and rationalize the deviation of IF in weighted log-rank test from that of SLR test which is often overlooked (Jiménez, Stalbovskaya, and Jones); second, although it is impossible to predict IF for a weighted log-rank test at the design stage, our decomposition of effects on IF provides a reasonable and practically feasible range of IF to work with. We illustrate our approach with an example and provide simulation results to evaluate operating characteristics.

Smoking cessation and survival among people diagnosed with non-metastatic cancer

Background

We aimed to estimate the effects of smoking cessation on survival among people diagnosed with cancer.

Methods

We used data from a Comprehensive Community Cancer Program that is part of a large urban safety-net hospital system. Eligible patients were diagnosed with primary invasive solid tumors between 2013 and 2015, and were current smokers at time of diagnosis. Our exposure of interest was initiation of smoking cessation within 6 months of cancer diagnosis. We estimated inverse probability weighted restricted mean survival time (RMST) differences and risk ratio (RR) for all cause 3-year mortality.

Results

Our study population comprised 369 patients, of whom 42% were aged < 55 years, 59% were male, 44% were racial/ethnic minorities, and 59% were uninsured. The 3-year RMST was 1.8 (95% CL: − 1.5, 5.1) months longer for individuals who initiated smoking cessation within 6 months of cancer diagnosis. The point estimate for risk of 3-year mortality was lower for initiation of smoking cessation within 6 months of diagnosis compared with no initiation within 6 months (RR = 0.72, 95% CL: 0.37, 1.4).

Conclusions

Our point estimates suggest longer 3-year survival, but the results are compatible with 1.5 month shorter or 5.1 longer 3-year overall survival after smoking cessation within 6 months of cancer diagnosis. Future studies with larger sample sizes that test the comparative effectiveness of different smoking cessation strategies are needed for more detailed evidence to inform decision-making about the effect of smoking cessation on survival among cancer patients.

Implications for Cancer survivors

The benefits of smoking cessation after cancer diagnosis may include longer survival, but the magnitude of benefit is unclear.

Optimality of testing procedures for survival data in the nonproportional hazards setting

Most statistical tests for treatment effects used in randomized clinical trials with survival outcomes are based on the proportional hazards assumption, which often fails in practice. Data from early exploratory studies may provide evidence of nonproportional hazards, which can guide the choice of alternative tests in the design of practice-changing confirmatory trials. We developed a test to detect treatment effects in a late-stage trial, which accounts for the deviations from proportional hazards suggested by early-stage data. Conditional on early-stage data, among all tests that control the frequentist Type I error rate at a fixed α level, our testing procedure maximizes the Bayesian predictive probability that the study will demonstrate the efficacy of the experimental treatment. Hence, the proposed test provides a useful benchmark for other tests commonly used in the presence of nonproportional hazards, for example, weighted log-rank tests. We illustrate this approach in simulations based on data from a published cancer immunotherapy phase III trial.

On permutation tests for comparing restricted mean survival time with small sample from randomized trials

Between-group comparison based on the restricted mean survival time (RMST) is getting attention as an alternative to the conventional logrank/hazard ratio approach for time-to-event outcomes in randomized controlled trials (RCTs). The validity of the commonly used nonparametric inference procedure for RMST has been well supported by large sample theories. However, we sometimes encounter cases with a small sample size in practice, where we cannot rely on the large sample properties. Generally, the permutation approach can be useful to handle these situations in RCTs. However, a numerical issue arises when implementing permutation tests for difference or ratio of RMST from two groups. In this article, we discuss the numerical issue and consider six permutation methods for comparing survival time distributions between two groups using RMST in RCTs setting. We conducted extensive numerical studies and assessed type I error rates of these methods. Our numerical studies demonstrated that the inflation of the type I error rate of the asymptotic methods is not negligible when sample size is small, and that all of the six permutation methods are workable solutions. Although some permutation methods became a little conservative, no remarkable inflation of the type I error rates were observed. We recommend using permutation tests instead of the asymptotic tests, especially when the sample size is less than 50 per arm.

Uses and Limitations of the Restricted Mean Survival Time: Illustrative Examples From Cardiovascular Outcomes and Mortality Trials in Type 2 Diabetes

The restricted mean survival time (RMST) has been advocated as an alternative or a supplement to the hazard ratio for reporting the effect of an intervention in a randomized clinical trial. The RMST difference allows quantification of the postponement of an outcome during a specified (restricted) interval and corresponds to the difference between the areas under the 2 survival curves for the intervention and control groups. This article presents examples of the use of the RMST in a research and a clinical context. First, the authors demonstrate how the RMST difference can answer research questions about the efficacy of different treatments. Estimates are presented for the effects of pharmacologic or strategy-driven glucose-lowering interventions for adults with type 2 diabetes from 36 trials and 9 follow-up studies reporting cardiovascular outcomes and mortality. The authors show how these measures may be used to mitigate uncertainty about the efficacy of intensive glucose control. Second, the authors demonstrate how the RMST difference may be used in the setting of a clinical consultation to guide the decision to start or discontinue a treatment. They then discuss the advantages of the RMST over the absolute risk difference, the number needed to treat, and the median survival time difference. They argue that the RMST difference is both easy to interpret and flexible in its application to different settings. Finally, they highlight the major limitations of the RMST, including difficulties in comparing studies of heterogeneous designs and in inferring the long-term effects of treatments using trials of short duration, and summarize the available statistical software for calculating the RMST.

Novel Risk Modeling Approach of Atrial Fibrillation With Restricted Mean Survival Times: Application in the Framingham Heart Study Community-Based Cohort

BACKGROUND

Risk prediction models for atrial fibrillation (AF) do not give information about when AF might develop. Restricted mean survival time (RMST) quantifies risk into the time domain. Our objective was to use RMST to re-express individualized AF risk predictions.

METHODS AND RESULTS

We included AF-free participants from the Framingham Heart Study community-based cohorts. We predicted new-onset AF over 10-year follow-up according to baseline covariates: age, height, weight, systolic blood pressure, diastolic blood pressure, current smoking, antihypertensive treatment, diabetes mellitus, prevalent heart failure, and prevalent myocardial infarction. First, we fitted a Cox regression model and estimated the 10-year predicted risk of AF. Second, we fitted an RMST model and estimated the predicted mean time free of AF and alive over a time horizon of 10 years. We included 7586 AF-free participants contributing to 11 088 examinations (mean age 61±11 years, 44% were men). During 10-year follow-up, 822 participants developed AF. The Cox and RMST models were in agreement regarding the direction, strength, and statistical significance of associations for all covariates. Low (<5%), intermediate (5%-15%), and high (>15%) 10-year predicted risk of AF corresponded to predicted mean time alive and free of AF of 9.9, 9.6, and 8.8 years, respectively. A 60-year-old woman with a body mass index of 25 kg/m2, no use of hypertension treatment and no history of heart failure had a predicted mean time alive and free of AF of 9.9 years, whereas a 70-year-old man with a body mass index of 30 kg/m2, use of hypertension treatment, and with prevalent heart failure had a predicted mean time alive and free of AF of 7.9 years.

CONCLUSIONS

The RMST can be used to develop risk prediction models to express results in a time scale. RMST may offer a complementary risk communication tool for AF in clinical practice.

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

Many clinical research studies evaluate a time-to-event outcome, illustrate survival functions, and conventionally report estimated hazard ratios to express the magnitude of the treatment effect when comparing between groups. However, it may not be straightforward to interpret the hazard ratio clinically and statistically when the proportional hazards assumption is invalid. In some recent papers published in clinical journals, the use of restricted mean survival time (RMST) or τ-year mean survival time is discussed as one of the alternative summary measures for the time-to-event outcome. The RMST is defined as the expected value of time to event limited to a specific time point corresponding to the area under the survival curve up to the specific time point. This article summarizes the necessary information to conduct statistical analysis using the RMST, including the definition and statistical properties of the RMST, adjusted analysis methods, sample size calculation, information fraction for the RMST difference, and clinical and statistical meaning and interpretation. Additionally, we discuss how to set the specific time point to define the RMST from two main points of view. We also provide developed SAS codes to determine the sample size required to detect an expected RMST difference with appropriate power and reconstruct individual survival data to estimate an RMST reference value from a reported survival curve.

Estimands and the Patient Journey: Addressing the Right Question in Oncology Clinical Trials

The diversity of patient journeys can raise fundamental questions regarding the evaluation of drug effects in clinical trials to inform clinical practice. When defining the treatment effect of interest in a trial, the researcher needs to account for events occurring after treatment initiation, such as the start of a new therapy, before observing the end point. We review the newly introduced estimand framework to structure discussions on the relationship between patient journeys and the treatment effect of interest in oncology trials. In 2017, the International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use released a draft addendum to its E9 guideline. The addendum introduces the concept of an estimand to precisely describe the treatment effect of interest. This estimand framework provides a structured approach to discuss how to account for intercurrent events that occur after random assignment and may affect the assessment or interpretation of the treatment effect. The framework is expected to improve coherence between trial objectives, design, analysis, and interpretation, as illustrated by examples in oncology disease settings. The estimand framework was applied to design a trial for a chimeric antigen receptor T-cell therapy. The treatment effect of interest was carefully defined considering the range of patient journeys expected for this particular indication and treatment. The trial design was developed accordingly to assess that treatment effect. All parties involved in the design of clinical trials need to consider possible patient journeys to define appropriate treatment effects and corresponding trial designs and analysis strategies. The estimand framework provides a common language to address the complexity introduced by varied patient journeys.

Validated Nomogram Predicting 6-Month Survival in Pancreatic Cancer Patients Receiving First-Line 5-Fluorouracil, Oxaliplatin, and Irinotecan

BACKGROUND

FOLFIRINOX (leucovorin, 5-fluorouracil, irinotecan, and oxaliplatin) is an option for fit patients with metastatic (MPC) and locally advanced unresectable (LAPC) pancreatic cancer. However, no criteria reliably identify patients with better outcomes.

PATIENTS AND METHODS

We investigated putative prognostic factors among 137 MPC/LAPC patients treated with triplet chemotherapy. Association with 6-month survival status (primary endpoint) was assessed by multivariate logistic regression models. A nomogram predicting the risk of death at 6 months was built by assigning a numeric score to each identified variable, weighted on its level of association with survival. External validation was performed in an independent data set of 206 patients. The study was registered at ClinicalTrials.gov (NCT03590275).

RESULTS

Four variables (performance status, liver metastases, baseline carbohydrate antigen 19-9 level, and neutrophil-to-lymphocyte ratio) were found to be associated with 6-month survival by multivariate analysis or had sufficient clinical plausibility to be included in the nomogram. Accuracy was confirmed in the validation cohort (C index = 0.762; 95% confidence interval, 0.713-0.825). After grouping all cases, 4 subsets with different outcomes were identified by 0, 1, 2, or > 2 poor prognostic features (P < .0001).

CONCLUSION

The nomogram we constructed accurately predicts the risk of death in the first 6 months after initiation of FOLFIRINOX in MPC/LAPC patients. This tool could be useful to guide communication about prognosis, and to inform the design and interpretation of clinical trials.