A Bayesian adaptive design for multi-arm phase III trials with non-proportional hazards utilizing the concept of relative time

BackgroundBayesian adaptive designs can improve the efficiency of trials, and lead to trials that can produce high quality evidence more quickly, with fewer patients and lower costs than traditional methods. The aim of this work was to determine how Bayesian adaptive designs can be constructed for phase III clinical trials in critical care, and to assess the influence that Bayesian designs would have on trial efficiency and study results.MethodsWe re-designed the High Frequency OSCillation in Acute Respiratory distress syndrome (OSCAR) trial using Bayesian adaptive design methods, to allow for the possibility of early stopping for success or futility. We constructed several alternative designs and studied their operating characteristics via simulation. We then performed virtual re-executions by applying the Bayesian adaptive designs using the OSCAR data to demonstrate the practical applicability of the designs.ResultsWe constructed five alternative Bayesian adaptive designs and identified a preferred design based on the simulated operating characteristics, which had similar power to the original design but recruited fewer patients on average. The virtual re-executions showed the Bayesian sequential approach and original OSCAR trial yielded similar trial conclusions. However, using a Bayesian sequential design could have led to a reduced sample size and earlier completion of the trial.ConclusionsUsing the OSCAR trial as an example, this case study found that Bayesian adaptive designs can be constructed for phase III critical care trials. If the OSCAR trial had been run using one of the proposed Bayesian adaptive designs, it would have terminated at a smaller sample size with fewer deaths in the trial, whilst reaching the same conclusions. We recommend the wider use of Bayesian adaptive approaches in phase III clinical trials.Trial registrationOSCAR Trial registration ISRCTN, ISRCTN10416500. Retrospectively registered 13 June 2007.

BackgroundBayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. Decisions at analysis points are usually based on the posterior distribution of the treatment effect. However, there is some confusion as to whether control of type I error is required for Bayesian designs as this is a frequentist concept.MethodsWe discuss the arguments for and against adjusting for multiplicities in Bayesian trials with interim analyses. With two case studies we illustrate the effect of including interim analyses on type I/II error rates in Bayesian clinical trials where no adjustments for multiplicities are made. We propose several approaches to control type I error, and also alternative methods for decision-making in Bayesian clinical trials.ResultsIn both case studies we demonstrated that the type I error was inflated in the Bayesian adaptive designs through incorporation of interim analyses that allowed early stopping for efficacy and without adjustments to account for multiplicity. Incorporation of early stopping for efficacy also increased the power in some instances. An increase in the number of interim analyses that only allowed early stopping for futility decreased the type I error, but also decreased power. An increase in the number of interim analyses that allowed for either early stopping for efficacy or futility generally increased type I error and decreased power.ConclusionsCurrently, regulators require demonstration of control of type I error for both frequentist and Bayesian adaptive designs, particularly for late-phase trials. To demonstrate control of type I error in Bayesian adaptive designs, adjustments to the stopping boundaries are usually required for designs that allow for early stopping for efficacy as the number of analyses increase. If the designs only allow for early stopping for futility then adjustments to the stopping boundaries are not needed to control type I error. If one instead uses a strict Bayesian approach, which is currently more accepted in the design and analysis of exploratory trials, then type I errors could be ignored and the designs could instead focus on the posterior probabilities of treatment effects of clinically-relevant values.

Bayesian adaptive trial design in acute heart failure syndromes: Moving beyond the mega trial

The use of Bayesian adaptive designs for clinical trials has increased in recent years, particularly during the COVID‐19 pandemic. Bayesian adaptive designs offer a flexible and efficient framework for conducting clinical trials and may provide results that are more useful and natural to interpret for clinicians, compared to traditional approaches. In this review, we provide an introduction to Bayesian adaptive designs and discuss its use in recent clinical trials conducted in respiratory medicine. We illustrate this approach by constructing a Bayesian adaptive design for a multi‐arm trial that compares two non‐invasive ventilation treatments to standard oxygen therapy for patients with acute cardiogenic pulmonary oedema. We highlight the benefits and some of the challenges involved in designing and implementing Bayesian adaptive trials.

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.

This article provides a regulatory view of the design of clinical trials using Bayesian statistics and adaptive methods. The foci are the similarities and differences between Bayesian and adaptive designs for clinical studies for medical devices and the contrast with trials of pharmaceutical drugs. The critical role of the U.S. Food and Drug Administration in such designs is highlighted. The previous device experience with Bayesian trials has provided some important insight into the planning of adaptive trials. This article discusses both frequentist and Bayesian adaptive designs and presents several real examples of designs for medical device studies. The crucial role that simulations play in assessing the operating characteristics of the designs is emphasized. The unique advantage of predictive modeling in the Bayesian adaptive design is explored. For adaptive designs there are challenging problems including operational bias and logistical issues. The reporting of both Bayesian and adaptive trials is discussed.

BackgroundTo perform virtual re-executions of a breast cancer clinical trial with a time-to-event outcome to demonstrate what would have happened if the trial had used various Bayesian adaptive designs instead.MethodsWe aimed to retrospectively “re-execute” a randomised controlled trial that compared two chemotherapy regimens for women with metastatic breast cancer (ANZ 9311) using Bayesian adaptive designs. We used computer simulations to estimate the power and sample sizes of a large number of different candidate designs and shortlisted designs with the either highest power or the lowest average sample size. Using the real-world data, we explored what would have happened had ANZ 9311 been conducted using these shortlisted designs.ResultsWe shortlisted ten adaptive designs that had higher power, lower average sample size, and a lower false positive rate, compared to the original trial design. Adaptive designs that prioritised small sample size reduced the average sample size by up to 37% when there was no clinical effect and by up to 17% at the target clinical effect. Adaptive designs that prioritised high power increased power by up to 5.9 percentage points without a corresponding increase in type I error. The performance of the adaptive designs when applied to the real-world ANZ 9311 data was consistent with the simulations.ConclusionThe shortlisted Bayesian adaptive designs improved power or lowered the average sample size substantially. When designing new oncology trials, researchers should consider whether a Bayesian adaptive design may be beneficial.

Bayesian adaptive designs have become popular because of the possibility of increasing the number of patients treated with more beneficial treatments, while still providing sufficient evidence for treatment efficacy comparisons. It can be essential, for regulatory and other purposes, to conduct frequentist analyses both before and after a Bayesian adaptive trial, and these remain challenging. In this paper, we propose a general simulation-based approach to compare frequentist designs with Bayesian adaptive designs based on frequentist criteria such as power and to compute valid frequentist p-values. We illustrate our approach by comparing the power of an equal randomization (ER) design with that of an optimal Bayesian adaptive (OBA) design. The Bayesian design considered here is the dynamic programming solution of the optimization of a specific utility function defined by the number of successes in a patient horizon, including patients whose treatment will be affected by the trial's results after the end of the trial. While the power of an ER design depends on treatment efficacy and the sample size, the power of the OBA design also depends on the patient horizon size. Our results quantify the trade-off between power and the optimal assignment of patients to treatments within the trial. We show that, for large patient horizons, the two criteria are in agreement, while for small horizons, differences can be substantial. This has implications for precision medicine, where patient horizons are decreasing as a result of increasing stratification of patients into subpopulations defined by molecular markers.

Recent publications indicate a strong interest in applying Bayesian adaptive designs in first time in humans (FTIH) studies outside of oncology. The objective of the present work was to assess the performance of a new approach that includes Bayesian adaptive design in single ascending dose (SAD) trials conducted in healthy volunteers, in comparison with a more traditional approach. A trial simulation approach was used and seven different scenarios of dose-response were tested. The new approach provided less biased estimates of maximum tolerated dose (MTD). In all scenarios, the number of subjects needed to define a MTD was lower with the new approach than with the traditional approach. With respect to duration of the trials, the two approaches were comparable. In all scenarios, the number of subjects exposed to a dose greater than the actual MTD was lower with the new approach than with the traditional approach. The new approach with Bayesian adaptive design shows a very good performance in the estimation of MTD and in reducing the total number of healthy subjects. It also reduces the number of subjects exposed to doses greater than the actual MTD.

Current designs used to optimise implementation strategies (e.g., sequential cluster randomised controlled trials (cRCTs) and multi-arm cRCTs) are inefficient and resource intensive. Bayesian adaptive designs may offer a more efficient alternative. We conducted a virtual trial re-execution to assess the impact of using a Bayesian adaptive design for optimising an existing implementation strategy (Physically Active Children in education (PACE)) used to support the delivery of school-based physical activity. The two previous, sequential, two-arm cRCTs used to optimise PACE were combined into a single three-arm cRCT. We assessed the performance of a fixed version of this trial design compared to an adaptive version incorporating one, two, or three interim analyses in a virtual re-execution. Adaptions included arm dropping and early stopping for futility, noninferiority, or efficacy. All adaptive designs stopped early for noninferiority, declaring the lower cost treatment as the optimal arm at interim analysis one. This was the same conclusion obtained in the fixed version of the three-arm cRCT and the original sequential two-arm cRCTs. Using adaptive designs, the same conclusion was reached using 50-75% fewer clusters. The adaptive trials would have taken approximately 40% less time than the sequential two-arm cRCTs, not accounting for the time to analyse the interim analysis. However, the treatment effect was biased towards the lower cost treatment, and this bias (away from the full-sample posterior estimate) increased when fewer clusters were randomised. The first 18 schools randomised were Catholic schools, and they responded better to the lower cost treatment compared to government schools. When the distribution of school type was balanced at each interim (i.e. matched the final sample proportions) the bias towards the lower cost treatment was reduced. Bayesian adaptive designs offer improved efficiency for trials aiming to optimise implementation strategies, reducing the time and sample size needed to find the optimal strategy. However, care is required to ensure confounding demographics are balanced at each interim analysis to reduce the risk of making a type 1 or 2 error or an incorrect adaptive design decision (e.g. dropping an effective arm, incorrectly stopping early). Not applicable.

The design of phase I studies is often challenging, because of limited evidence to inform study protocols. Adaptive designs are now well established in cancer but much less so in other clinical areas. A phase I study to assess the safety, pharmacokinetic profile and antiretroviral efficacy of C34‐PEG4‐Chol, a novel peptide fusion inhibitor for the treatment of HIV infection, has been set up with Medical Research Council funding. During the study workup, Bayesian adaptive designs based on the continual reassessment method were compared with a more standard rule‐based design, with the aim of choosing a design that would maximise the scientific information gained from the study. The process of specifying and evaluating the design options was time consuming and required the active involvement of all members of the trial's protocol development team. However, the effort was worthwhile as the originally proposed rule‐based design has been replaced by a more efficient Bayesian adaptive design. While the outcome to be modelled, design details and evaluation criteria are trial specific, the principles behind their selection are general. This case study illustrates the steps required to establish a design in a novel context. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd

<p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d626691e83"> <b>Objectives:</b> Traditional Phase I dose-escalation strategies in Phase I oncology trials, such as the ‘3+3’ method, are widely used but estimate the MTD (maximum tolerated dose) poorly, being vulnerable to both bias (underestimation of MTD) and the risk of subtherapeutic dosing. Bayesian adaptive designs offer a model-based alternative that incorporates accumulating data to refine dose selection in real time. Here we present a novel approach for the assessment of Phase I MTD, based on the integration of a Bayesian decision metric with a dose escalation algorithm to estimate the MTD. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d626691e88"> <b>Methods:</b> We have previously presented [ <a class="xref-link" href="#r1">1</a>] a novel decision metric for estimating Phase I MTD based on a Bayesian algorithm, the Population Response Estimate (PRE). PRE applies Maximum Likelihood Theory to graded toxicity data to estimate both the toxicity central tendency curve and population heterogeneity, which are then used to estimate the likelihood of encountering dose-limiting toxicities at each dose. Here we extend our method to incorporate a novel dose escalation algorithm that leverages the PRE to calculate the highest safe dose (HSD) given the current certainty level, defined as the highest dose with ≤15% posterior probability of DLT &gt; grade 4. Patients are then dosed at this HSD, and the posterior distribution is updated iteratively following each dosing cohort. Dose escalation continues until the standard deviation of the MTD estimate falls below a prespecified threshold, defined as <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d626691e96"> <b>Results:</b> The Bayesian adaptive method identified the true MTD within ±20% in 73% of simulated trials, compared to only 38% using the 3+3 design. Notably, the probability of overestimating the MTD (i.e., selecting a dose above the true MTD) was only 1% with the Bayesian method, versus 12% for 3+3. The adaptive design required fewer patients on average and concentrated observations near the MTD, enhancing trial efficiency and ethical conduct. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d626691e101"> <b>Conclusions:</b> The Bayesian adaptive design outperforms the conventional 3+3 method in both accuracy and efficiency of MTD estimation. By focusing data collection near the target toxicity threshold and continuously updating model estimates, this method supports faster, safer, and more informative Phase I trials. These findings align with FDA guidance encouraging the use of model-based designs and highlight the role of pharmacometric methods in optimizing early-phase clinical development.

Bayesian adaptive designs for clinical trials have gained popularity in the recent years due to the flexibility and efficiency that they offer. We consider the scenario where the outcome of interest comprises events with relatively low risk of occurrence and different case definitions resulting in varying control group risk assumptions. This is a scenario that occurs frequently for infectious diseases in global health research. We propose a Bayesian adaptive design that incorporates different case definitions of the outcome of interest that vary in stringency. A set of stopping rules are proposed where superiority and futility may be concluded with respect to different outcome definitions and therefore maintain a realistic probability of stopping in trials with low event rates. Through a simulation study, a variety of stopping rules and design configurations are compared. The simulation results are provided in an interactive web application that allows the user to explore and compare the design operating characteristics for a variety of assumptions and design parameters with respect to different outcome definitions. The results for select simulation scenarios are provided in the article. Bayesian adaptive designs offer the potential for maximizing the information learned from the data collected through clinical trials. The proposed design enables monitoring and utilizing multiple composite outcomes based on rare events to optimize the trial design operating characteristics.

Using Bayesian pre-trial simulations to optimize the design of adaptive clinical trials in childhood nephrotic syndrome.

Bayesian adaptive designs with response adaptive randomization (RAR) have the potential to benefit more participants in a clinical trial. While there are many papers that describe RAR designs and results, there is a scarcity of works reporting the details of RAR implementation from a statistical point exclusively. In this paper, we introduce the statistical methodology and implementation of the trial Changing the Default (CTD). CTD is a single-center prospective RAR comparative effectiveness trial to compare opt-in to opt-out tobacco treatment approaches for hospitalized patients. The design assumed an uninformative prior, conservative initial allocation ratio, and a higher threshold for stopping for success to protect results from statistical bias. A particular emerging concern of RAR designs is the possibility that time trends will occur during the implementation of a trial. If there is a time trend and the analytic plan does not prespecify an appropriate model, this could lead to a biased trial. Adjustment for time trend was not pre-specified in CTD, but post hoc time-adjusted analysis showed no presence of influential drift. This trial was an example of a successful two-armed confirmatory trial with a Bayesian adaptive design using response adaptive randomization.