A flexible multi-metric Bayesian framework for decision-making in Phase II multi-arm multi-stage studies.

We propose a multi-metric flexible Bayesian framework to support efficient interim decision-making in multi-arm multi-stage phase II clinical trials. Multi-arm multi-stage phase II studies increase the efficiency of drug development, but early decisions regarding the futility or desirability of a given arm carry considerable risk since sample sizes are often low and follow-up periods may be short. Further, since intermediate outcomes based on biomarkers of treatment response are rarely perfect surrogates for the primary outcome and different trial stakeholders may have different levels of risk tolerance, a single hypothesis test is insufficient for comprehensively summarizing the state of the collected evidence. We present a Bayesian framework comprised of multiple metrics based on point estimates, uncertainty, and evidence towards desired thresholds (a Target Product Profile) for (1) ranking of arms and (2) comparison of each arm against an internal control. Using a large public-private partnership targeting novel TB arms as a motivating example, we find via simulation study that our multi-metric framework provides sufficient confidence for decision-making with sample sizes as low as 30 patients per arm, even when intermediate outcomes have only moderate correlation with the primary outcome. Our reframing of trial design and the decision-making procedure has been well-received by research partners and is a practical approach to more efficient assessment of novel therapeutics.

Adding experimental treatment arms to multi-arm multi-stage platform trials in progress.

Multi-arm multi-stage (MAMS) platform trials efficiently compare several treatments with a common control arm. Crucially MAMS designs allow for adjustment for multiplicity if required. If for example, the active treatment arms in a clinical trial relate to different dose levels or different routes of administration of a drug, the strict control of the family-wise error rate (FWER) is paramount. Suppose a further treatment becomes available, it is desirable to add this to the trial already in progress; to access both the practical and statistical benefits of the MAMS design. In any setting where control of the error rate is required, we must add corresponding hypotheses without compromising the validity of the testing procedure.To strongly control the FWER, MAMS designs use pre-planned decision rules that determine the recruitment of the next stage of the trial based on the available data. The addition of a treatment arm presents an unplanned change to the design that we must account for in the testing procedure. We demonstrate the use of the conditional error approach to add hypotheses to any testing procedure that strongly controls the FWER. We use this framework to add treatments to a MAMS trial in progress. Simulations illustrate the possible characteristics of such procedures.

Multi-arm multi-stage (MAMS) randomised selection designs: impact of treatment selection rules on the operating characteristics.

BACKGROUND: Multi-arm multi-stage (MAMS) randomised trial designs have been proposed to evaluate multiple research questions in the confirmatory setting. In designs with several interventions, such as the 8-arm 3-stage ROSSINI-2 trial for preventing surgical wound infection, there are likely to be strict limits on the number of individuals that can be recruited or the funds available to support the protocol. These limitations may mean that not all research treatments can continue to accrue the required sample size for the definitive analysis of the primary outcome measure at the final stage. In these cases, an additional treatment selection rule can be applied at the early stages of the trial to restrict the maximum number of research arms that can progress to the subsequent stage(s). This article provides guidelines on how to implement treatment selection within the MAMS framework. It explores the impact of treatment selection rules, interim lack-of-benefit stopping boundaries and the timing of treatment selection on the operating characteristics of the MAMS selection design. METHODS: We outline the steps to design a MAMS selection trial. Extensive simulation studies are used to explore the maximum/expected sample sizes, familywise type I error rate (FWER), and overall power of the design under both binding and non-binding interim stopping boundaries for lack-of-benefit. RESULTS: Pre-specification of a treatment selection rule reduces the maximum sample size by approximately 25% in our simulations. The familywise type I error rate of a MAMS selection design is smaller than that of the standard MAMS design with similar design specifications without the additional treatment selection rule. In designs with strict selection rules - for example, when only one research arm is selected from 7 arms - the final stage significance levels can be relaxed for the primary analyses to ensure that the overall type I error for the trial is not underspent. When conducting treatment selection from several treatment arms, it is important to select a large enough subset of research arms (that is, more than one research arm) at early stages to maintain the overall power at the pre-specified level. CONCLUSIONS: Multi-arm multi-stage selection designs gain efficiency over the standard MAMS design by reducing the overall sample size. Diligent pre-specification of the treatment selection rule, final stage significance level and interim stopping boundaries for lack-of-benefit are key to controlling the operating characteristics of a MAMS selection design. We provide guidance on these design features to ensure control of the operating characteristics.

A comparison of alternative ranking methods in two-stage clinical trials with multiple interventions: An application to the anxiolysis for laceration repair in children trial.

BACKGROUND/AIMS: Multi-arm, multi-stage trials frequently include a standard care to which all interventions are compared. This may increase costs and hinders comparisons among the experimental arms. Furthermore, the standard care may not be evident, particularly when there is a large variation in standard practice. Thus, we aimed to develop an adaptive clinical trial that drops ineffective interventions following an interim analysis before selecting the best intervention at the final stage without requiring a standard care. METHODS: We used Bayesian methods to develop a multi-arm, two-stage adaptive trial and evaluated two different methods for ranking interventions, the probability that each intervention was optimal (Pbest) and using the surface under the cumulative ranking curve (SUCRA), at both the interim and final analysis. The proposed trial design determines the maximum sample size for each intervention using the Average Length Criteria. The interim analysis takes place at approximately half the pre-specified maximum sample size and aims to drop interventions for futility if either Pbest or the SUCRA is below a pre-specified threshold. The final analysis compares all remaining interventions at the maximum sample size to conclude superiority based on either Pbest or the SUCRA. The two ranking methods were compared across 12 scenarios that vary the number of interventions and the assumed differences between the interventions. The thresholds for futility and superiority were chosen to control type 1 error, and then the predictive power and expected sample size were evaluated across scenarios. A trial comparing three interventions that aim to reduce anxiety for children undergoing a laceration repair in the emergency department was then designed, known as the Anxiolysis for Laceration Repair in Children Trial (ALICE) trial. RESULTS: As the number of interventions increases, the SUCRA results in a higher predictive power compared with Pbest. Using Pbest results in a lower expected sample size when there is an effective intervention. Using the Average Length Criterion, the ALICE trial has a maximum sample size for each arm of 100 patients. This sample size results in a 86% and 85% predictive power using Pbest and the SUCRA, respectively. Thus, we chose Pbest as the ranking method for the ALICE trial. CONCLUSION: Bayesian ranking methods can be used in multi-arm, multi-stage trials with no clear control intervention. When more interventions are included, the SUCRA results in a higher power than Pbest. Future work should consider whether other ranking methods may also be relevant for clinical trial design.

Multi-arm multi-stage survival trial design with arm-specific stopping rule.

Traditional two-arm randomized trial designs have played a pivotal role in establishing the efficacy of medical interventions. However, their efficiency is often compromised when confronted with multiple experimental treatments or limited resources. In response to these challenges, the multi-arm multi-stage designs have emerged, enabling the simultaneous evaluation of multiple treatments within a single trial. In such an approach, if an arm meets efficacy success criteria at an interim stage, the whole trial stops and the arm is selected for further study. However when multiple treatment arms are active, stopping the trial at the moment one arm achieves success diminishes the probability of selecting the best arm. To address this issue, we have developed a group sequential multi-arm multi-stage survival trial design with an arm-specific stopping rule. The proposed method controls the familywise type I error in a strong sense and selects the best promising treatment arm with a high probability.

Adjusting for treatment selection in phase II/III clinical trials with time to event data.

Phase II/III clinical trials are efficient two-stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed-up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.

Fully order restricted multi-arm multi-stage clinical trial design.

We consider a multi-arm trial with two or more active treatments plus a control where it is reasonable to assume an order for the treatment effects of the active arms compared to control. For example, the arms could be a high dose and low dose of a new drug and a placebo. The objective of the trial is to compare each active arm to control while maintaining strong control of the type 1 error rate. We show that when the study is powered to identify all promising treatments, a design that uses the order of the treatment effects to calculate the test statistic and to set the order of testing requires a smaller sample size than a design where each active arm is tested against the control arm independently. Under the considered settings, the sample size for a single-stage trial and a two-stage trial was reduced by at least 20%.

A Bayesian multi-arm multi-stage clinical trial design incorporating information about treatment ordering.

Multi-Arm Multi-Stage (MAMS) designs can notably improve efficiency in later stages of drug development, but they can be suboptimal when an order in the effects of the arms can be assumed. In this work, we propose a Bayesian multi-arm multi-stage trial design that selects all promising treatments with high probability and can efficiently incorporate information about the order in the treatment effects as well as incorporate prior knowledge on the treatments. A distinguishing feature of the proposed design is that it allows taking into account the uncertainty of the treatment effect order assumption and does not assume any parametric arm-response model. The design can provide control of the family-wise error rate under specific values of the control mean and we illustrate its operating characteristics in a study of symptomatic asthma. Via simulations, we compare the novel Bayesian design with frequentist multi-arm multi-stage designs and a frequentist order restricted design that does not account for the order uncertainty and demonstrate the gains in the sample sizes the proposed design can provide. We also find that the proposed design is robust to violations of the assumptions on the order.

Group sequential multi-arm multi-stage trial design with treatment selection.

A multi-arm trial allows simultaneous comparison of multiple experimental treatments with a common control and provides a substantial efficiency advantage compared to the traditional randomized controlled trial. Many novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining total sample size and sequential stopping boundaries. In this paper, we develop a group sequential MAMS trial design based on the sequential conditional probability ratio test. The proposed method provides analytical solutions for futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational effort for the methods proposed by Magirr et al. Simulation results showed that the proposed method has several advantages compared to the methods implemented in R package MAMS by Magirr et al.

Group sequential multi-arm multi-stage survival trial design with treatment selection.

Multi-arm trials are increasingly of interest because for many diseases; there are multiple experimental treatments available for testing efficacy. Several novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining stopping boundaries. For example, the method of Jaki and Magirr for time-to-event endpoint, implemented in R package MAMS, requires complicated computational efforts to obtain stopping boundaries. In this study, we develop a group sequential MAMS survival trial design based on the sequential conditional probability ratio test. The proposed method is an improvement of the Jaki and Magirr's method in the following three directions. First, the proposed method provides explicit solutions for both futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational efforts for the trial design. Second, the proposed method provides an accurate number of events for the fixed sample and group sequential designs. Third, the proposed method uses a new procedure for interim analysis which preserves the study power.

Determining the minimum duration of treatment in tuberculosis: An order restricted non-inferiority trial design.

Tuberculosis (TB) is one of the biggest killers among infectious diseases worldwide. Together with the identification of drugs that can provide benefits to patients, the challenge in TB is also the optimisation of the duration of these treatments. While conventional duration of treatment in TB is 6 months, there is evidence that shorter durations might be as effective but could be associated with fewer side effects and may be associated with better adherence. Based on a recent proposal of an adaptive order-restricted superiority design that employs the ordering assumptions within various duration of the same drug, we propose a non-inferiority (typically used in TB trials) adaptive design that effectively uses the order assumption. Together with the general construction of the hypothesis testing and expression for type I and type II errors, we focus on how the novel design was proposed for a TB trial concept. We consider a number of practical aspects such as choice of the design parameters, randomisation ratios, and timings of the interim analyses, and how these were discussed with the clinical team.

An order restricted multi-arm multi-stage clinical trial design.

One family of designs that can noticeably improve efficiency in later stages of drug development are multi-arm multi-stage (MAMS) designs. They allow several arms to be studied concurrently and gain efficiency by dropping poorly performing treatment arms during the trial as well as by allowing to stop early for benefit. Conventional MAMS designs were developed for the setting, in which treatment arms are independent and hence can be inefficient when an order in the effects of the arms can be assumed (eg, when considering different treatment durations or different doses). In this work, we extend the MAMS framework to incorporate the order of treatment effects when no parametric dose-response or duration-response model is assumed. The design can identify all promising treatments with high probability. We show that the design provides strong control of the family-wise error rate and illustrate the design in a study of symptomatic asthma. Via simulations we show that the inclusion of the ordering information leads to better decision-making compared to a fixed sample and a MAMS design. Specifically, in the considered settings, reductions in sample size of around 15% were achieved in comparison to a conventional MAMS design.

Design and implementation of an international, multi-arm, multi-stage platform master protocol for trials of novel SARS-CoV-2 antiviral agents: Therapeutics for Inpatients with COVID-19 (TICO/ACTIV-3).

BACKGROUND/AIMS: Safe and effective therapies for COVID-19 are urgently needed. In order to meet this need, the Accelerating COVID-19 Therapeutic Interventions and Vaccines public-private partnership initiated the Therapeutics for Inpatients with COVID-19. Therapeutics for Inpatients with COVID-19 is a multi-arm, multi-stage platform master protocol, which facilitates the rapid evaluation of the safety and efficacy of novel candidate antiviral therapeutic agents for adults hospitalized with COVID-19. Five agents have so far entered the protocol, with rapid answers already provided for three of these. Other agents are expected to enter the protocol throughout 2021. This protocol contains a number of key design and implementation features that, along with challenges faced by the protocol team, are presented and discussed. METHODS: Three clinical trial networks, encompassing a global network of clinical sites, participated in the protocol development and implementation. Therapeutics for Inpatients with COVID-19 utilizes a multi-arm, multi-stage design with an agile and robust approach to futility and safety evaluation at 300 patients enrolled, with subsequent expansion to full sample size and an expanded target population if the agent shows an acceptable safety profile and evidence of efficacy. Rapid recruitment to multiple agents is enabled through the sharing of placebo, the confining of agent-specific information to protocol appendices, and modular consent forms. In collaboration with the Food and Drug Administration, a thorough safety data collection and Data and Safety Monitoring Board schedule was developed for the study of potential therapeutic agents with limited in-human data in hospitalized patients with COVID-19. RESULTS: As of 8 August 2021, five agents have entered the Therapeutics for Inpatients with COVID-19 master protocol and a total of 1909 participants have been randomized to one of these agents or matching placebo. There were a number of challenges faced by the study team that needed to be overcome in order to successfully implement Therapeutics for Inpatients with COVID-19 across a global network of sites. These included ensuring drug supply and reliable recruitment allowing for changing infection rates across the global network of sites, the need to balance the collection of data and samples without overburdening clinical staff and obtaining regulatory approvals across a global network of sites. CONCLUSION: Through a robust multi-network partnership, the Therapeutics for Inpatients with COVID-19 protocol has been successfully used across a global network of sites for rapid generation of efficacy data on multiple novel antiviral agents. The protocol design and implementation features used in this protocol, and the approaches to address challenges, will have broader applicability. Mechanisms to facilitate improved communication and harmonization among country-specific regulatory bodies are required to achieve the full potential of this approach in dealing with a global outbreak.

Combining factorial and multi-arm multi-stage platform designs to evaluate multiple interventions efficiently.

BACKGROUND: Factorial designs and multi-arm multi-stage (MAMS) platform designs have many advantages, but the practical advantages and disadvantages of combining the two designs have not been explored. METHODS: We propose practical methods for a combined design within the platform trial paradigm where some interventions are not expected to interact and could be given together. RESULTS: We describe the combined design and suggest diagrams that can be used to represent it. Many properties are common both to standard factorial designs, including the need to consider interactions between interventions and the impact of intervention efficacy on power of other comparisons, and to standard multi-arm multi-stage designs, including the need to pre-specify procedures for starting and stopping intervention comparisons. We also identify some specific features of the factorial-MAMS design: timing of interim and final analyses should be determined by calendar time or total observed events; some non-factorial modifications may be useful; eligibility criteria should be broad enough to include any patient eligible for any part of the randomisation; stratified randomisation may conveniently be performed sequentially; and analysis requires special care to use only concurrent controls. CONCLUSION: A combined factorial-MAMS design can combine the efficiencies of factorial trials and multi-arm multi-stage platform trials. It allows us to address multiple research questions under one protocol and to test multiple new treatment options, which is particularly important when facing a new emergent infection such as COVID-19.

Experiences of running a stratified medicine adaptive platform trial: Challenges and lessons learned from 10 years of the FOCUS4 trial in metastatic colorectal cancer.

BACKGROUND: Complex innovative design trials are becoming increasingly common and offer potential for improving patient outcomes in a faster time frame. FOCUS4 was the first molecularly stratified trial in metastatic colorectal cancer and it remains one of the first umbrella trial designs to be launched globally. Here, we aim to describe lessons learned from delivery of the trial over the last 10 years. METHODS: FOCUS4 was a Phase II/III molecularly stratified umbrella trial testing the safety and efficacy of targeted therapies in metastatic colorectal cancer. It used adaptive statistical methodology to decide which sub-trial should close early, and new therapies were added as protocol amendments. Patients with newly diagnosed metastatic colorectal cancer were registered, and central laboratory testing was used to stratify their tumour into molecular subtypes. Following 16 weeks of first-line therapy, patients with stable or responding disease were eligible for randomisation into either a molecularly stratified sub-trial (FOCUS4-B, C or D) or non-stratified FOCUS4-N. The primary outcome for all studies was progression-free survival comparing the intervention with active monitoring/placebo. At the close of the trial, feedback was elicited from all investigators through surveys and interviews and consolidated into a series of recommendations and lessons learned for the delivery of similar future trials. RESULTS: Between January 2014 and October 2020, 1434 patients were registered from 88 UK hospitals. Of the 20 drug combinations that were explored for inclusion in the platform trial, three molecularly targeted sub-trials were activated: FOCUS4-D (February 2014-March 2016) evaluated AZD8931 in the BRAF-PIK3CA-RAS wildtype subgroup; FOCUS4-B (February 2016-July 2018) evaluated aspirin in the PIK3CA mutant subgroup and FOCUS4-C (June 2017-October 2020) evaluated adavosertib in the RAS+TP53 double mutant subgroup. FOCUS4-N was active throughout and evaluated capecitabine monotherapy versus a treatment break. A total of 361 (25%) registered patients were randomised into a sub-trial. Feedback on the experiences of delivery of FOCUS4 could be grouped into three main areas of challenge: funding/infrastructure, biomarker testing procedures and trial design efficiencies within which 20 recommendations are summarised. CONCLUSION: Adaptive stratified medicine platform studies are feasible in common cancers but present challenges. Our stakeholder feedback has helped to inform how these trial designs can succeed and answer multiple questions efficiently, providing resource is adequate.

Analysis of adaptive platform trials using a network approach.

BACKGROUND: Adaptive platform trials allow randomized controlled comparisons of multiple treatments using a common infrastructure and the flexibility to adapt key design features during the study. Nonetheless, they have been criticized due to the potential for time trends in the underlying risk level of the population. Such time trends lead to confounding between design features and risk level, which may introduce bias favoring one or more treatments. This is particularly true when experimental treatments are not all randomized during the same time period as the control, leading to the potential for bias from non-concurrent controls. METHODS: Two analysis methods addressing this bias are stratification and adjustment. Stratification uses only comparisons between treatment cohorts randomized during identical time periods and does not use non-concurrent randomizations. Adjustment uses a modeled analysis including time period adjustment, allowing all data to be used, even from periods without concurrent randomization. We show that these competing approaches may be embedded in a common framework using network meta-analysis principles. We interpret the stages between adaptations in a platform trial as separate fixed design trials. This allows platform trials to be viewed as networks of direct randomized comparisons and indirect non-randomized comparisons. Network meta-analysis methodology can be re-purposed to aggregate the total information from a platform trial and to transparently decompose this total information into direct randomized evidence and indirect non-randomized evidence. This allows sensitivity to indirect information to be assessed and the two analysis methods to be clearly compared. RESULTS: Simulations of platform trials were analyzed using a network approach implemented in the netmeta package in R. The results demonstrated bias of unadjusted methods in the presence of time trends in risk level. Adjustment and stratification were both unbiased when direct evidence and indirect evidence were consistent. Network tests of inconsistency may be used to diagnose inconsistency when it exists. In an illustrative network analysis of one of the treatment comparisons from the STAMPEDE platform trial in metastatic prostate cancer, indirect comparisons using non-concurrent controls were inconsistent with the information from direct randomized comparisons. This supports the primary analysis approach of STAMPEDE, which used only direct randomized comparisons. CONCLUSION: Network meta-analysis provides a natural methodology for analyzing the network of direct and indirect treatment comparisons from a platform trial. Such analyses provide transparent separation of direct and indirect evidence, allowing assessment of the impact of non-concurrent controls. We recommend time-stratified analysis of concurrently controlled comparisons for primary analyses, with time-adjusted analyses incorporating non-concurrent controls reserved for secondary analyses. However, regardless of which methodology is used, a network analysis provides a useful supplement to the primary analysis.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs.

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

Adding new experimental arms to randomised clinical trials: Impact on error rates.

BACKGROUND: Experimental treatments pass through various stages of development. If a treatment passes through early-phase experiments, the investigators may want to assess it in a late-phase randomised controlled trial. An efficient way to do this is adding it as a new research arm to an ongoing trial while the existing research arms continue, a so-called multi-arm platform trial. The familywise type I error rate is often a key quantity of interest in any multi-arm platform trial. We set out to clarify how it should be calculated when new arms are added to a trial some time after it has started. METHODS: We show how the familywise type I error rate, any-pair and all-pairs powers can be calculated when a new arm is added to a platform trial. We extend the Dunnett probability and derive analytical formulae for the correlation between the test statistics of the existing pairwise comparison and that of the newly added arm. We also verify our analytical derivation via simulations. RESULTS: Our results indicate that the familywise type I error rate depends on the shared control arm information (i.e. individuals in continuous and binary outcomes and primary outcome events in time-to-event outcomes) from the common control arm patients and the allocation ratio. The familywise type I error rate is driven more by the number of pairwise comparisons and the corresponding (pairwise) type I error rates than by the timing of the addition of the new arms. The familywise type I error rate can be estimated using Sidák's correction if the correlation between the test statistics of pairwise comparisons is less than 0.30. CONCLUSIONS: The findings we present in this article can be used to design trials with pre-planned deferred arms or to add new pairwise comparisons within an ongoing platform trial where control of the pairwise error rate or familywise type I error rate (for a subset of pairwise comparisons) is required.

Assessing the impact of efficacy stopping rules on the error rates under the multi-arm multi-stage framework.

BACKGROUND: The multi-arm multi-stage framework uses intermediate outcomes to assess lack-of-benefit of research arms at interim stages in randomised trials with time-to-event outcomes. However, the design lacks formal methods to evaluate early evidence of overwhelming efficacy on the definitive outcome measure. We explore the operating characteristics of this extension to the multi-arm multi-stage design and how to control the pairwise and familywise type I error rate. Using real examples and the updated nstage program, we demonstrate how such a design can be developed in practice. METHODS: We used the Dunnett approach for assessing treatment arms when conducting comprehensive simulation studies to evaluate the familywise error rate, with and without interim efficacy looks on the definitive outcome measure, at the same time as the planned lack-of-benefit interim analyses on the intermediate outcome measure. We studied the effect of the timing of interim analyses, allocation ratio, lack-of-benefit boundaries, efficacy rule, number of stages and research arms on the operating characteristics of the design when efficacy stopping boundaries are incorporated. Methods for controlling the familywise error rate with efficacy looks were also addressed. RESULTS: Incorporating Haybittle-Peto stopping boundaries on the definitive outcome at the interim analyses will not inflate the familywise error rate in a multi-arm design with two stages. However, this rule is conservative; in general, more liberal stopping boundaries can be used with minimal impact on the familywise error rate. Efficacy bounds in trials with three or more stages using an intermediate outcome may inflate the familywise error rate, but we show how to maintain strong control. CONCLUSION: The multi-arm multi-stage design allows stopping for both lack-of-benefit on the intermediate outcome and efficacy on the definitive outcome at the interim stages. We provide guidelines on how to control the familywise error rate when efficacy boundaries are implemented in practice.

Simulation optimization for Bayesian multi-arm multi-stage clinical trial with binary endpoints.

Multi-arm multi-stage designs, in which multiple active treatments are compared to a control and accumulated information from interim data are used to add or remove arms from the trial, may reduce development costs and shorten the drug development timeline. As such, this adaptive update is a natural complement to Bayesian methodology in which the prior clinical belief is sequentially updated using the observed probability of success. Simulation is often required for planning clinical trials to accommodate the complexity of the design and to optimize key design characteristics. This paper addresses two key limiting factors in simulations, namely the computational burden and the time needed to obtain results. We first introduce a generic process for simulating Bayesian multi-arm multi-stage designs with binary endpoints. Then, to address the computational burden and time, we optimize the method for calculating the posterior probability and posterior predictive probability of success.