Are non-constant rates and non-proportional treatment effects accounted for in the design and analysis of randomised controlled trials? A review of current practice

Stochastic curtailment tests for phase II trial with time-to-event outcome using the concept of relative time in the case of non-proportional hazards

As part of the drug development process, interim analysis is frequently used to design efficient phase II clinical trials. A stochastic curtailment framework is often deployed wherein a decision to continue or curtail the trial is taken at each interim look based on the likelihood of observing a positive or negative treatment effect if the trial were to continue to its anticipated end. Thus, curtailment can take place due to evidence of early efficacy or futility. Traditionally, in the case of time-to-event endpoints, interim monitoring is conducted in a two-arm clinical trial using the log-rank test, often with the assumption of proportional hazards. However, when this is violated, the log-rank test may not be appropriate, resulting in loss of power and subsequently inaccurate sample sizes. In this paper, we propose stochastic curtailment methods for two-arm phase II trial with the flexibility to allow non-proportional hazards. The proposed methods are built utilizing the concept of relative time assuming that the survival times in the two treatment arms follow two different Weibull distributions. Three methods - conditional power, predictive power and Bayesian predictive probability - are discussed along with corresponding sample size calculations. The monitoring strategy is discussed with a real-life example.

Evaluation of the proportional hazards assumption and covariate adjustment methods in comparative surgical observational studies with time-to-event endpoints

INTRODUCTION

Comparative studies on surgical treatments with time-to-event endpoints have provided substantial evidence for clinical practice, but the accurate use of survival data analysis and the control of confounding bias remain big challenges.

METHODS

This was a survey of surgical studies with survival outcomes published in four general medical journals and five general surgical journals in 2021. The two most concerned statistical issues were evaluated, including confounding control by propensity score analysis (PSA) or multivariable analysis and testing of proportional hazards (PH) assumption in Cox model.

RESULTS

A total of 74 studies were included, comprising 63 observational studies and 11 randomized controlled trials. Among the observational studies, the proportion of studies utilizing PSA in surgical oncology and non-oncology studies was similar (40.9 % versus 36.8 %, P = 0.762). However, the former reported a significantly lower proportion of PH assumption assessments compared to the latter (13.6 % versus 42.1 %, P = 0.020). Twenty-five observational studies (25/63) used PSA methods, but two-thirds of them (17/25) showed unclear balance of baseline data after PSA. And the proportion of PH assumption testing after PSA was slightly lower than that before PSA, but the difference was not statistically significant (24.0 % versus 28.0 %, P = 0.317). Comprehensive suggestions were given on confounding control in survival analysis and alternative resolutions for non-compliance with PH assumption.

CONCLUSION

This study highlights suboptimal reporting of PH assumption evaluation in observational surgical studies both before and after PSA. Efforts and consensus are needed with respect to the underlying assumptions of statistical methods.

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.

The impact of stent-graft sizing on venous stenosis re-intervention and arteriovenous graft patency: Free-floating stent outflow is associated with improved outcomes

BACKGROUND

Early cannulation arteriovenous grafts (ecAVG) for dialysis access are limited by reintervention for venous stenosis (VS) despite their good initial patency. Whilst stent-grafts (SG) have shown promise, the optimal sizing is unclear. Therefore, this study aims to determine if outflow vein diameter, SG diameter or these relative to each other (V:Sr) alters outcomes, and if so, which is more important.

METHODS

Retrospective analysis was performed of Gore® Acuseal® ecAVGs with VS treated with Gore® Viabahn® SG over a 7-year period. Primary patency (PP), time to thrombosis and functional patency were analysed by SG length/diameter, vein diameter and V:Sr.

RESULTS

We identified 114 ecAVGs with median follow-up 492 days (IQR 189-770). SG length and diameter did not correlate with PP, however, there was a significant relationship between vein diameter and PP (RR = 0.901 (0.832-0.975), p = 0.01) and between V:Sr and PP (RR = 0.462 (0.255-0.838), x2 = 5.866, p = 0.0015). The optimal V:Sr was ⩾1.4 (i.e. vein diameter at least 40% greater than the stent-graft; or 'free-floating' stent outflow) (RR = 2.759 (1.670-4.558), p < 0.001), translating to a difference in median PP of 252 versus 496 days (IQR: 188-316; 322-670). On multivariate analysis, absolute vein diameter lost significance, whilst V:Sr remained an independently significant predictor of PP (RR = 3.247 (1.560-6.759), p = 0.02).

CONCLUSIONS

Placement of the SG outflow into a relatively larger segment of vein was associated with a significant increase in PP independent of the absolute vein diameter. This suggests that larger calibre SG which are apposed to the vein wall are not required for optimal primary patency, and indeed should be actively avoided. Instead, a 'free-floating' stent outflow which is undersized relative to the recipient vein (whilst maintaining a minimum anchoring calibre) is recommended where possible. This should be considered during intervention and may require selection of longer devices, where practical, to bring the stent outflow into a larger vein segment.

LEVEL OF EVIDENCE

Level 3a, Non-randomised controlled cohort/follow-up study.

The Inverse Log-Rank Test: A Versatile Procedure for Late Separating Survival Curves

Often in the planning phase of a clinical trial, a researcher will need to choose between a standard versus weighted log-rank test (LRT) for investigating right-censored survival data. While a standard LRT is optimal for analyzing evenly distributed but distinct survival events (proportional hazards), an appropriately weighted LRT test may be better suited for handling non-proportional, delayed treatment effects. The "a priori" misspecification of this alternative may result in a substantial loss of power when determining the effectiveness of an experimental drug. In this paper, the standard unweighted and inverse log-rank tests (iLRTs) are compared with the multiple weight, default Max-Combo procedure for analyzing differential late survival outcomes. Unlike combination LRTs that depend on the arbitrary selection of weights, the iLRT by definition is a single weight test and does not require implicit multiplicity correction. Empirically, both weighted methods have reasonable flexibility for assessing continuous survival curve differences from the onset of a study. However, the iLRT may be preferable for accommodating delayed separating survival curves, especially when one arm finishes first. Using standard large-sample methods, the power and sample size for the iLRT are easily estimated without resorting to complex and timely simulations.

Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards

The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards, a log-rank test is commonly performed to investigate whether there is a difference in survival or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire range of time. Once the model's suitability is proven the method provides a noticeable power benefit, irrespectively of the shape of the hazard ratio. On the other hand, model selection should be carried out carefully as misspecification may cause type I error inflation in some situations. We investigate the robustness and demonstrate the advantages and disadvantages of the proposed methods by means of a simulation study. Finally, we demonstrate the validity of the methods by a clinical trial example.

Pre-emptive or reactive treatment, angioplasty or stent-graft? The outcome for interventions for venous stenosis in early-cannulation arteriovenous grafts

BACKGROUND

Early-cannulation arteriovenous grafts (ecAVG) have good initial patency, but frequent episodes of reintervention for venous stenosis (VS) and thrombosis limit their use. Stent grafts (SG) have shown promise in reducing re-interventions and improving functional patency for dysfunctional ecAVG and recurrent VS. There is little data on the impact of stent grafts as the first elective procedure for VS. The aim of this study was to determine firstly, if treating VS whilst asymptomatic has a better outcome than treating after presentation with thrombosis; and secondly, to determine the best initial treatment for asymptomatic VS: SG or angioplasty.

METHODS

A retrospective study was performed of 259 ecAVG with a sutured anastomosis. The case-mix and outcomes of 153 who presented with VS was analysed by presentation (elective at surveillance or emergency following thrombosis), and then for only elective patients, by treatment (SG vs angioplasty).

RESULTS

There was no significant difference in case-mix and time to presentation by mode of presentation (100 elective and 53 with thrombosis) other than a higher rate of pro-thrombotic disorders in thrombosed ecAVG. Thrombosed ecAVG had poorer outcomes with increased re-intervention rates and thrombosis in the following year, and reduced long-term functional patency. In patients presenting electively, primary SG rather than angioplasty led to significantly reduced thrombosis rates, a longer time to re-intervention in the following year, and superior long-term functional patency. The use of SG was the same in both groups. Both the mode of presentation and the type of intervention performed were independently predictive of a poorer subsequent functional patency.

CONCLUSIONS

Primary elective stent-grafting may be the optimal strategy to reducing maintenance costs with ecAVG.

Examining evidence of time-dependent treatment effects: an illustration using regression methods

BACKGROUND

For the design and analysis of clinical trials with time-to-event outcomes, the Cox proportional hazards model and the logrank test have been the cornerstone methods for many decades. Increasingly, the key assumption of proportionality-or time-fixed effects-that underpins these methods has been called into question. The availability of novel therapies with new mechanisms of action and clinical trials of longer duration mean that non-proportional hazards are now more frequently encountered.

METHODS

We compared several regression-based methods to model time-dependent treatment effects. For illustration purposes, we used selected endpoints from a large, community-based clinical trial of low dose daily aspirin in older persons. Relative and absolute estimands were defined, and analyses were conducted in all participants. Additional exploratory analyses were undertaken by selected subgroups of interest using interaction terms in the regression models.

DISCUSSION

In the trial with median 4.7 years follow-up, we found evidence for non-proportionality and a time-dependent treatment effect of aspirin on cancer mortality not previously reported in trial findings. We also found some evidence of time-dependence to an aspirin by age interaction for major adverse cardiovascular events. For other endpoints, time-fixed treatment effect estimates were confirmed as appropriate.

CONCLUSIONS

The consideration of treatment effects using both absolute and relative estimands enhanced clinical insights into potential dynamic treatment effects. We recommend these analytical approaches as an adjunct to primary analyses to fully explore findings from clinical trials.

Mortality risk and temporal patterns of atrial fibrillation in the nationwide registry

AIMS

Persistent and permanent atrial fibrillation (AF) often occurs in the presence of multiple comorbidities and is linked to adverse outcomes. It is unclear whether the sustained pattern of AF itself is prognostic or if it is confounded by underlying comorbidities. Here, we tested the association between the temporal patterns of AF and the risks of ischemic stroke and all-cause mortality.

METHODS AND RESULTS

In a prospective multicenter cohort, 3046 non-valvular AF patients were consecutively enrolled and followed for adverse outcomes of all-cause mortality and ischemic stroke. The risks of both outcomes were adjusted for underlying comorbidities, and compared between the patterns of AF. At baseline, the patients were classified as paroxysmal (N = 963, 31.6%), persistent (N = 604, 19.8%), and permanent AF (N = 1479, 45.6%) according to the standard definition. Anticoagulants were administered in 75% of all patients and 83% of those with CHA2DS2-VASc score ≥2 in males or ≥3 in females. During a mean follow up of 26 (SD 10.5) months, all-cause mortality occurred less in paroxysmal AF (2.5 per 100 patient-years) than in persistent AF (4.4 per 100 patient-years; adjusted hazard ratio [HR] 0.66, 95% CI, 0.46-0.96; P = .029) and permanent AF (4.1 per 100 patient-years; adjusted HR 0.71, 95% CI, 0.52-0.98; P = .036). The risk of ischemic stroke was similar across all patterns of AF.

CONCLUSIONS

In this multicenter cohort of AF patients, persistent and permanent AF was associated with higher all-cause mortality than paroxysmal AF, independent of baseline comorbidities.

CLINICAL TRIAL REGISTRATION

Thai Clinical Trial Registration; Study ID: TCTR20160113002 (http://www.thaiclinicaltrials.org/show/TCTR20160113002).

Impact of a non-constant baseline hazard on detection of time-dependent treatment effects: a simulation study

Background

Non-proportional hazards are common with time-to-event data but the majority of randomised clinical trials (RCTs) are designed and analysed using approaches which assume the treatment effect follows proportional hazards (PH). Recent advances in oncology treatments have identified two forms of non-PH of particular importance - a time lag until treatment becomes effective, and an early effect of treatment that ceases after a period of time. In sample size calculations for treatment effects on time-to-event outcomes where information is based on the number of events rather than the number of participants, there is crucial importance in correct specification of the baseline hazard rate amongst other considerations. Under PH, the shape of the baseline hazard has no effect on the resultant power and magnitude of treatment effects using standard analytical approaches. However, in a non-PH context the appropriateness of analytical approaches can depend on the shape of the underlying hazard.

Methods

A simulation study was undertaken to assess the impact of clinically plausible non-constant baseline hazard rates on the power, magnitude and coverage of commonly utilized regression-based measures of treatment effect and tests of survival curve difference for these two forms of non-PH used in RCTs with time-to-event outcomes.

Results

In the presence of even mild departures from PH, the power, average treatment effect size and coverage were adversely affected. Depending on the nature of the non-proportionality, non-constant event rates could further exacerbate or somewhat ameliorate the losses in power, treatment effect magnitude and coverage observed. No single summary measure of treatment effect was able to adequately describe the full extent of a potentially time-limited treatment benefit whilst maintaining power at nominal levels.

Conclusions

Our results show the increased importance of considering plausible potentially non-constant event rates when non-proportionality of treatment effects could be anticipated. In planning clinical trials with the potential for non-PH, even modest departures from an assumed constant baseline hazard could appreciably impact the power to detect treatment effects depending on the nature of the non-PH. Comprehensive analysis plans may be required to accommodate the description of time-dependent treatment effects.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01372-0.

Patient characteristics predict patency of early-cannulation arteriovenous grafts

There is a new emphasis on tailoring appropriate vascular access for hemodialysis to patients and their life-plans, but there is little known about the optimal use of newer devices such as early-cannulation arteriovenous grafts (ecAVG), with studies utilising them in a wide variety of situations. The aim of this study was to determine if the outcome of ecAVG can be predicted by patient characteristics known pre-operatively. This retrospective analysis of 278 consecutive ecAVG with minimum one-year follow-up correlated functional patency with demographic data, renal history, renal replacement and vascular access history. On univariate analysis, aetiology of renal disease, indication for an ecAVG, the number of previous tunnelled central venous catheters (TCVC) prior to insertion of an ecAVG, peripheral vascular disease, and BMI were significant associates with functional patency. On multivariate analysis the number of previous TCVC, the presence of peripheral vascular disease and indication were independently associated with outcome after allowing for age, sex and BMI. When selecting for vascular access, understanding the clinical circumstances such as indication and previous vascular access can identify patients with differing outcomes. Importantly, strategies that result in TCVC exposure have an independent and cumulative association with decreasing long-term patency for subsequent ecAVG. As such, TCVC exposure is best avoided or minimised particularly when ecAVG can be considered.