Conference Agenda

Background:

Repeat events analyses are sometimes used as the primary outcome in randomized trials in heart failure, often due to a perception that including more events will increase statistical power. Such analyses frequently use negative binomial or LWYY models – extensions of Poisson and Cox regression. These models allow for variation in underlying disease risk between patients, but ignore the time-dependency of events within a patient. We aimed to assess (i) the time-clustering of repeat outcomes over time; (ii) whether using repeat events analyses improves statistical power

Methods:

We use data from four large trials in chronic heart failure (EMPEROR-Reduced, EMPEROR-Preserved, DAPA-HF and DELIVER), each with a primary outcome of heart failure hospitalisation (HFH) or cardiovascular death. We explore the time-clustering of outcome events and develop a method for quantifying it. We compare the use of time-to-first event versus recurrent events for estimating treatment benefit. To do so we use two non-parametric methods: the win ratio method and the area under the curve (AUC) method – an extension of restricted mean survival time for repeat events.

Results:

With 20,725 patients in all four trials, there were 1,844 cardiovascular deaths, and 3,913 HFHs in 2,494 patients. The distribution of HFHs was highly skewed, with a few patients having many events. The mean time between consecutive HFHs within a patient was 20%-24% shorter than if they occurred randomly over time. Following an HFH, subsequent rehospitalization for heart failure or cardiovascular death were markedly more common, particularly in the first 3 months post-discharge (adjusted hazard ratios: 5.5 to 10.5 and 6.3 to 8.8, respectively). While decreasing over time, the risk of subsequent rehospitalization or cardiovascular death remains significantly elevated, even after 1 year post-discharge. In analyses using the win ratio and AUC, using repeat event analyses rather than time-to-first event led to a less statistically significant estimate of treatment effect in 3 out of 4 trials. Similar findings occurred using negative binomial and LWYY models, though the value of these approaches can be questioned given they do not take account of time-clustering.

Discussion:

The perception that using repeat events rather than time-to-first event gains statistical power in heart failure trials appears to be misplaced. This appears due to the highly skew distribution of repeat events, and the strong time-clustering of events within patients. We looked at drug treatment trials in chronic heart failure; findings may be different for other trial types.

We revisit the question of what randomization ratio (RR) maximizes power of the logrank test in event-driven survival trials under proportional hazards (PH). By comparing three approximations of the logrank test (Schoenfeld, Freedman, Rubinstein) to empirical simulations, we find that the RR that maximizes power is the RR that balances number of events across treatment arms at the end of the trial. This contradicts the common misconception implied by Schoenfeld's approximation that 1:1 randomization maximizes power. Besides power, we consider other factors that might influence the choice of RR (accrual, trial duration, sample size, etc.). We perform simulations to better understand how unequal randomization might impact these factors in practice. Altogether, we derive 5 insights to guide statisticians in the design of survival trials considering unequal randomization.

Background / Introduction: We consider a two-arm randomized clinical trial in precision oncology with time-to-event endpoint. The control arm consists of standard of care (SOC) whereas patients in the treatment arm are offered personalized treatment, when available. Patients in the personalized treatment arm, for which no personalized treatment is available or who do not consent to treatment also receive SOC. Intention-to-treat analysis hence involves comparing the outcomes of a group of patients receiving either personalized treatment or SOC to patients receiving exclusively SOC. This does not lead to an unbiased estimator of the treatment effect for those eligible for personalized treatment in the classical intention-to-treat approach.

Methods: We investigate the performance of intention-to-treat and per-protocol analyses and develop more appropriate alternative analysis schemes. For this purpose, the patients are divided into groups based on whether they receive their intended treatment or not. An extension of the Cox proportional hazards model is proposed for estimating the conditional intensities in each group simultaneously via Maximum Likelihood estimation on the partial likelihoods. Counting process theory as well as martingale theory is used to develop suitable test statistics for various settings of interest. Both groups can be evaluated distinctly, thus enabling comparison between groups. This includes the investigation of a possible selection effect via the groups’ respective regression coefficients.

Results: A regression model is proposed that allows for modelling the differences between complying patients and non-complying patients, which enables the evaluation of the selection effect in the case of asymmetric trial arms. An in-depth simulation study and a real data example complement the theoretical results.

Conclusion: A novel more rigorous model for the analysis of the treatment effect in the presence of mixtures or asymmetric trials is proposed. Guidelines are provided to identify scenarios where this model is necessary or appropriate, and when a classical intention-to-treat analysis remains preferable.

Background: Two-Stage-Randomization-Design (TSRD) trials are common in clinical research, where patients firstly randomized between two induction regimens followed by another randomization to different maintenance therapies conditional on response to induction. In cancer trials using TSRD, patients seek to understand the failure-free survival (FFS) and overall survival (OS) for a specific combination of induction and maintenance therapies. However, the primary analysis usually focuses on survival estimates of the maintenance part limited to patients randomized in maintenance phase, neglecting the efficacy of adaptive treatment combinations of induction and maintenance according to the intention-to-treat (ITT) principle. Inverse-Propensity -Weighting (IPW) has been proposed to estimate the survival including non-randomized patients. However, it relies heavily on the accurate selection of baseline characteristics and assumes no confounding factors are present. We propose a novel and a simpler method for estimating the intent-to-treat effect: retrospective randomization.

Methods: The principle of retrospective randomization is to mimic a study design of prospective, up-front randomization. In our approach, the non-randomized patients undergo retrospective randomization between maintenance arms during the statistical analysis steps, using the same stratification factors employed in the patients prospectively randomized. This process of retrospective randomization is repeated multiple times. The FFS and associated hazard ratios are then estimated by combining the results obtained from each iteration, including patients prospectively and retrospectively randomized for maintenance treatment.

Clinical data with TSRD were simulated to contain patients’ demographics, response status and time to response to the induction therapy and FFS from the maintenance phase randomization. The disease response rate to the induction therapy, randomization proportion out of all responders and the outcome by remission status varied across scenarios. For comparison purpose, the IPW method was also applied for the FFS estimation. The performance of the proposed retrospective randomization method was evaluated using bias and root mean squared error (RMSE) compared to the true estimates of FFS. Analysis was also performed in a double randomized Mantle Cell Lymphoma (MCL) elderly trial of the European MCL Network.

Results and conclusion: Across different simulation scenarios and in the case study, the retrospective randomization method delivers survival estimates close to the actual values of the intention-to-treat population and a more meaningful estimate than the estimates provided in primary maintenance analysis. Our method achieves comparable or even better performance in some scenarios than the IPW method in terms of bias and RMSE, while offering advantages in implementation simplicity and reduced reliance on assumption.

We consider how to compare treatments based on a randomized clinical trial (RCT) when
the outcome of interest is the number of recurrent events. The interest from the medical
perspective is to find the treatment that leads to the lowest expected number of recurrent
events. This question can often be addressed by using Andersen-Gill type models with robust
standard errors. The efficiency can be improved by using auxiliary covariate information that
is often available. We show how this can accomplished by extending the augmentation
approach of Lu & Tsiatis (2008a), and that this ensures robustness to misspecifications
when testing for no-treatment effects.The efficiency gain obtained from auxiliary covariates
is closely related to the use of covariate adaptive randomization techniques, and we also
point out how to compute standard errors when the RCT is based on such techniques (Ye
& Shao, 2018; Bugni et al., 2018). Further, we demonstrate that the efficiency gain can be
large and can be obtained without relying on any modeling assumptions. The techniques are
shown to work in simulations and illustrated in practical use by the RCT that motivated the
work. In particular we develop an RCT augmented baseline estimator.