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Flexible designs allow large modifications of a design during an experiment. In particular, the sample size can be modified in response to interim data or external information. A standard flexible methodology combines such design modifications with a weighted test, which guarantees the type I error level. However, this inference violates basic inference principles. In an example with independent N(μ, 1) observations, the test rejects the null hypothesis of μ ≤ 0 while the average of the observations is negative. We conclude that flexible design in its most general form with the corresponding weighted test is not valid. Several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests.

Determination of a clinical trial's size is an important task in the planning of any trial because of the direct implications of the sample size on feasibility, costs and timelines. However, sample size calculations are often subject to substantial uncertainty due to limited prior information on the size of nuisance parameters such as variances or event rates. Continuous monitoring of the nuisance parameter in clinical trials has been proposed as a tool to size trials appropriately. With this approach, the nuisance parameter is continuously monitored during the trial. The trial is stopped when the actual estimate for the nuisance parameter and sample size fulfil a stopping criterion. Continuous monitoring can therefore be viewed as a stochastic process with stopping time. We describe the bias that occurs with unblinded continuous monitoring of the variance in clinical trials by means of a simulation study. Then we propose a procedure for blinded continuous monitoring that does not require breaking the treatment code during the on-going study and show that the procedure does not suffer from the same biases as observed in unblinded monitoring. Results on the performance properties of such designs are given and the designs are compared with blinded re-estimation procedures with a single data look. By means of asymptotic theoretical arguments and finite sample size simulations we find that the variability in sample size is smaller with blinded continuous monitoring than with blinded sample size re-estimation whenever the power for both designs is close to the target value. Repeated sample size re-estimation is in between continuous monitoring and sample size re-estimation in this respect. Furthermore, we present a hypertension trial where blinded sample size re-estimation with a single data look was applied and we investigate the properties of blinded continuous monitoring in this setting. Finally we close with a brief discussion.

Clinical trials are constantly evolving in the context of increasingly complex research questions and potentially limited resources. In this review article, we discuss the emergence of “adaptive” clinical trials that allow for the preplanned modification of an ongoing clinical trial based on the accumulating evidence with application across translational research. These modifications may include terminating a trial before completion due to futility or efficacy, re-estimating the needed sample size to ensure adequate power, enriching the target population enrolled in the study, selecting across multiple treatment arms, revising allocation ratios used for randomization, or selecting the most appropriate endpoint. Emerging topics related to borrowing information from historic or supplemental data sources, sequential multiple assignment randomized trials (SMART), master protocol and seamless designs, and phase I dose-finding studies are also presented. Each design element includes a brief overview with an accompanying case study to illustrate the design method in practice. We close with brief discussions relating to the statistical considerations for these contemporary designs.

Background Ventilator-associated pneumonia (VAP) is an important healthcare acquired infection, which is associated with high morbidity and mortality. Conducting conventional randomised controlled trials (RCTs) on VAP prevention is often challenging, due to low numbers of eligible patients and events per site, especially for pathogen-specific interventions. We explored how group sequential designs (GSD) and sample size re-estimation (SSR) trial designs could improve RCT efficiency in simulated superiority trials to prevent VAP. Methods Simulations were informed using data from the prospective observational Hospital Network Study – Preparation for a Randomised Evaluation of anti-Pneumonia Strategies (HONEST-PREPS). We tested the impact of different GSD and SSR designs on expected sample size (considering early stopping) and maximum sample size (no early stopping). We varied the type of stopping boundary, number and timepoint of interim analyses, and assumed and true prevention effect. We applied time-to-event analyses, with effect estimates expressed as hazard ratios, for the primary endpoint. Results The estimated 28-day cumulative incidence of VAP in HONEST-PREPS was 15.5%. For a 30% reduction in VAP (hazard ratio of 0.68), a standard RCT (power 80%) would require a sample size of 1291 patients. For GSD, Pocock boundaries result in a smaller expected sample size (E[N] = 1128), but a larger maximum sample size (max(N) = 1578) than O’Brien Fleming boundaries (E[N] = 1170 and max(N) = 1389), when utilising the optimal placement of a single interim analysis, 48% and 64% of the maximum number of events for Pocock and O’Brien Fleming boundaries, respectively. SSR is more efficient compared to GSD when the incorrect prevention effect is initially used to plan the trial, as it maintains a power closer to the pre-specified desired power without substantial impact on the expected sample size. Conclusions GSD and SSR are effective adaptive designs, preferable to fixed RCTs in a superiority trial comparing the effectiveness of an investigational intervention with a standard of care in preventing VAP among critically ill, ventilated patients. They can reduce the expected sample size between 9% and 12% and should be considered at the trial design stage.

Adaptive designs allow planned modifications based on data accumulating within a study. The promise of greater flexibility and efficiency stimulates increasing interest in adaptive designs from clinical, academic, and regulatory parties. When adaptive designs are used properly, efficiencies can include a smaller sample size, a more efficient treatment development process, and an increased chance of correctly answering the clinical question of interest. However, improper adaptations can lead to biased studies. A broad definition of adaptive designs allows for countless variations, which creates confusion as to the statistical validity and practical feasibility of many designs. Determining properties of a particular adaptive design requires careful consideration of the scientific context and statistical assumptions. We first review several adaptive designs that garner the most current interest. We focus on the design principles and research issues that lead to particular designs being appealing or unappealing in particular applications. We separately discuss exploratory and confirmatory stage designs in order to account for the differences in regulatory concerns. We include adaptive seamless designs, which combine stages in a unified approach. We also highlight a number of applied areas, such as comparative effectiveness research, that would benefit from the use of adaptive designs. Finally, we describe a number of current barriers and provide initial suggestions for overcoming them in order to promote wider use of appropriate adaptive designs. Given the breadth of the coverage all mathematical and most implementation details are omitted for the sake of brevity. However, the interested reader will find that we provide current references to focused reviews and original theoretical sources which lead to details of the current state of the art in theory and practice.

Introduction Sample size calculations require assumptions regarding treatment response and variability. Incorrect assumptions can result in under- or overpowered trials, posing ethical concerns. Sample size re-estimation (SSR) methods investigate the validity of these assumptions and increase the sample size if necessary. The “promising zone” (Mehta and Pocock, Stat Med 30:3267–3284, 2011) concept is appealing to researchers for its design simplicity. However, it is still relatively new in the application and has been a source of controversy. Objectives This research aims to synthesise current approaches and practical implementation of the promising zone design. Methods This systematic review comprehensively identifies the reporting of methodological research and of clinical trials using promising zone. Databases were searched according to a pre-specified search strategy, and pearl growing techniques implemented. Results The combined search methods resulted in 270 unique records identified; 171 were included in the review, of which 30 were trials. The median time to the interim analysis was 60% of the original target sample size (IQR 41–73%). Of the 15 completed trials, 7 increased their sample size. Only 21 studies reported the maximum sample size that would be considered, for which the median increase was 50% (IQR 35–100%). Conclusions Promising zone is being implemented in a range of trials worldwide, albeit in low numbers. Identifying trials using promising zone was difficult due to the lack of reporting of SSR methodology. Even when SSR methodology was reported, some had key interim analysis details missing, and only eight papers provided promising zone ranges.

Background Adaptive clinical trials may use conditional power (CP) to make decisions at interim analyses, requiring assumptions about the treatment effect for remaining patients. It is critical that these assumptions are understood by those using CP in decision-making, as well as timings of these decisions. Methods Data for 21 outcomes from 14 published clinical trials were made available for re-analysis. CP curves for accruing outcome information were calculated using and compared with a pre-specified objective criteria for original and transformed versions of the trial data using four future treatment effect assumptions: (i) observed current trend, (ii) hypothesised effect, (iii) 80% optimistic confidence limit, (iv) 90% optimistic confidence limit. Results The hypothesised effect assumption met objective criteria when the true effect was close to that planned, but not when smaller than planned. The opposite was seen using the current trend assumption. Optimistic confidence limit assumptions appeared to offer a compromise between the two, performing well against objective criteria when the end observed effect was as planned or smaller. Conclusion The current trend assumption could be the preferable assumption when there is a wish to stop early for futility. Interim analyses could be undertaken as early as 30% of patients have data available. Optimistic confidence limit assumptions should be considered when using CP to make trial decisions, although later interim timings should be considered where logistically feasible.

Background Obstructive sleep apnoea is caused by closure of the upper airway during sleep due to excessive muscle relaxation. It is treated with continuous positive airway pressure (CPAP), a machine connected to a mask worn by a patient during sleep, which generates pressure to keep the throat open. CPAP is highly effective, but often not tolerated, sometimes due to the required pressure of the machine. Mandibular advancement devices advance the lower jaw, increasing airway space. Using such a device may open the airway enough to allow CPAP pressure to be reduced, resulting in more patients being able to tolerate using the CPAP machine. Methods/design The PAPMAT trial is a multicentre, randomised controlled crossover trial. It will measure CPAP machine adherence for participants with obstructive sleep apnoea, comparing their adherence when using a CPAP machine alone to using a CPAP machine in conjunction with a mandibular advancement device. The sample size will be re-estimated after at least 50% of participants have completed follow-up. This document is the statistical analysis plan, which gives details of the planned analysis, including the sample size re-estimation. Trial registration ISRCTN 33966032. Registered 18th February 2022.

Background The NOTACS trial will assess the efficacy, safety and cost-effectiveness of high-flow nasal therapy (HFNT) compared to standard oxygen therapy (SOT) on the outcomes of patients after cardiac surgery. Methods/design NOTACS is an adaptive, international, multicentre, parallel group, randomised controlled trial, with a pre-planned interim sample size re-estimation (SSR). A minimum of 850 patients will be randomised 1:1 to receive either HFNT or SOT. The primary outcome is days alive and at home in the first 90 days after the planned surgery (DAH90), with a number of secondary analyses and cost-effectiveness analyses also planned. The interim SSR will take place after a minimum of 300 patients have been followed up for 90 days and will allow for the sample size to increase up to a maximum of 1280 patients. Results This manuscript provides detailed descriptions of the design of the NOTACS trial and the analyses to be undertaken at the interim and final analyses. The main purpose of the interim analysis is to assess safety and to perform a sample size re-estimation. The main purpose of the final analysis is to examine the safety, efficacy and cost-effectiveness of HFNT compared to SOT on the outcomes of patients after cardiac surgery. Discussion This manuscript outlines the key features of the NOTACS statistical analysis plan and was submitted to the journal before the final analysis in order to preserve scientific integrity under an adaptive design framework. A previous version of this SAP was published prior to the interim analysis (Dawson, 2022). The NOTACS SAP closely follows published guidelines for the content of SAPs in clinical trials (Gamble, 2017). Trial registration ISRCTN14092678 . (13 May 2020).

Background Obstructive sleep apnoea (OSA) involves repeated breathing pauses during sleep due to upper airway obstruction. It causes excessive daytime sleepiness and has other health impacts. Continuous positive airway pressure (CPAP) therapy is effective first line treatment for moderate to severe OSA. Unfortunately, many patients have difficulty tolerating CPAP and pressure intolerance is probably an important contributing factor. Mandibular advancement devices (MAD) are an alternative to CPAP. They are worn in the mouth during sleep to reduce airway obstruction. There is some evidence that, when used in combination with CPAP, MADs improve airway anatomy enough to reduce the CPAP pressure required to treat OSA and that this combination therapy could improve CPAP adherence. Methods Consecutive patients starting on CPAP for moderate to severe OSA will be recruited at a regional NHS sleep service. Patients with high CPAP pressure requirements after initial titration, who satisfy all entry criteria and consent to participate, will undertake a 2-arm randomised crossover trial. The arms will be (i) standalone CPAP and (ii) CPAP + MAD therapy. Each arm will last 12 weeks, including 2 weeks acclimatisation. CPAP machines will be auto-titrating and with facility for data download, so the impact of MAD on CPAP pressure requirements and CPAP adherence can be easily measured. The primary outcome will be CPAP adherence. Secondary outcomes will include measures of OSA severity, patient-reported outcome measures including subjective daytime sleepiness, quality of life, and treatment preference at the trial exit and health service use. Cost-effectiveness analyses will be undertaken. Discussion If the intervention is shown to be effective and cost-effective in improving adherence in this standard CPAP-eligible OSA patient population it would be relatively straightforward to introduce into existing OSA treatment pathways, within the wider NHS and more widely. Both MAD and CPAP are already used by sleep services so their combination would require only minor adjustments to existing clinical pathways. It would be straightforward to disseminate the results of the study through regional, national, and international respiratory meetings. The health economics analysis would provide cost-effectiveness data to inform service planning and clinical guidelines through policy briefing papers, including those by NICE and SIGN. Trial registration PAPMAT was registered with ISRCTN prior to recruitment beginning (ISRCTN Registry 2021): https://www.isrctn.com/ISRCTN33966032 . Registered on 17th November 2021.