Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome

BACKGROUND: Designs and analyses of clinical trials with a time-to-event outcome almost invariably rely on the hazard ratio to estimate the treatment effect and implicitly, therefore, on the proportional hazards assumption. However, the results of some recent trials indicate that there is no guarantee that the assumption will hold. Here, we describe the use of the restricted mean survival time as a possible alternative tool in the design and analysis of these trials. METHODS: The restricted mean is a measure of average survival from time 0 to a specified time point, and may be estimated as the area under the survival curve up to that point. We consider the design of such trials according to a wide range of possible survival distributions in the control and research arm(s). The distributions are conveniently defined as piecewise exponential distributions and can be specified through piecewise constant hazards and time-fixed or time-dependent hazard ratios. Such designs can embody proportional or non-proportional hazards of the treatment effect. RESULTS: We demonstrate the use of restricted mean survival time and a test of the difference in restricted means as an alternative measure of treatment effect. We support the approach through the results of simulation studies and in real examples from several cancer trials. We illustrate the required sample size under proportional and non-proportional hazards, also the significance level and power of the proposed test. Values are compared with those from the standard approach which utilizes the logrank test. CONCLUSIONS: We conclude that the hazard ratio cannot be recommended as a general measure of the treatment effect in a randomized controlled trial, nor is it always appropriate when designing a trial. Restricted mean survival time may provide a practical way forward and deserves greater attention

How do you design randomised trials for smaller populations? A framework.

How should we approach trial design when we can get some, but not all, of the way to the numbers required for a randomised phase III trial?We present an ordered framework for designing randomised trials to address the problem when the ideal sample size is considered larger than the number of participants that can be recruited in a reasonable time frame. Staying with the frequentist approach that is well accepted and understood in large trials, we propose a framework that includes small alterations to the design parameters. These aim to increase the numbers achievable and also potentially reduce the sample size target. The first step should always be to attempt to extend collaborations, consider broadening eligibility criteria and increase the accrual time or follow-up time. The second set of ordered considerations are the choice of research arm, outcome measures, power and target effect. If the revised design is still not feasible, in the third step we propose moving from two- to one-sided significance tests, changing the type I error rate, using covariate information at the design stage, re-randomising patients and borrowing external information.We discuss the benefits of some of these possible changes and warn against others. We illustrate, with a worked example based on the Euramos-1 trial, the application of this framework in designing a trial that is feasible, while still providing a good evidence base to evaluate a research treatment.This framework would allow appropriate evaluation of treatments when large-scale phase III trials are not possible, but where the need for high-quality randomised data is as pressing as it is for common diseases

Facilities for optimizing and designing multiarm multistage (MAMS) randomized controlled trials with binary outcomes

We introduce two commands, nstagebin and nstagebinopt, that can be used to facilitate the design of multiarm multistage (MAMS) trials with binary outcomes. MAMS designs are a class of efficient and adaptive randomized clinical trials that have successfully been used in many disease areas, including cancer, tuberculosis, maternal health, COVID-19, and surgery. The nstagebinopt command finds a class of efficient “admissible” designs based on an optimality criterion using a systematic search procedure. The nstagebin command calculates the stagewise sample sizes, trial timelines, and overall operating characteristics of MAMS designs with binary outcomes. Both commands allow the use of Dunnett’s correction to account for multiple testing. We also use the ROSSINI 2 MAMS design, an ongoing MAMS trial in surgical wound infection, to illustrate the capabilities of both commands. The new commands facilitate the design of MAMS trials with binary outcomes where more than one research question can be addressed under one protocol

How to design a MAMS-ROCI (aka DURATIONS) randomised trial: the REFINE-Lung case study

Background. The DURATIONS design has been recently proposed as a practical alternative to a standard two-arm non-inferiority design when the goal is to optimise some continuous aspect of treatment administration, e.g. duration or frequency, preserving efficacy but improving on secondary outcomes such as safety, costs or convenience. The main features of this design are that (i) it randomises patients to a moderate number of arms across the continuum and (ii) it uses a model to share information across arms. While papers published to date about the design have focused on analysis aspects, here we show how to design such a trial in practice. We use the REFINE-Lung trial as an example; this is a trial seeking the optimal frequency of immunotherapy treatment for non-small cell lung cancer patients. Because the aspect of treatment administration to optimise is frequency, rather than duration, we propose to rename the design as Multi-Arm Multi-Stage Response Over Continuous Intervention (MAMS-ROCI). Methods. We show how simulations can be used to design such a trial. We propose to use the ADEMP framework to plan such simulations, clearly specifying aims, data generating mechanisms, estimands, methods and performance measures before coding and analysing the simulations. We discuss the possible choices to be made using the REFINE-Lung trial as an example. Results. We describe all the choices made while designing the REFINE-Lung trial, and the results of the simulations performed. We justify our choice of total sample size based on these results. Conclusions. MAMS-ROCI trials can be designed using simulation studies that have to be carefully planned and conducted. REFINE-Lung has been designed using such an approach and we have shown how researchers could similarly design their own MAMS-ROCI trial.Comment: 25 pages, 1 table, 5 figure

Rethinking non-inferiority: a practical trial design for optimising treatment duration.

Background Trials to identify the minimal effective treatment duration are needed in different therapeutic areas, including bacterial infections, tuberculosis and hepatitis C. However, standard non-inferiority designs have several limitations, including arbitrariness of non-inferiority margins, choice of research arms and very large sample sizes. Methods We recast the problem of finding an appropriate non-inferior treatment duration in terms of modelling the entire duration-response curve within a pre-specified range. We propose a multi-arm randomised trial design, allocating patients to different treatment durations. We use fractional polynomials and spline-based methods to flexibly model the duration-response curve. We call this a 'Durations design'. We compare different methods in terms of a scaled version of the area between true and estimated prediction curves. We evaluate sensitivity to key design parameters, including sample size, number and position of arms. Results A total sample size of ~ 500 patients divided into a moderate number of equidistant arms (5-7) is sufficient to estimate the duration-response curve within a 5% error margin in 95% of the simulations. Fractional polynomials provide similar or better results than spline-based methods in most scenarios. Conclusion Our proposed practical randomised trial 'Durations design' shows promising performance in the estimation of the duration-response curve; subject to a pending careful investigation of its inferential properties, it provides a potential alternative to standard non-inferiority designs, avoiding many of their limitations, and yet being fairly robust to different possible duration-response curves. The trial outcome is the whole duration-response curve, which may be used by clinicians and policymakers to make informed decisions, facilitating a move away from a forced binary hypothesis testing paradigm

Treatment selection in multi-arm multi-stage designs: With application to a postpartum haemorrhage trial

Background: Multi-arm multi-stage trials are an efficient, adaptive approach for testing many treatments simultaneously within one protocol. In settings where numbers of patients available to be entered into trials and resources might be limited, such as primary postpartum haemorrhage, it may be necessary to select a pre-specified subset of arms at interim stages even if they are all showing some promise against the control arm. This will put a limit on the maximum number of patients required and reduce the associated costs. Motivated by the World Health Organization Refractory HaEmorrhage Devices trial in postpartum haemorrhage, we explored the properties of such a selection design in a randomised phase III setting and compared it with other alternatives. The objectives are: (1) to investigate how the timing of treatment selection affects the operating characteristics; (2) to explore the use of an information-rich (continuous) intermediate outcome to select the best-performing arm, out of four treatment arms, compared with using the primary (binary) outcome for selection at the interim stage; and (3) to identify factors that can affect the efficiency of the design. / Methods: We conducted simulations based on the refractory haemorrhage devices multi-arm multi-stage selection trial to investigate the impact of the timing of treatment selection and applying an adaptive allocation ratio on the probability of correct selection, overall power and familywise type I error rate. Simulations were also conducted to explore how other design parameters will affect both the maximum sample size and trial timelines. / Results: The results indicate that the overall power of the trial is bounded by the probability of ‘correct’ selection at the selection stage. The results showed that good operating characteristics are achieved if the treatment selection is conducted at around 17% of information time. Our results also showed that although randomising more patients to research arms before selection will increase the probability of selecting correctly, this will not increase the overall efficiency of the (selection) design compared with the fixed allocation ratio of 1:1 to all arms throughout. / Conclusions: Multi-arm multi-stage selection designs are efficient and flexible with desirable operating characteristics. We give guidance on many aspects of these designs including selecting the intermediate outcome measure, the timing of treatment selection, and choosing the operating characteristics