Analysis of the restricted mean survival time (RMST) has become increasingly common in biomedical studies during the last decade as a means of estimating treatment or covariate effects on survival. Advantages of RMST over the hazard ratio (HR) include increased interpretability and lack of reliance on the often tenuous proportional hazards assumption. Some authors have argued that RMST regression should generally be the frontline analysis as opposed to methods based on counting process increments. However, in order for the use of the RMST to be more mainstream, it is necessary to broaden the range of data structures to which pertinent methods can be applied. In this report, we address this issue from two angles. First, most of existing methodological development for directly modeling RMST has focused on multiplicative models. An additive model may be preferred due to goodness of fit and/or parameter interpretation. Second, many settings encountered nowadays feature high-dimensional categorical (nuisance) covariates, for which parameter estimation is best avoided. Motivated by these considerations, we propose stratified additive models for direct RMST analysis. The proposed methods feature additive covariate effects. Moreover, nuisance factors can be factored out of the estimation, akin to stratification in Cox regression, such that focus can be appropriately awarded to the parameters of chief interest. Large-sample properties of the proposed estimators are derived, and a simulation study is performed to assess finite-sample performance. In addition, we provide techniques for evaluating a fitted model with respect to risk discrimination and predictive accuracy. The proposed methods are then applied to liver transplant data to estimate the effects of donor characteristics on posttransplant survival time.

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.

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.

BACKGROUND: For biliary tract cancer (BTC), the addition of immunotherapy (durvalumab or pembrolizumab) to gemcitabine and cisplatin (GemCis) significantly improved overall survival (OS) in phase 3 clinical trials (RCTs). However, the interpretation and magnitude of the treatment effect is challenging because OS Kaplan-Meier curves violate the proportional hazards (PH) assumption. Analysis using restricted mean survival time (RMST) allows quantification of the benefits in the absence of PH. This systematic review and meta-analysis aims to assess the benefit of immunotherapy-based regimens for OS at 24 months using RMST analysis.
METHODS: A systematic review was conducted using studies published up to 8 November 2023. Only phase 3 RCTs evaluating the use of anti-PD-1/PD-L1 combined with GemCis and reporting OS were included. KM curves for OS were digitized, and the data were reconstructed. A meta-analysis for OS by RMST at 24 months was performed.
RESULTS: A total of 1754 participants from the TOPAZ-1 and KEYNOTE-966 trials were included. In TOPAZ-1, RMSTs at 24 months were 13.52 (7.92) and 12.21 (7.22) months with GemCis plus durvalumab and GemCis alone, respectively. In KEYNOTE-966, RMSTs at 24 months were 13.60 (7.76) and 12.45 (7.73) months with GemCis plus pembrolizumab and GemCis alone, respectively. Immunotherapy-based regimens showed a mean OS difference at 24 months by an RMST of 1.21 months [(95% CI: 0.49-1.93), p < 0.001, I2 = 0%].
CONCLUSIONS: Immunotherapy-based regimens improve OS in advanced BTC. Given this magnitude of benefit, it is essential to weigh up individual patient factors, preferences, and potential risks. RMST analysis provides valuable information to patients and physicians, facilitating decision-making in a value-based medical environment.

OBJECTIVE: Reduced handgrip strength (HGS) is associated with adverse clinical outcomes. We analyzed and compared associations of HGS with mortality risk in dialysis patients, using different normalization methods of HGS.
METHODS: HGS and clinical and laboratory parameters were measured in a cohort of 446 incident dialysis patients (median age 56 y, 62% men). The area under the receiver operating characteristic curve (AUROC) was used to compare different normalization methods of HGS as predictors of mortality: absolute HGS in kilograms; HGS normalized to height, weight, or body mass index; and HGS of a reference population of sex-matched controls (percentage of the mean HGS value [HGS%]). Multivariate linear regression analysis was used to assess HGS predictors. Competing risk regression analysis was used to evaluate 5-year all-cause mortality risk. Differences in survival time between HGS% tertiles were quantitated by analyzing the restricted mean survival time.
RESULTS: The AUROC for HGS% was higher than the AUROCs for absolute or normalized HGS values. Compared with the high HGS% tertile, low HGS% (subdistribution hazard ratio [sHR] = 2.36; 95% CI, 1.19-3.70) and middle HGS% (sHR = 1.79; 95% CI, 1.12-2.74) tertiles were independently associated with higher all-cause mortality and those with high HGS% tertile survived on average 7.95 mo (95% CI, 3.61-12.28) and 18.99 mo (95% CI, 14.42-23.57) longer compared with middle and low HGS% tertile, respectively.
CONCLUSIONS: HGS% was a strong predictor of all-cause mortality risk in incident dialysis patients and a better discriminator of survival than absolute HGS or HGS normalized to body size dimensions.

OBJECTIVE: The lymph node ratio (LNR) indicates the number of involved lymph nodes divided by the number of lymph nodes found during axillary exploration. This study investigated the prognostic value of the LNR in de novo metastatic breast cancer (dnMBC). We hypothesized that LNR might predict long-term survival even in cases where the disease has already disseminated beyond the regional stage.
METHODS: Patients with dnMBC were selected from the Surveillance, Epidemiology, and End Results (SEER) 9-registries database 1988-2012. Positive lymph nodes (npos) were categorized as pN0 (npos=0), pN1 (npos=1 to 3), pN2 (npos=4 to 9), and pN3 (npos≥10). The LNR was categorized as Lnr0 (LNR=0), Lnr1 (LNR=0.01 to 0.20), Lnr2 (LNR=0.21 to 0.65), and Lnr3 (LNR≥0.65). The prognostic values were compared using Gini\'s mean difference Δ of the restricted mean overall survival time (RMST) according to npos versus LNR groups.
RESULTS: A total of 12,085 patients with dnMBC had LNR data. At 25 years follow-up, the npos RMSTs were 10.4, 5.1, 5.8, and 5.0 years, for pN0 to pN3, respectively. The npos Gini\'s Δ was 2.8 years (standard error ±0.2). The LNR RMSTs were 10.4, 9.9, 7.6, and 4.0 years for Lnr0 to Lnr3, respectively. Δ for LNR was 3.6 (±0.2) years. Among node positive cases, the LNR low-risk group had an RMST of 9.9 years, approaching node-negative cases, while the high-risk group had an RMST of 4.0 years.
CONCLUSIONS: LNR identified different prognostic groups, suggesting a possible role of lymph node involvement as a marker of lymphangiogenesis or lymphatic changes in the immune microenvironment, which warrants further investigation in dnMBC.

Individual patient data (IPD) meta-analyses build upon traditional (aggregate data) meta-analyses by collecting IPD from the individual studies rather than using aggregated summary data. Although both traditional and IPD meta-analyses produce a summary effect estimate, IPD meta-analyses allow for the analysis of data to be performed as a single dataset. This allows for standardization of exposure, outcomes, and analytic methods across individual studies. IPD meta-analyses also allow the utilization of statistical methods typically used in cohort studies, such as multivariable regression, survival analysis, propensity score matching, uniform subgroup and sensitivity analyses, better management of missing data, and incorporation of unpublished data. However, they are more time-intensive, costly, and subject to participation bias. A separate issue relates to the meta-analytic challenges when the proportional hazards assumption is violated. In these instances, alternative methods of reporting time-to-event estimates, such as restricted mean survival time should be used. This statistical primer summarizes key concepts in both scenarios and provides pertinent examples.

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.

To evaluate the efficacy and safety of the polytetrafluoroethylene (PTFE) mesh by comparing conventionally used polypropylene (PP) mesh in tension-free vaginal mesh (TVM) surgery for pelvic organ prolapse (POP).
We conducted an observational cohort study of patients who underwent TVM using a PTFE or PP mesh. PTFE was used from June 2019 to May 2021, and PP mesh from January 2018 to May 2019. Outcomes included POP recurrence, perioperative complications, and patient satisfaction. Restricted mean survival time was used to analyze POP recurrence, comparing the time to recurrence between the two groups at 1year after TVM.
Of 171 patients, 104 underwent PP mesh placement (PP group) and 67 underwent PTFE mesh placement (PTFE group). POP recurrence was observed in 10 and nine patients in the PP and PTFE groups, respectively. The mean time until the recurrence in the PTFE group was significantly shorter than that in the PP group (restricted mean survival time difference: -20.3days; 95% CI, -40.1 to -0.5; P = .044). Subgroup analysis revealed the meantime until recurrence was significantly shorter in the PTFE group for postoperative periods 3months or less, ages >70years, and POP stage ≥3. There were no intervention cases in either group and no significant differences in the perioperative complications. Patient satisfaction was greater in the PTFE group after 3months postoperatively.
TVM surgery with a PTFE mesh is more prone to recurrence than that with a PP mesh, but with higher patient satisfaction. Within 3months of surgery, elderly patients and those with advanced-stage POP require care to prevent recurrence.

BACKGROUND: In health technology assessment, restricted mean survival time and life expectancy are commonly evaluated. Parametric models are typically used for extrapolation. Spline models using a relative survival framework have been shown to estimate life expectancy of cancer patients more reliably; however, more research is needed to assess spline models using an all-cause survival framework and standard parametric models using a relative survival framework.
OBJECTIVE: To assess survival extrapolation using standard parametric models and spline models within relative survival and all-cause survival frameworks.
METHODS: From the Swedish Cancer Registry, we identified patients diagnosed with 5 types of cancer (colon, breast, melanoma, prostate, and chronic myeloid leukemia) between 1981 and 1990 with follow-up until 2020. Patients were categorized into 15 cancer cohorts by cancer and age group (18-59, 60-69, and 70-99 y). We right-censored the follow-up at 2, 3, 5, and 10 y and fitted the parametric models within an all-cause and a relative survival framework to extrapolate to 10 y and lifetime in comparison with the observed Kaplan-Meier survival estimates. All cohorts were modeled with 6 standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal, and generalized gamma) and 3 spline models (on hazard, odds, and normal scales).
RESULTS: For predicting 10-y survival, spline models generally performed better than standard parametric models. However, using an all-cause or a relative survival framework did not show any distinct difference. For lifetime survival, extrapolating from a relative survival framework agreed better with the observed survival, particularly using spline models.
CONCLUSIONS: For extrapolation to 10 y, we recommend spline models. For extrapolation to lifetime, we suggest extrapolating in a relative survival framework, especially using spline models.
CONCLUSIONS: For survival extrapolation to 10 y, spline models generally performed better than standard parametric models did. However, using an all-cause or a relative survival framework showed no distinct difference under the same parametric model.Survival extrapolation to lifetime within a relative survival framework agreed well with the observed data, especially using spline models.Extrapolating parametric models within an all-cause survival framework may overestimate survival proportions at lifetime; models for the relative survival approach may underestimate instead.