Nonparametric estimation of average effects of a continuous treatment for survival data with a cured fraction.

BackgroundThe data from immuno-oncology (IO) therapy trials often show delayed effects, cure rate, crossing hazards, or some mixture of these phenomena. Thus, the proportional hazards (PH) assumption is often violated such that the commonly used log-rank test can be very underpowered. In these trials, the conventional hazard ratio for describing the treatment effect may not be a good estimand due to the lack of an easily understandable interpretation. To overcome this challenge, restricted mean survival time (RMST) has been strongly recommended for survival analysis in clinical literature due to its independence of the PH assumption as well as a more clinically meaningful interpretation. The RMST also aligns well with the estimand associated with the analysis from the recommendation in ICH E-9 (R1), and the test/estimation coherency. Currently, the Kaplan Meier (KM) curve is commonly applied to RMST related analyses. Due to some drawbacks of the KM approach such as the limitation in extrapolating to time points beyond the follow-up time, and the large variance at time points with small numbers of events, the RMST may be hindered.MethodsThe dynamic RMST curve using a mixture model is proposed in this paper to fully enhance the RMST method for survival analysis in clinical trials. It is constructed that the RMST difference or ratio is computed over a range of values to the restriction time τ which traces out an evolving treatment effect profile over time.ResultsThis new dynamic RMST curve overcomes the drawbacks from the KM approach. The good performance of this proposal is illustrated through three real examples.ConclusionsThe RMST provides a clinically meaningful and easily interpretable measure for survival clinical trials. The proposed dynamic RMST approach provides a useful tool for assessing treatment effect over different time frames for survival clinical trials. This dynamic RMST curve also allows ones for checking whether the follow-up time for a study is long enough to demonstrate a treatment difference. The prediction feature of the dynamic RMST analysis may be used for determining an appropriate time point for an interim analysis, and the data monitoring committee (DMC) can use this evaluation tool for study recommendation.

The difference in mean survival time, which quantifies the treatment effect in terms most meaningful to patients and retains its interpretability regardless of the shape of the survival distribution or the proportionality of the treatment effect, is an alternative endpoint that could be used more often as the primary endpoint to design clinical trials. The underuse of this endpoint is due to investigators' lack of familiarity with the test comparing the 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 restricted mean survival time as the primary endpoint. A closed-form formula for the asymptotic power of the test of restricted mean survival time difference is presented. The effects of design parameters on power were evaluated for the mean survival time test and log-rank test. An R package which calculates the power or the sample size for user-specified parameter values and provides power plots for each design parameter is provided. The R package also calculates the probability that the restricted mean survival time is estimable for user-defined trial designs. Under proportional hazards and late differences in survival, the power of the mean survival time test can approach that of the log-rank test if the restriction time is late. Under early differences, the power of the restricted mean survival time test is higher than that of the log-rank test. Duration of accrual and follow-up have little influence on the power of the restricted mean survival time test. The choice of restriction time, on the other hand, has a large impact on power. Because the power depends on the interplay among the design factors, plotting the relationship between each design parameter and power allows the users to select the designs most appropriate for their trial. When modification is necessary to ensure the difference in restricted mean survival time is estimable, the three available modifications all perform adequately in the scenarios studied. The restricted mean survival time is a survival endpoint that is meaningful to investigators and to patients and at the same time requires less restrictive assumptions. The biggest challenge with this endpoint is selection of the restriction time. We recommend selecting a restriction time that is clinically relevant to the disease and the clinical setting of the trial of interest. The practical considerations and the R package provided in this work are readily available tools that researchers can use to design trials with restricted mean survival time as the primary endpoint.

e16222 Background: Recently, immunotherapy has played a crucial role in treating liver cancer, one of the major cancers that contributes to global cancer burden. Overall survival (OS) is widely applied in cancer trials to evaluate the treatment effects of new therapies. However, it requires more patients and longer follow-up time comparing with progression-free survival (PFS). In addition, while assessing the treatment effects of cancer immunotherapy, proportional hazard (PH) assumption is often violated due to issues such as delayed treatment effects. Restricted Mean Survival Time (RMST) ratio is increasingly used for treatment effect evaluation when the PH assumption is violated. Such change prompts an important question whether the surrogacy value of PFS will be affected when RMST ratio is used to characterize treatment effect. The aim of this study is to examine the feasibility of using PFS as a surrogate endpoint for OS when the treatment effect is measured using hazard ratio (HR) versus RMST ratio. Methods: The surrogacy of PFS on OS was evaluated through examining the association between PFS and OS using HR and RMST ratio. Seven immunotherapy studies published between 2000 and 2021 were included (Table). Information of examined studies such as treatment arms information, OS and PFS were collected. RMST ratio for PFS and OS were calculated based on the Kaplan-Meier plots extracted from each article using WebPlotDigitizer 4.4. The weighted least square regression lines and R^2 between OS and PFS for HR and RMST ratio were calculated. Results: Among 7 immunotherapy studies, 4 gave placebos to the control arms as treatments. 2 provided Sorafenib and 1 assigned the same drug as treatment arm but with different schedule. All 7 studies had OS and PFS as the endpoints. 2 studies violated the PH assumptions. Based on the data extracted from examined articles, a moderate correlation (0.52) between PFS and OS was observed for HR while low correlation (0.10) was observed for RMST ratio. Conclusions: The R^2 values differ greatly depending on whether HR or RMST ratio was used for assessing surrogacy. Our finding may have important implications for the design of future immunotherapy liver cancer trials. For future work, increasing the number of included studies for a more comprehensive analysis is needed. Moreover, trial-level surrogacy analysis should be conducted to complement the study-level investigation.[Table: see text]

Estimating the difference in restricted mean survival time accounting for trial effect in individual patient data meta-analyses

Validating Restricted Mean Survival Time Estimates From Reconstructed Kaplan-Meier Data Against Original Trial Individual Patient Data From Trials Conducted by the Canadian Cancer Trials Group

Azacitidine Treatment in MDS: A Systematic Literature Review and Meta-Analysis Comparing the Efficacy of Real World Data with Randomized Controlled Trials

Parametric Survival Extrapolation of Early Survival Data in Economic Analyses: A Comparison of Projected Versus Observed Updated Survival

597 Background: In advanced hepatocellular carcinoma (aHCC), the evaluation of overall survival (OS) and progression-free survival (PFS) through restricted mean survival time (RMST) provides a nuanced understanding of treatment efficacy. The RMST analysis serves as a valuable complement to the hazard ratio (HR) analysis, offering insights into the average survival time over a specified period. This study compares RMST analyses of OS at 24 and 36 months, and PFS at 12 and 18 months, across five pivotal phase III trials: IMbrave-150, ORIENT-32, CARES-310, HIMALAYA, and CM-9DW. Methods: Data from the experimental arms of the five phase III trials were analyzed. The RMST was calculated using the area under the Kaplan-Meier survival curves up to the specified time points. Specifically, OS was evaluated at 24 and 36 months, and PFS at 12 and 18 months. The RMST provides an estimate of the average time that patients survive (for OS) or remain progression-free (for PFS) within a specific timeframe. Kaplan-Meier survival curves were digitized if not available in raw form, and the area under the curve (AUC) was computed using numerical integration methods. RMST values were extracted from the AUC for the specified periods. This approach accounts for censored data and provides a robust comparison of survival times across different treatment groups. Results: The results for OS RMST at 24 and 36 months and PFS RMST at 12 and 18 months are summarized in the table. Conclusions: Angiogenesis inhibitor + immune checkpoint inhibitor combinations (Atezolizumab + Bevacizumab; Sintilimab + IBI305) provide the most favorable RMST outcomes in terms of OS and PFS. Restricted mean survival time (RMST) comparison of OS and PFS (months). aHCC 1L Phase III Trials Treatment Arm OS 24m OS 36m PFS 12m PFS 18m IMbrave-150 1, 2 Atezolizumab + Bevacizumab 17.50 22.79 9.69 13.29 ORIENT-32 3 Sinitilimab + IBI305 17.01 21.09 9.18 12.54 CARES-310 4 Camrelizumab + Rivoracenib 16.34 19.75 9.29 12.14 HIMALAYA 5, 6 Tremelimumab + Durvalumab 15.36 18.76 8.95 12.02 CM-9DW 7, 8 Nivolumab + Ipilimumab 15.87 20.08 8.74 11.78 1 Finn et al. N Engl J Med 2020;382:1894-905; 2 Cheng et al. J Hepatol 2022;76:862-873; 3 Ren et al. Lancet Oncol 2021;22:977–90; 4 Qin et al. Lancet 2023;402:1133–46; 5 Abou-Alfa et al. NEJM Evid 2022;1(8):EVIDoa2100070; 6 Sangro et al. Ann Oncol 2024;35:448-457; 7 Galle et al. J Clin Oncol 2024;42(suppl 17):abstr LBA4008; 8 Decaens et al. Ann Oncol 2024;35:S657.

The t-year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window [0, t]. RMST is the patient's life expectancy until time t and can be estimated nonparametrically by the area under the Kaplan-Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between-group-difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, t] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data-dependent. The standard inferential procedures for the corresponding RMST, which is also data-dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random "parameter." Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow-up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulationstudy.

At the 2020 ASCO Meeting, important findings have been presented on the effectiveness of idecabtagene vicleucel (ie, CAR-T by Bristol/Bluebird also denoted as ide-cel-bb2121) in heavily pretreated multiple myeloma patients. The outcomes in 128 patients given idecabtagene vicleucel in the KarMMa trial (dose: 150 to 450 × 106 CAR+ T cells) were indirectly compared with those of 190 patients selected from a real-world database of 1949 patients. The subgroup of 190 patients was identified through propensity matching to represent an adequate control group for the 128 patients of the KarMMa trial. All patients had received at least three previous lines of treatment. The endpoint was progression-free survival (PFS). The median PFS was 11.3 months in the treatment group and 3.5 months in the controls [1]. In the last years, an extensive literature has accumulated on the use of restricted mean survival time (RMST) for the interpretation of survival curves [2-10]. In comparison with traditional analyses based on hazard ratio (HR) and medians, the RMST has important advantages because it examines the entire survival curve (like the HR) and expresses the survival outcomes using a scale of time (like medians). Most previous experiences on the application of RMST are focused on oncology [2-8]. Quite recently, the application of RMST has been investigated in the field of CAR-T [11, 12]. Briefly, the RMST combines the main advantages of HR and medians without possessing their disadvantages. From a practical point of view, the RMST is characterized by a high mathematical complexity of its statistical calculations [2-10]. However, recent papers have suggested an original method of calculation, drawn from the field of pharmacokinetics, that allows for an extreme simplification of RMST estimation. This new method [13-15], derived from pharmacokinetics, first requires to digitize the published graph of the Kaplan-Meier curve [16]; this generates around 50-100 data pairs of survival probability-versus-time (ie, y-vs-x data pairs); then, as in pharmacokinetics, the trapezoidal rule is applied to determine the area under the curve (AUC) using a simple Excel subroutine [17]. The AUC is known to be equal to the RMST. In the present analysis, we employed the RMST to assess the PFS gain for heavily pretreated patients given idecabtagene vicleucel (experimental group) versus matched control patients of the real world (Figure 1). Our results based on the RMST were compared with those based on the medians originally reported in the study by Jagannath and co-workers [1] (Table 1). The main original finding expected from our indirect comparison was to estimate the PFS gain for CAR-T compared with the controls according to the RMST methodology. Apart from its level of statistical significance, the extent of this PFS improvement in favor of CART-T was quite small when assessed through the RMST (gain of 3.41 months at 18 months, ie, the difference of 7.80 minus 3.41 months; Table 1). In contrast, the gain estimated from the medians by Jagannath et al. [1] was much longer (7.80 months). The RMST in fact generates more stable and more reliable gains than the median because the median has a “punctiform” nature and, therefore, is strongly influenced by the small portion of follow-up when residual survival goes from >50% to <50%. Of course, beyond the milestone currently set at 18 months, the patients given CAR-T might have, in future perspective, a longer additional PFS than those not given CAR-T, but this hypothesis will need confirmation by studying the patients of the KarMMa trial on the long term. Because the information about the efficacy of CAR-T in multiple myeloma is still very limited, the comparison presented herein is interesting because it is the only one that can presently be made. Two conclusions are suggested by our analysis. First, the RMST is shown to be a suitable parameter for managing the PFS data of multiple myeloma patients receiving a CAR-T. Second, the RMST analysis based on the outcomes currently available does not demonstrate any breakthrough PFS advantage for idecabtagene vicleucel in comparison with treatments not involving any gene manipulations. In conclusion, when the RMST is employed as the outcome measure of the analysis, the relevance of the clinical advantage generated by CAR-T in patients with myeloma seems to be more limited than that suggested by the medians and reported in the KarMMa trial [1]. The author declares no conflict of interest.

Restricted Mean Survival Time for Analysis and Interpretation of Clinical Trials for Heart Failure Devices

Programmed Death-1 or Programmed Death Ligand-1 Blockade in Patients with Platinum-resistant Metastatic Urothelial Cancer: A Systematic Review and Meta-analysis

Utility of Restricted Mean Survival Time Analysis for Heart Failure Clinical Trial Evaluation and Interpretation

HomeCirculationVol. 143, No. 6Letter by Ferracane et al Regarding Article, “Comparative Efficacy and Safety of Oral P2Y12 Inhibitors in Acute Coronary Syndrome: Network Meta-Analysis of 52 816 Patients From 12 Randomized Trials” Free AccessLetterPDF/EPUBAboutView PDFView EPUBSections ToolsAdd to favoritesDownload citationsTrack citationsPermissions ShareShare onFacebookTwitterLinked InMendeleyRedditDiggEmail Jump toFree AccessLetterPDF/EPUBLetter by Ferracane et al Regarding Article, “Comparative Efficacy and Safety of Oral P2Y12 Inhibitors in Acute Coronary Syndrome: Network Meta-Analysis of 52 816 Patients From 12 Randomized Trials” Elisa Ferracane, PharmD, Laura Bartoli, PharmD and Andrea Messori, PharmD Elisa FerracaneElisa Ferracane https://orcid.org/0000-0001-6888-8040 HTA Unit, Toscana Region Health Service, Firenze, Italy. Search for more papers by this author , Laura BartoliLaura Bartoli HTA Unit, Toscana Region Health Service, Firenze, Italy. Search for more papers by this author and Andrea MessoriAndrea Messori https://orcid.org/0000-0002-5829-107X HTA Unit, Toscana Region Health Service, Firenze, Italy. Search for more papers by this author Originally published8 Feb 2021https://doi.org/10.1161/CIRCULATIONAHA.120.050472Circulation. 2021;143:e232–e233To the Editor:Navarese and coworkers1 performed a network meta-analysis to compare oral P2Y12 inhibitors in acute coronary syndrome. Twelve randomized trials were studied. The main efficacy end points included cardiovascular mortality, nonfatal myocardial infarction, all-cause mortality, stroke, and stent thrombosis, which were assessed separately. The composite end point of major cardiovascular events was not included. The hazard ratio (HR) was the outcome measure.Regarding efficacy, the results showed that ticagrelor and prasugrel reduced cardiovascular mortality compared with clopidogrel.1 Similar advantages were found for ticagrelor or prasugrel concerning most of the other end points of efficacy. In contrast, ticagrelor and prasugrel increased major bleeding compared with clopidogrel.A wide literature has recently focused on some important disadvantages of the HR because this measure frequently violates the proportional hazard model and also because of its nature of relative outcome measure2,3; more important, the HR tends to overemphasize the difference in favor of the more effective treatment. The restricted mean survival time (RMST), an absolute outcome measure similar to the median, is increasingly recognized to perform better. In particular, the RMST is more stable than the median and, unlike the median, can be computed from any Kaplan-Meier curve irrespective of the cumulative event frequency reached in the curve.2,3According to the composite end point of major cardiovascular events, we reanalyzed the 12 randomized trials of Navarese et al1 using the RMST rather than the HR. Three studies were excluded because they did not report any Kaplan-Meier curves. Another was excluded because its follow-up lasted 6 months. The remaining 8 trials (based on clopidogrel, prasugrel, or ticagrelor) were reexamined using the RMST as opposed to the HR. The RMST (estimated from the Kaplan-Meier curves) was applied in its model-independent method.5In a separate report,4 we have presented these RMST results, including an analysis that ranked the RMSTs across the 16 cohorts. Prasugrel ranked 1st (11.39 months), 3rd (11.32 months), 8th (11.08 months), 9th (10.99 months), and 14th (10.52 months); ticagrelor 4th (11.28 months), 5th (11.15 months), 6th (11.13 months), 7th (11.10 months), and 11th (10.98 months); clopidogrel 2nd (11.36 months), 10th (10.99 months), 12th (10.95 months), 13th (10.86), 15th (10.52 months), and 16th (10.15 months).These results clearly convey that the 16 cohorts have a nearly identical effectiveness; eg, the greatest difference across these 16 cohorts is between prasugrel in the trial by Schüpke et al (ranking first with 11.39 months) and clopidogrel in the trial by Wang and Wang (ranking last with 10.15 months)1; this difference is of only 1.2 months.Although this reanalysis consists of indirect comparisons managed narratively and has lost its linkage with randomization, the overall picture emerging from these RMSTs is a strong message of equivalent effectiveness across clopidogrel, prasugrel, and ticagrelor. Although some pairwise comparisons reached statistical significance, the criterion of clinical relevance guides the interpretation of these results because all pairwise differences are small. The message of the HR focused on differences is reinterpreted as a message of equivalent effectiveness based on the RMST.Disclosures None.Footnoteshttps://www.ahajournals.org/journal/circ

BackgroundRestricted mean survival time (RMST) endpoints are becoming commonly used as trialists look to analyse time-to-event outcomes without the restrictions of the proportional hazards assumption. An additional benefit of RMST endpoints which has so far remained unexplored is their capability to combine treatment main effects and treatment-by-covariate interaction terms into single one-dimensional estimators under both proportional and non-proportional hazards. By utilising RMST estimators, trialists may assess treatment effects associated with multiple covariates, including interaction terms — an inherent limitation of proportional hazards models when this assumption is violated.MethodsWe present a simulation study using a case study of a randomised controlled trial of Gamma interferon for the treatment of chronic granulomatous disease. We evaluate the power and type I error rate of parametric and non-parametric RMST estimators of combined treatment effects under both proportional and non-proportional hazards. Performance is evaluated when the model or the knot point is specified correctly or misspecified. We also explore the effect of truncation time.ResultsSimulations show that parametric RMST estimators offer greater power when covariate effects and knot-point locations are correctly specified or only mildly misspecified. However, their performance deteriorates as omitted covariate effects increase or knot locations become more misspecified. Under substantial misspecification, the non-parametric estimator is more robust, maintaining stable type I error rates and improved power. For the non-parametric approach, power increases with later truncation times.ConclusionsThis paper demonstrates the role of RMST estimators for survival analysis in the presence of main treatment effects and treatment-by-covariate interactions — highlighting the utility of RMST estimators in the analysis of trials with combined treatment effects. This paper offers further practical guidance on the strengths and limitations of parametric and non-parametric RMST estimators in the presence of model misspecification. It also serves as a case study for trialists wishing to explore RMST estimators by simulations tailored to their own research context.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13063-026-09666-8.