Non-proportional Hazards Research Articles

Eight‐Year Outcomes of Cardiosphere‐Derived Cells in Single Ventricle Congenital Heart Disease

Background Cardiosphere‐derived cell (CDC) infusion was associated with better clinical outcomes at 2 years in patients with single ventricle heart disease. The current study investigates time‐to‐event outcomes at 8 years. Methods and Results This cohort enrolled patients with single ventricles who underwent stage 2 or stage 3 palliation from January 2011 to January 2015 at 8 centers in Japan. The primary outcomes were time‐dependent CDC treatment effects on death and late complications during 8 years of follow‐up, assessed by restricted mean survival time. Among 93 patients enrolled (mean age, 2.3±1.3 years; 56% men), 40 received CDC infusion. Overall survival for CDC‐treated versus control patients did not differ at 8 years (hazard ratio [HR], 0.60 [95% CI, 0.21–1.77]; P =0.35). Treatment effect had nonproportional hazards for death favoring CDCs at 4 years (restricted mean survival time difference +0.33 years [95% CI, 0.01–0.66]; P =0.043). In patients with heart failure with reduced ejection fraction, CDC treatment effect on survival was greater over 8 years (restricted mean survival time difference +1.58 years [95% CI, 0.05–3.12]; P =0.043). Compared with control participants, CDC‐treated patients showed lower incidences of late failure (HR, 0.45 [95% CI, 0.21–0.93]; P =0.027) and adverse events (subdistribution HR, 0.50 [95% CI, 0.27–0.94]; P =0.036) at 8 years. Conclusions By 8 years, CDC infusion was associated with lower hazards of late failure and adverse events in single ventricle heart disease. CDC treatment effect on survival was notable by 4 years and showed a durable clinical benefit in patients with heart failure with reduced ejection fraction over 8 years. Registration URL: https://www.clinicaltrials.gov ; Unique identifiers: NCT01273857 and NCT01829750.

Treatment Effect Measures Under Nonproportional Hazards.

'Treatment effect measures under nonproportional hazards' by Snapinn etal. (Pharmaceutical Statistics, 22, 181-193) recently proposed some novel estimates of treatment effect for time-to-event endpoints. In this note, we clarify three points related to the proposed estimators that help to elucidate their properties. We hope that their work, and this commentary, will motivate further discussion concerning treatment effect measures that do not require the proportional hazards assumption.

The Time-Dependent Effect of Assistance on Peritoneal Dialysis Duration: An Analysis of Data from the French Language Peritoneal Dialysis Registry.

Key Points It is unknown whether the benefit of assisted peritoneal dialysis (PD) programs appears immediately after PD initiation or rather after some time spent on PD.The protective effect of assisted PD on the risk of transfer to hemodialysis was not constant over time; it started after the first 6 months on PD.Assisted PD programs should be sustainable for at least 6 months to observe their benefits. Background Peritoneal dialysis (PD) patient compliance is crucial for the prevention of complications. Assistance is associated with a lower risk of transfer to hemodialysis. As the risk of noncompliance increases over time, the protective effect of assistance on the risk of transfer to hemodialysis may not be immediate after PD initiation, but rather may appear after some time on PD. We aimed to analyze the time-varying effect of assistance on the risk of PD cessation. Methods This retrospective study was conducted using data from the French Language PD Registry of incident PD patients between 2002 and 2018. Because of nonproportional hazards, with a change in the effect of the assistance modality on the different outcomes appearing at 6 months after PD initiation, the associations between the assistance modality and the different outcomes were explored using time-dependent coefficient Cox regression. Results The study included 15,675 patients; 6717 deaths, 4973 transfers to hemodialysis, and 3065 kidney transplantations occurred. Both patients receiving nurse- and family-assisted PD had a lower risk of transfer to hemodialysis (mean cause-specific hazard ratio [cs-HR], 0.67; 95% confidence interval [CI], 0.62 to 0.72; and mean cs-HR, 0.75; 95% CI, 0.67 to 0.84). In the first 6 months after PD initiation, nurse-assisted PD patients had a greater risk of transfer to hemodialysis (<6 months cs-HR, 1.18; 95% CI, 1.03 to 1.36) but had a lower likelihood afterward (≥6 months cs-HR, 0.57; 95% CI, 0.53 to 0.62). Family-assisted PD was not associated with the risk of transfer to hemodialysis in the first 6 months after PD initiation, and those patients had a lower risk of transfer to hemodialysis afterward (≥6 months cs-HR, 0.72; 95% CI, 0.63 to 0.82). Conclusions When implementing a national nurse-assisted PD program, its positive impact on PD duration should not be expected immediately after PD initiation. Assisted PD programs should be sustainable for at least 6 months to observe their benefits. Podcast This article contains a podcast at https://www.asn-online.org/media/podcast/K360/2024_10_31_KID0000000577.mp3

FDA Approval Summary: Belzutifan for Patients with Advanced Renal Cell Carcinoma.

On December 14, 2023, the United States Food and Drug Administration (FDA) approved belzutifan (Welireg, Merck & Co., Inc.) for patients with advanced renal cell carcinoma (RCC) following a programmed death receptor-1 or programmed death-ligand 1 (PD-1/PD-L1) inhibitor and a vascular endothelial growth factor tyrosine kinase inhibitor (VEGF-TKI). FDA granted traditional approval based on LITESPARK-005 (NCT04195750), an open-label, randomized, head-to-head trial of 746 patients with advanced RCC that progressed following both a PD-1/PD-L1 inhibitor and a VEGF-TKI. Patients were randomized (1:1) to receive belzutifan or everolimus. The primary endpoints were progression-free survival (PFS) assessed by blinded independent central review (BICR) and overall survival (OS). A statistically significant improvement in PFS was demonstrated for belzutifan compared with everolimus [hazard ratio (HR)=0.75 (95% CI: 0.63, 0.90); 1-sided p-value=0.0008]. Kaplan-Meier curves reflected non-proportional hazards with similar median PFS estimates of 5.6 months (95% CI: 3.9, 7.0) in the belzutifan arm and 5.6 months (95% CI: 4.8, 5.8) in the everolimus arm. While not reaching full maturity, OS results appeared to show a favorable trend in the belzutifan arm compared to everolimus [HR=0.88 (95% CI: 0.73, 1.07)]. The confirmed objective response rate by BICR was 22% and 3.6% in belzutifan and everolimus arms, respectively. Observed toxicities differed between treatment arms, but drug discontinuations and interruptions due to treatment-emergent adverse events were lower on the belzutifan arm compared to the everolimus arm, and a descriptive analysis of patient-reported symptom and functional outcomes was suggestive of favorable tolerability for belzutifan compared to everolimus.

Hazard Ratios and Alternative Effect Measures: AnAppliedIllustration.

Although the limitations of hazard ratios (HRs) for quantifying treatment effects in right-censored data have been widely discussed, HRs are still preferentially reported over other, more interpretable effect measures. This may stem from the fact that there are few applied examples that directly contrast the HR and its interpretation with alternative effect measures. We analyzed data from two randomized clinical trials comparing panitumumab plus standard-of-care chemotherapy (SOCC) with SOCC alone as first- and second-line treatment for metastatic colorectal cancer. We report the effect of treatment with panitumumab on progression-free survival (PFS) using a Cox proportional hazards model to estimate the HR and the Kaplan-Meier estimator of cumulative incidence (risk). Further analyses included examining the cumulative incidence curves; kernel-smoothed, non-parametric hazards curves; fitting the Cox model with a continuous time variable; and estimating restricted mean survival as well as median survival. The HR was 0.82 (95% confidence interval [CI]: 0.71, 0.93), while the risk ratio (or relative risk [i.e., ratio of the cumulative incidence among the treated versus comparator]) was 0.99 (95% CI: 0.96, 1.02). These two measures suggest apparently different conclusions: either a treatment benefit or no effect. Through subsequent analyses, we demonstrated that, while the cumulative incidence of the outcome was similar by the end of follow-up regardless of treatment, the panitumumab treated group experienced longer PFS than those randomized to SOCC. Substantial nonproportional hazards were evident with panitumumab treatment reducing the hazard of progression/mortality during the first ~1.75 years but associated with an increased hazard of progress/mortality thereafter. This example underscores the difficulties in interpreting HRs, particularly in the setting of qualitative violations of proportional hazards, and the value of quantifying treatment effects via multiple effect measures.

Sample Size Reestimation in Stochastic Curtailment Tests With Time-to-Events Outcome in the Case of Nonproportional Hazards Utilizing Two Weibull Distributions With Unknown Shape Parameters.

Stochastic curtailment tests for Phase II two-arm trials with time-to-event end points are traditionally performed using the log-rank test. Recent advances in designing time-to-event trials have utilized the Weibull distribution with a known shape parameter estimated from historical studies. As sample size calculations depend on the value of this shape parameter, these methods either cannot be used or likely underperform/overperform when the natural variation around the point estimate is ignored. We demonstrate that when the magnitude of the Weibull shape parameters changes, unblinded interim information on the shape of the survival curves can be useful to enrich the final analysis for reestimation of the sample size. For such scenarios, we propose two Bayesian solutions to estimate the natural variations of the Weibull shape parameter. We implement these approaches under the framework of the newly proposed relative time method that allows nonproportional hazards and nonproportional time. We also demonstrate the sample size reestimation for the relative time method using three different approaches (internal pilot study approach, conditional power, and predictive power approach) at the interim stage of the trial. We demonstrate our methods using a hypothetical example and provide insights regarding the practical constraints for the proposed methods.

Sample Size Calculation Under Nonproportional Hazards Using Average Hazard Ratios.

Many clinical trials assess time-to-event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time-dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N-PHs). The findings suggest that a simulation-based sample size calculation approach can be useful for designing clinical trials with N-PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient samplesizes.

Proportional Hazards Violations in Phase III Cancer Clinical Trials: A Potential Source of Trial Misinterpretation.

Survival analyses of novel agents with long-term responders often exhibit differential hazard rates over time. Such proportional hazards violations (PHV) may reduce the power of the log-rank test and lead to misinterpretation of trial results. We aimed to characterize the incidence and study attributes associated with PHVs in phase III oncology trials and assess the utility of restricted mean survival time and maximum combination test as additional analyses. Clinicaltrials.gov and PubMed were searched to identify two-arm, randomized, phase III superiority-design cancer trials with time-to-event primary endpoints and published results through 2020. Patient-level data were reconstructed from published Kaplan-Meier curves. PHVs were assessed using Schoenfeld residuals. Three hundred fifty-seven Kaplan-Meier comparisons across 341 trials were analyzed, encompassing 292,831 enrolled patients. PHVs were identified in 85/357 [23.8%; 95% confidence interval (CI), 19.7%, 28.5%] comparisons. In multivariable analysis, non-overall survival endpoints [OR, 2.16 (95% CI, 1.21, 3.87); P = 0.009] were associated with higher odds of PHVs, and immunotherapy comparisons [OR 1.94 (95% CI, 0.98, 3.86); P = 0.058] were weakly suggestive of higher odds of PHVs. Few trials with PHVs (25/85, 29.4%) prespecified a statistical plan to account for PHVs. Fourteen trials with PHVs exhibited discordant statistical signals with restricted mean survival time or maximum combination test, of which 10 (71%) reported negative results. PHVs are common across therapy types, and attempts to account for PHVs in statistical design are lacking despite the potential for results exhibiting nonproportional hazards to be misinterpreted.

Mortality risk for kidney transplant candidates with diabetes: a population cohort study.

It is unclear whether kidney transplant candidates with diabetes have equitable transplantation opportunities or have divergent survival probabilities stratified by kidney replacement therapy. The aim of this study was to investigate these two issues using national transplant registry data in the UK. A cohort study was undertaken of prospectively collected registry data of all wait-listed people with kidney failure receiving dialysis in the UK. All people listed for their first kidney-alone transplant between 2000 and 2019 were included. Stratification was done for cause of kidney failure. Primary outcome was all-cause mortality. Time-to-death from listing was analysed using adjusted non-proportional hazard Cox regression models, with transplantation handled as a time-dependent covariate. A total of 47,917 wait-listed people with kidney failure formed the total study cohort, of whom 6594 (13.8%) had diabetes classified as cause of kidney failure. People with kidney failure with diabetes comprised 27.6% of the cohort (n=3681/13,359) that did not proceed to transplantation vs only 8.4% (n=2913/34,558) of the cohort that received a transplant (p<0.001). Kidney transplant candidates with diabetes were more likely to be older, of male sex and of ethnic minority background compared with those without diabetes. In an adjusted analysis, compared with remaining on dialysis, any kidney transplant provided survival benefit for wait-listed kidney transplant candidates regardless of diabetes as cause of kidney failure (RR 0.26 [95% CI 0.25, 0.27], p<0.001). Kidney transplant candidates with diabetes have a lower chance of transplantation despite better survival after kidney transplantation vs remaining on dialysis. The reasons for this require further investigation to ensure equal transplantation opportunities.

Survival analysis methods for time-to-event data under non-proportional hazards

Survival analysis methods for time-to-event data under non-proportional hazards

Overall survival with non-proportional hazards in first-line treatment for patients with metastatic colorectal cancer: Systematic review and network meta-analysis

This study aimed to identify the most effective first-line treatment for patients with metastatic colorectal cancer based on overall survival, identify the most commonly used treatment, and generate a meaningful ranking among all available treatments based on their relative effectiveness. Researchers used the ANOVA parametrization method to fit the second-order fractional polynomial network meta-analysis with a random-effect model. Using a non-proportional hazards network meta-analysis, 46 treatments were compared by considering a combination of direct and indirect evidence extracted from clinical trial studies. Included in the review were 46 trials involving 21350 patients. Between January 2000 and January 2023, researchers conducted a thorough search through Embase, PubMed/Medline, and Scopus. To undertake a secondary analysis of this data, we recreate individual patient data from published Kaplan-Meier (K-M) survival curves and assess the accuracy of that reconstruction. A random-effects model was used to evaluate the pooled overall survival and hazard ratio with a 95 percent confidence interval. The predicted survival curves for the network meta-analysis showed that GOLFIG and FOLFOX + Cetuximab treatments have higher survival, respectively. Our results provide moderate quality evidence and comparative effective estimates for various available first-line treatments for metastasis colorectal cancer based on network meta-analysis.

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

BackgroundPocock-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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au$$\\end{document}, both of which can be extended to adjust for randomisation stratification factors.MethodsWe 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.ResultsAcross 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.ConclusionsThe 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.

Challenges of estimating treatment effects after a positive interim analysis

BackgroundThis research investigates why a beneficial treatment effect reported at the first interim analysis (IA) may diminish at a subsequent analysis (SA). We examined three challenges in interpreting treatment effects from randomized clinical trials (RCTs) after the first positive IA: overestimation bias; non-proportional hazards; and heterogeneity in recruitment. We investigate how a penalized estimation method can address overestimation bias, and discuss additional factors to consider when interpreting positive IA results. MethodsWe identified oncology RCTs reporting positive results at the initial IA and a SA for event-free (EFS) and overall survival (OS). We modeled: (1) the hazard ratio at IA (HRIA) versus its timing as measured by the information fraction (IF; i.e., events at IA versus total events sought); and (2), the ratio of HRIA to HRSA (rHR) versus the IF. This was repeated for HRIA adjusted for overestimation bias. Examples of the other two challenges were sought. ResultsAmongst 71 RCTs, HRIA were positively associated with the IF (slope: EFS 0.83, 95 % CI 0.44–1.22; OS 0.25, 95 % CI 0.10–0.41). HRIA tended to exaggerate HRSA, and more so the lower the IF (slope rHR versus IF: EFS 0.10, 95 % CI − 0.22 to 0.42; OS 0.26, 95 % CI 0.07–0.46). Adjusted HRIA did not exaggerate HRSA (slope rHR versus IF: EFS − 0.14, 95 % CI − 0.67 to 0.39; OS 0.02, 95 % CI − 0.26 to 0.30). Examples of two other challenges are shown. ConclusionOverestimation bias, non-proportional hazards, and heterogeneity in recruitment and other important treatments should be considered when communicating estimates of treatment effects from positive IAs.

Comparative Risk of Serious Infection With Vedolizumab vs Anti-Tumor Necrosis Factor in Inflammatory Bowel Disease: Results From Nationwide Swedish Registers.

We aimed to assess the risk of serious infection in patients with inflammatory bowel disease (IBD) treated with vedolizumab compared with those treated with anti-tumor necrosis factors (TNF) and the general population. In this Swedish cohort study, treatment episodes were identified from nationwide health registers. We used Cox regression with propensity score-matched cohorts to estimate hazard ratios (HRs) for incident serious infections, defined as infections requiring hospital admission. During 1,376 treatment episodes in Crohn's disease, the rate of serious infections per 100 person-years (PY) was 5.18 (95% CI = 3.98-6.63) with vedolizumab vs 3.54 (95% CI = 2.50-4.85) with anti-TNF; HR = 1.72 (95% CI = 1.12-2.65), partly explained by more gastrointestinal infections. Compared with the rate of 0.75/100 PY (95% CI = 0.59-0.92) in a matched general population cohort, vedolizumab demonstrated higher risk (HR = 7.00; 95% CI = 5.04-9.72). During 1,294 treatment episodes in ulcerative colitis, the corresponding rates were 3.74/100 PY (95% CI = 2.66-5.11) with vedolizumab vs 3.42/100 PY (95% CI = 2.31-4.89) with anti-TNF; HR = 0.80 (95% CI = 0.47-1.36) during the initial 1.1 years and HR = 2.03 (95% CI = 0.65-6.32) after 1.1 years (truncated due to nonproportional hazards). Pneumonia accounted for 40% of all infections among anti-TNF, whereas no case was observed among vedolizumab episodes. Compared with the rate of 0.69/100 PYs (95% CI = 0.53-0.87) in a matched general population cohort, vedolizumab showed an HR of 5.45 (95% CI = 3.67-8.11). Vedolizumab was associated with increased risks of serious infections compared with anti-TNF in Crohn's disease but not in ulcerative colitis. Nonetheless, the panorama of serious infections seemed to differ between the drugs. Our findings underscore the importance of clinical awareness of infections and the safety profile of the 2 therapies.

The changing educational and social class gradients in union dissolution: Evidence from a latecomer of the Second Demographic Transition

Most studies on the changing socioeconomic gradient of divorce have operationalized individuals’ socioeconomic status (SES) through education, often neglecting social class differences. Education may proxy cultural and cognitive skills, whereas social class could more accurately capture economic means. Additionally, existing research has predominantly focused on women and marital dissolutions. This study addresses these oversights by analyzing the educational and social class gradients of both marriage and cohabitation dissolutions among men and women in Italy—a latecomer to the Second Demographic Transition. We used non-proportional hazard models to estimate survival curves and union dissolution probabilities stratified by education, social class, and cohort. Our findings reveal a vanishing socioeconomic gradient of marital dissolution among women and a reversal from positive to negative among men across cohorts. These results challenge the conventional view that men’s higher SES always stabilizes unions and support Goode’s hypothesis on the reversal of the socioeconomic gradient of divorce for both genders. No clear SES gradient was found for cohabiting unions. Overall, the study demonstrates the significant predictive power of social class for marital dissolutions, even when controlling for education, emphasizing the need to consider both measures of SES to comprehensively account for different underlying mechanisms.

Comparison of Cox regression and generalized Cox regression models to machine learning in predicting survival of children with diffuse large B-cell lymphoma.

The incidence of diffuse large B-cell lymphoma (DLBCL) in children is increasing globally. Due to the immature immune system in children, the prognosis of DLBCL is quite different from that of adults. We aim to use the multicenter large retrospective analysis for prognosis study of the disease. For our retrospective analysis, we retrieved data from the Surveillance, Epidemiology and End Results (SEER) database that included 836 DLBCL patients under 18 years old who were treated at 22 central institutions between 2000 and 2019. The patients were randomly divided into a modeling group and a validation group based on the ratio of 7:3. Cox stepwise regression, generalized Cox regression and eXtreme Gradient Boosting (XGBoost) were used to screen all variables. The selected prognostic variables were used to construct a nomogram through Cox stepwise regression. The importance of variables was ranked using XGBoost. The predictive performance of the model was assessed by using C-index, area under the curve (AUC) of receiver operating characteristic (ROC) curve, sensitivity and specificity. The consistency of the model was evaluated by using a calibration curve. The clinical practicality of the model was verified through decision curve analysis (DCA). ROC curve demonstrated that all models except the non-proportional hazards and non-log linearity (NPHNLL) model, achieved AUC values above 0.7, indicating high accuracy. The calibration curve and DCA further confirmed strong predictive performance and clinical practicability. In this study, we successfully constructed a machine learning model by combining XGBoost with Cox and generalized Cox regression models. This integrated approach accurately predicts the prognosis of children with DLBCL from multiple dimensions. These findings provide a scientific basis for accurate clinical prognosis prediction.

Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL)-2 Trial: Analysis of the Timing and Causes of Death in Participants Randomised to an Infrapopliteal Vein Bypass or Best Endovascular Treatment First Revascularisation Strategy

The Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL)-2 trial enrolled participants with chronic limb threatening ischaemia who required an infrapopliteal, with or without a femoropopliteal, revascularisation procedure to restore limb perfusion. Participants randomised to a vein bypass (VB) first revascularisation strategy were over one third more likely than those randomised to a best endovascular treatment (BET) first revascularisation strategy to die from any cause during a median follow up of 40.0 (interquartile range 20.9, 60.6) months. The aim of the present study was to describe the timing and causes of death in BASIL-2 as a first step towards trying to better understand why randomisation to a VB first revascularisation strategy was associated with this excess mortality. A 10 person international panel comprising vascular and endovascular surgeons as well as vascular interventional radiologists, who had all been principal investigators in BASIL-2, took part in a modified Delphi consensus exercise to adjudicate the primary cause of death and, in particular, whether the cause was primarily cardiac or non-cardiac. In 151 of 168 deaths (89.9%), the Delphi panel achieved a consensus regarding the cause of death being probably cardiac or non-cardiac. In the BET group, 16 of 77 deaths (21%) were classified as probably cardiac compared with 32 of 91 (35%) in the VB group (unadjusted subdistribution hazard ratio 2.16, 95% confidence interval [CI] 1.20 - 3.87; unadjusted cause specific hazard ratio 2.15, 95% CI 1.19 - 3.90). At the point of randomisation, 64 of 344 (18.6%), 40 of 342 (11.7%), and 37 of 344 (10.8%) participants had a previous myocardial infarction (MI), percutaneous coronary intervention (PCI), and coronary artery bypass graft (CABG), respectively. There was no evidence of varying treatment effects for cause of death in subgroup analyses of previous PCI, CABG, or MI. The excess mortality observed in the VB first revascularisation strategy group in BASIL-2 was largely due to deaths that were adjudicated by the Delphi panel as probably primarily cardiac. These excess cardiac deaths were observed throughout follow up and there was no evidence of non-proportional hazards. Further work is ongoing to try to better understand the reasons for these findings.

A Bayesian adaptive phase III design for multi-arm trials with time-to-event endpoint for nonproportional hazards utilizing the generalized gamma distribution

In case of trials with time-to-event endpoints, sample size calculations are well-studied under the assumption of proportional hazards or when the endpoint of interest follows an exponential distribution. When prior evidence suggests otherwise, using traditional approaches may lead to inefficiently designed and underpowered studies. In such situations, a recently introduced frequentist approach proposes a sample size calculation for a fixed two-arm trial based on the accelerated failure time model thereby allowing nonproportional hazards and can be utilized for any distribution from the generalized gamma family. Advances in the field of clinical trials research have focused on the need for adaptive phase III designs with complex features, however, existing methods in literature have ignored the nonproportional hazards scenario. In this article, we propose a Bayesian adaptive design for a multi-arm phase III trial with nonproportional hazards allowing many complex features such as incorporation of prior knowledge of early phase studies, arms dropping, and response adaptive randomization. We extend the frequentist approach utilizing a generalized gamma distribution to a Bayesian setting while simultaneously addressing one of the key limitations of the frequentist approach. Extensive simulations are performed to study the operation characteristics of the proposed design using two examples representing real-life applications.

Methods for non-proportional hazards in clinical trials: A systematic review.

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under non-proportional hazard. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific non-proportional hazard situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles.

Group sequential design for time-to-event outcome with non-proportional hazards using the concept of relative time utilizing two different Weibull distributions

A group sequential design allows investigators to sequentially monitor efficacy and safety as part of interim testing in phase III trials. Literature is well developed in the case of continuous and binary outcomes, however, in case of trials with a time-to-event outcome, popular methods of sample size calculation often assume proportional hazards. In situations where the proportional hazards assumption is inappropriate as indicated by historical data, these popular methods are very restrictive. In this paper, a novel simulation-based group sequential design is proposed for a two-arm randomized phase III clinical trial with a survival endpoint for the non-proportional hazards scenario. By assuming that the survival times for each treatment arm follow two different Weibull distributions, the proposed method utilizes the concept of Relative Time to calculate the efficacy and safety boundaries at selected interim testing points. The test statistic used to generate these boundaries is asymptotically normal, allowing p-value calculation at each boundary. Many design features specific to time-to-event data can be incorporated with ease. Additionally, the proposed method allows the flexibility of having the accelerated failure time model and the proportional hazards model as constrained special cases. Real life applications are discussed demonstrating the practicality of the proposed method.