Bayesian sample size determination in basket trials borrowing information between subsets.

Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomized basket trial design where patients are randomly assigned to the new treatment or control within each trial subset ("subtrial" for short). Closed-form sample size formulae are derived to ensure that each subtrial has a specified chance of correctly deciding whether the new treatment is superior to or not better than the control by some clinically relevant difference. Given prespecified levels of pairwise (in)commensurability, the subtrial sample sizes are solved simultaneously. The proposed Bayesian approach resembles the frequentist formulation of the problem in yielding comparable sample sizes for circumstances of no borrowing. When borrowing is enabled between commensurate subtrials, a considerably smaller trial sample size is required compared to the widely implemented approach of no borrowing. We illustrate the use of our sample size formulae with two examples based on real basket trials. A comprehensive simulation study further shows that the proposed methodology can maintain the true positive and false positive rates at desired levels.

A Bayesian approach to pilot-pivotal trials for bioequivalence assessment.

BACKGROUND: To demonstrate bioequivalence between two drug formulations, a pilot trial is often conducted prior to a pivotal trial to assess feasibility and gain preliminary information about the treatment effect. Due to the limited sample size, it is not recommended to perform significance tests at the conventional 5% level using pilot data to determine if a pivotal trial should take place. Whilst some authors suggest to relax the significance level, a Bayesian framework provides an alternative for informing the decision-making. Moreover, a Bayesian approach also readily permits possible incorporation of pilot data in priors for the parameters that underpin the pivotal trial. METHODS: We consider two-sequence, two-period crossover designs that compare test (T) and reference (R) treatments. We propose a robust Bayesian hierarchical model, embedded with a scaling factor, to elicit a Go/No-Go decision using predictive probabilities. Following a Go decision, the final analysis to formally establish bioequivalence can leverage both the pilot and pivotal trial data jointly. A simulation study is performed to evaluate trial operating characteristics. RESULTS: Compared with conventional procedures, our proposed method improves the decision-making to correctly allocate a Go decision in scenarios of bioequivalence. By choosing an appropriate threshold, the probability of correctly (incorrectly) making a No-Go (Go) decision can be ensured at a desired target level. Using both pilot and pivotal trial data in the final analysis can result in a higher chance of declaring bioequivalence. The false positive rate can be maintained in situations when T and R are not bioequivalent. CONCLUSIONS: The proposed methodology is novel and effective in different stages of bioequivalence assessment. It can greatly enhance the decision-making process in bioequivalence trials, particularly in situations with a small sample size.

A hybrid approach to comparing parallel-group and stepped-wedge cluster-randomized trials with a continuous primary outcome when there is uncertainty in the intra-cluster correlation.

BACKGROUND/AIMS: To evaluate how uncertainty in the intra-cluster correlation impacts whether a parallel-group or stepped-wedge cluster-randomized trial design is more efficient in terms of the required sample size, in the case of cross-sectional stepped-wedge cluster-randomized trials and continuous outcome data. METHODS: We motivate our work by reviewing how the intra-cluster correlation and standard deviation were justified in 54 health technology assessment reports on cluster-randomized trials. To enable uncertainty at the design stage to be incorporated into the design specification, we then describe how sample size calculation can be performed for cluster- randomized trials in the 'hybrid' framework, which places priors on design parameters and controls the expected power in place of the conventional frequentist power. Comparison of the parallel-group and stepped-wedge cluster-randomized trial designs is conducted by placing Beta and truncated Normal priors on the intra-cluster correlation, and a Gamma prior on the standard deviation. RESULTS: Many Health Technology Assessment reports did not adhere to the Consolidated Standards of Reporting Trials guideline of indicating the uncertainty around the assumed intra-cluster correlation, while others did not justify the assumed intra-cluster correlation or standard deviation. Even for a prior intra-cluster correlation distribution with a small mode, moderate prior densities on high intra-cluster correlation values can lead to a stepped-wedge cluster-randomized trial being more efficient because of the degree to which a stepped-wedge cluster-randomized trial is more efficient for high intra-cluster correlations. With careful specification of the priors, the designs in the hybrid framework can become more robust to, for example, an unexpectedly large value of the outcome variance. CONCLUSION: When there is difficulty obtaining a reliable value for the intra-cluster correlation to assume at the design stage, the proposed methodology offers an appealing approach to sample size calculation. Often, uncertainty in the intra-cluster correlation will mean a stepped-wedge cluster-randomized trial is more efficient than a parallel-group cluster-randomized trial design.

Advantages of multi-arm non-randomised sequentially allocated cohort designs for Phase II oncology trials.

BACKGROUND: Efficient trial designs are required to prioritise promising drugs within Phase II trials. Adaptive designs are examples of such designs, but their efficiency is reduced if there is a delay in assessing patient responses to treatment. METHODS: Motivated by the WIRE trial in renal cell carcinoma (NCT03741426), we compare three trial approaches to testing multiple treatment arms: (1) single-arm trials in sequence with interim analyses; (2) a parallel multi-arm multi-stage trial and (3) the design used in WIRE, which we call the Multi-Arm Sequential Trial with Efficient Recruitment (MASTER) design. The MASTER design recruits patients to one arm at a time, pausing recruitment to an arm when it has recruited the required number for an interim analysis. We conduct a simulation study to compare how long the three different trial designs take to evaluate a number of new treatment arms. RESULTS: The parallel multi-arm multi-stage and the MASTER design are much more efficient than separate trials. The MASTER design provides extra efficiency when there is endpoint delay, or recruitment is very quick. CONCLUSIONS: We recommend the MASTER design as an efficient way of testing multiple promising cancer treatments in non-comparative Phase II trials.

Improving power in PSA response analyses of metastatic castration-resistant prostate cancer trials.

BACKGROUND: To determine how much an augmented analysis approach could improve the efficiency of prostate-specific antigen (PSA) response analyses in clinical practice. PSA response rates are commonly used outcome measures in metastatic castration-resistant prostate cancer (mCRPC) trial reports. PSA response is evaluated by comparing continuous PSA data (e.g., change from baseline) to a threshold (e.g., 50% reduction). Consequently, information in the continuous data is discarded. Recent papers have proposed an augmented approach that retains the conventional response rate, but employs the continuous data to improve precision of estimation. METHODS: A literature review identified published prostate cancer trials that included a waterfall plot of continuous PSA data. This continuous data was extracted to enable the conventional and augmented approaches to be compared. RESULTS: Sixty-four articles, reporting results for 78 mCRPC treatment arms, were re-analysed. The median efficiency gain from using the augmented analysis, in terms of the implied increase to the sample size of the original study, was 103.2% (IQR [89.8,190.9%]). CONCLUSIONS: Augmented PSA response analysis requires no additional data to be collected and can be performed easily using available software. It improves precision of estimation to a degree that is equivalent to a substantial sample size increase. The implication of this work is that prostate cancer trials using PSA response as a primary endpoint could be delivered with fewer participants and, therefore, more rapidly with reduced cost.

Response adaptive intervention allocation in stepped-wedge cluster randomized trials.

BACKGROUND: Stepped-wedge cluster randomized trial (SW-CRT) designs are often used when there is a desire to provide an intervention to all enrolled clusters, because of a belief that it will be effective. However, given there should be equipoise at trial commencement, there has been discussion around whether a pre-trial decision to provide the intervention to all clusters is appropriate. In pharmaceutical drug development, a solution to a similar desire to provide more patients with an effective treatment is to use a response adaptive (RA) design. METHODS: We introduce a way in which RA design could be incorporated in an SW-CRT, permitting modification of the intervention allocation during the trial. The proposed framework explicitly permits a balance to be sought between power and patient benefit considerations. A simulation study evaluates the methodology. RESULTS: In one scenario, for one particular RA design, the proportion of cluster-periods spent in the intervention condition was observed to increase from 32.2% to 67.9% as the intervention effect was increased. A cost of this was a 6.2% power drop compared to a design that maximized power by fixing the proportion of time in the intervention condition at 45.0%, regardless of the intervention effect. CONCLUSIONS: An RA approach may be most applicable to settings for which the intervention has substantial individual or societal benefit considerations, potentially in combination with notable safety concerns. In such a setting, the proposed methodology may routinely provide the desired adaptability of the roll-out speed, with only a small cost to the study's power.

Conditional power and friends: The why and how of (un)planned, unblinded sample size recalculations in confirmatory trials.

Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty. Since the sample size is usually determined by an argument based on the power of the trial, an interim analysis raises the question of how the final sample size should be determined conditional on the accrued information. To this end, we first review and compare common approaches to estimating conditional power, which is often used in heuristic sample size recalculation rules. We then discuss the connection of heuristic sample size recalculation and optimal two-stage designs, demonstrating that the latter is the superior approach in a fully preplanned setting. Hence, unplanned design adaptations should only be conducted as reaction to trial-external new evidence, operational needs to violate the originally chosen design, or post hoc changes in the optimality criterion but not as a reaction to trial-internal data. We are able to show that commonly discussed sample size recalculation rules lead to paradoxical adaptations where an initially planned optimal design is not invariant under the adaptation rule even if the planning assumptions do not change. Finally, we propose two alternative ways of reacting to newly emerging trial-external evidence in ways that are consistent with the originally planned design to avoid such inconsistencies.

Optimised point estimators for multi-stage single-arm phase II oncology trials.

The uniform minimum variance unbiased estimator (UMVUE) is, by definition, a solution to removing bias in estimation following a multi-stage single-arm trial with a primary dichotomous outcome. However, the UMVUE is known to have large residual mean squared error (RMSE). Therefore, we develop an optimisation approach to finding estimators with reduced RMSE for many response rates, which attain low bias. We demonstrate that careful choice of the optimisation parameters can lead to an estimator with often substantially reduced RMSE, without the introduction of appreciable bias.

A stochastically curtailed single-arm phase II trial design for binary outcomes.

Phase II clinical trials are a critical aspect of the drug development process. With drug development costs ever increasing, novel designs that can improve the efficiency of phase II trials are extremely valuable.Phase II clinical trials for cancer treatments often measure a binary outcome. The final trial decision is generally to continue or cease development. When this decision is based solely on the result of a hypothesis test, the result may be known with certainty before the planned end of the trial. Unfortunately, there is often no opportunity for early stopping when this occurs.Some existing designs do permit early stopping in this case, accordingly reducing the required sample size and potentially speeding up drug development. However, more improvements can be achieved by stopping early when the final trial decision is very likely, rather than certain, known as stochastic curtailment. While some authors have proposed approaches of this form, these approaches have various limitations.In this work we address these limitations by proposing new design approaches for single-arm phase II binary outcome trials that use stochastic curtailment. We use exact distributions, avoid simulation, consider a wider range of possible designs and permit early stopping for promising treatments. As a result, we are able to obtain trial designs that have considerably reduced sample sizes on average.

A stochastically curtailed two-arm randomised phase II trial design for binary outcomes.

Randomised controlled trials are considered the gold standard in trial design. However, phase II oncology trials with a binary outcome are often single-arm. Although a number of reasons exist for choosing a single-arm trial, the primary reason is that single-arm designs require fewer participants than their randomised equivalents. Therefore, the development of novel methodology that makes randomised designs more efficient is of value to the trials community. This article introduces a randomised two-arm binary outcome trial design that includes stochastic curtailment (SC), allowing for the possibility of stopping a trial before the final conclusions are known with certainty. In addition to SC, the proposed design involves the use of a randomised block design, which allows investigators to control the number of interim analyses. This approach is compared with existing designs that also use early stopping, through the use of a loss function comprised of a weighted sum of design characteristics. Comparisons are also made using an example from a real trial. The comparisons show that for many possible loss functions, the proposed design is superior to existing designs. Further, the proposed design may be more practical, by allowing a flexible number of interim analyses. One existing design produces superior design realisations when the anticipated response rate is low. However, when using this design, the probability of rejecting the null hypothesis is sensitive to misspecification of the null response rate. Therefore, when considering randomised designs in phase II, we recommend the proposed approach be preferred over other sequential designs.

Treatment allocation strategies for umbrella trials in the presence of multiple biomarkers: A comparison of methods.

Umbrella trials are an innovative trial design where different treatments are matched with subtypes of a disease, with the matching typically based on a set of biomarkers. Consequently, when patients can be positive for more than one biomarker, they may be eligible for multiple treatment arms. In practice, different approaches could be applied to allocate patients who are positive for multiple biomarkers to treatments. However, to date there has been little exploration of how these approaches compare statistically. We conduct a simulation study to compare five approaches to handling treatment allocation in the presence of multiple biomarkers - equal randomisation; randomisation with fixed probability of allocation to control; Bayesian adaptive randomisation (BAR); constrained randomisation; and hierarchy of biomarkers. We evaluate these approaches under different scenarios in the context of a hypothetical phase II biomarker-guided umbrella trial. We define the pairings representing the pre-trial expectations on efficacy as linked pairs, and the other biomarker-treatment pairings as unlinked. The hierarchy and BAR approaches have the highest power to detect a treatment-biomarker linked interaction. However, the hierarchy procedure performs poorly if the pre-specified treatment-biomarker pairings are incorrect. The BAR method allocates a higher proportion of patients who are positive for multiple biomarkers to promising treatments when an unlinked interaction is present. In most scenarios, the constrained randomisation approach best balances allocation to all treatment arms. Pre-specification of an approach to deal with treatment allocation in the presence of multiple biomarkers is important, especially when overlapping subgroups are likely.

A web application for the design of multi-arm clinical trials.

BACKGROUND: Multi-arm designs provide an effective means of evaluating several treatments within the same clinical trial. Given the large number of treatments now available for testing in many disease areas, it has been argued that their utilisation should increase. However, for any given clinical trial there are numerous possible multi-arm designs that could be used, and choosing between them can be a difficult task. This task is complicated further by a lack of available easy-to-use software for designing multi-arm trials. RESULTS: To aid the wider implementation of multi-arm clinical trial designs, we have developed a web application for sample size calculation when using a variety of popular multiple comparison corrections. Furthermore, the application supports sample size calculation to control several varieties of power, as well as the determination of optimised arm-wise allocation ratios. It is built using the Shiny package in the R programming language, is free to access on any device with an internet browser, and requires no programming knowledge to use. It incorporates a variety of features to make it easier to use, including help boxes and warning messages. Using design parameters motivated by a recently completed phase II oncology trial, we demonstrate that the application can effectively determine and evaluate complex multi-arm trial designs. CONCLUSIONS: The application provides the core information required by statisticians and clinicians to review the operating characteristics of a chosen multi-arm clinical trial design. The range of designs supported by the application is broader than other currently available software solutions. Its primary limitation, particularly from a regulatory agency point of view, is its lack of validation. However, we present an approach to efficiently confirming its results via simulation.

Admissible multiarm stepped-wedge cluster randomized trial designs.

Numerous publications have now addressed the principles of designing, analyzing, and reporting the results of stepped-wedge cluster randomized trials. In contrast, there is little research available pertaining to the design and analysis of multiarm stepped-wedge cluster randomized trials, utilized to evaluate the effectiveness of multiple experimental interventions. In this paper, we address this by explaining how the required sample size in these multiarm trials can be ascertained when data are to be analyzed using a linear mixed model. We then go on to describe how the design of such trials can be optimized to balance between minimizing the cost of the trial and minimizing some function of the covariance matrix of the treatment effect estimates. Using a recently commenced trial that will evaluate the effectiveness of sensor monitoring in an occupational therapy rehabilitation program for older persons after hip fracture as an example, we demonstrate that our designs could reduce the number of observations required for a fixed power level by up to 58%. Consequently, when logistical constraints permit the utilization of any one of a range of possible multiarm stepped-wedge cluster randomized trial designs, researchers should consider employing our approach to optimize their trials efficiency.

Re-formulating Gehan's design as a flexible two-stage single-arm trial.

BACKGROUND: Gehan's two-stage design was historically the design of choice for phase II oncology trials. One of the reasons it is less frequently used today is that it does not allow for a formal test of treatment efficacy, and therefore does not control conventional type-I and type-II error-rates. METHODS: We describe how recently developed methodology for flexible two-stage single-arm trials can be used to incorporate the hypothesis test commonly associated with phase II trials in to Gehan's design. We additionally detail how this hypothesis test can be optimised in order to maximise its power, and describe how the second stage sample sizes can be chosen to more readily provide the operating characteristics that were originally envisioned by Gehan. Finally, we contrast our modified Gehan designs to Simon's designs, based on two examples motivated by real clinical trials. RESULTS: Gehan's original designs are often greatly under- or over-powered when compared to type-II error-rates typically used in phase II. However, we demonstrate that the control parameters of his design can be chosen to resolve this problem. With this, though, the modified Gehan designs have operating characteristics similar to the more familiar Simon designs. CONCLUSIONS: The trial design settings in which Gehan's design will be preferable over Simon's designs are likely limited. Provided the second stage sample sizes are chosen carefully, however, one scenario of potential utility is when the trial's primary goal is to ascertain the treatment response rate to a certain precision.

Group sequential clinical trial designs for normally distributed outcome variables.

In a group sequential clinical trial, accumulated data are analyzed at numerous time points to allow early decisions about a hypothesis of interest. These designs have historically been recommended for their ethical, administrative, and economic benefits. In this article, we first discuss a collection of new commands for computing the stopping boundaries and required group size of various classical group sequential designs, assuming a normally distributed outcome variable. Then, we demonstrate how the performance of several designs can be compared graphically.

Blinded and unblinded sample size reestimation in crossover trials balanced for period.

The determination of the sample size required by a crossover trial typically depends on the specification of one or more variance components. Uncertainty about the value of these parameters at the design stage means that there is often a risk a trial may be under- or overpowered. For many study designs, this problem has been addressed by considering adaptive design methodology that allows for the re-estimation of the required sample size during a trial. Here, we propose and compare several approaches for this in multitreatment crossover trials. Specifically, regulators favor reestimation procedures to maintain the blinding of the treatment allocations. We therefore develop blinded estimators for the within and between person variances, following simple or block randomization. We demonstrate that, provided an equal number of patients are allocated to sequences that are balanced for period, the proposed estimators following block randomization are unbiased. We further provide a formula for the bias of the estimators following simple randomization. The performance of these procedures, along with that of an unblinded approach, is then examined utilizing three motivating examples, including one based on a recently completed four-treatment four-period crossover trial. Simulation results show that the performance of the proposed blinded procedures is in many cases similar to that of the unblinded approach, and thus they are an attractive alternative.

Blinded and unblinded sample size reestimation procedures for stepped-wedge cluster randomized trials.

The ability to accurately estimate the sample size required by a stepped-wedge (SW) cluster randomized trial (CRT) routinely depends upon the specification of several nuisance parameters. If these parameters are misspecified, the trial could be overpowered, leading to increased cost, or underpowered, enhancing the likelihood of a false negative. We address this issue here for cross-sectional SW-CRTs, analyzed with a particular linear-mixed model, by proposing methods for blinded and unblinded sample size reestimation (SSRE). First, blinded estimators for the variance parameters of a SW-CRT analyzed using the Hussey and Hughes model are derived. Following this, procedures for blinded and unblinded SSRE after any time period in a SW-CRT are detailed. The performance of these procedures is then examined and contrasted using two example trial design scenarios. We find that if the two key variance parameters were underspecified by 50%, the SSRE procedures were able to increase power over the conventional SW-CRT design by up to 41%, resulting in an empirical power above the desired level. Thus, though there are practical issues to consider, the performance of the procedures means researchers should consider incorporating SSRE in to future SW-CRTs.

Group sequential designs for stepped-wedge cluster randomised trials.

BACKGROUND/AIMS: The stepped-wedge cluster randomised trial design has received substantial attention in recent years. Although various extensions to the original design have been proposed, no guidance is available on the design of stepped-wedge cluster randomised trials with interim analyses. In an individually randomised trial setting, group sequential methods can provide notable efficiency gains and ethical benefits. We address this by discussing how established group sequential methodology can be adapted for stepped-wedge designs. METHODS: Utilising the error spending approach to group sequential trial design, we detail the assumptions required for the determination of stepped-wedge cluster randomised trials with interim analyses. We consider early stopping for efficacy, futility, or efficacy and futility. We describe first how this can be done for any specified linear mixed model for data analysis. We then focus on one particular commonly utilised model and, using a recently completed stepped-wedge cluster randomised trial, compare the performance of several designs with interim analyses to the classical stepped-wedge design. Finally, the performance of a quantile substitution procedure for dealing with the case of unknown variance is explored. RESULTS: We demonstrate that the incorporation of early stopping in stepped-wedge cluster randomised trial designs could reduce the expected sample size under the null and alternative hypotheses by up to 31% and 22%, respectively, with no cost to the trial's type-I and type-II error rates. The use of restricted error maximum likelihood estimation was found to be more important than quantile substitution for controlling the type-I error rate. CONCLUSION: The addition of interim analyses into stepped-wedge cluster randomised trials could help guard against time-consuming trials conducted on poor performing treatments and also help expedite the implementation of efficacious treatments. In future, trialists should consider incorporating early stopping of some kind into stepped-wedge cluster randomised trials according to the needs of the particular trial.

Do single-arm trials have a role in drug development plans incorporating randomised trials?

Often, single-arm trials are used in phase II to gather the first evidence of an oncological drug's efficacy, with drug activity determined through tumour response using the RECIST criterion. Provided the null hypothesis of 'insufficient drug activity' is rejected, the next step could be a randomised two-arm trial. However, single-arm trials may provide a biased treatment effect because of patient selection, and thus, this development plan may not be an efficient use of resources. Therefore, we compare the performance of development plans consisting of single-arm trials followed by randomised two-arm trials with stand-alone single-stage or group sequential randomised two-arm trials. Through this, we are able to investigate the utility of single-arm trials and determine the most efficient drug development plans, setting our work in the context of a published single-arm non-small-cell lung cancer trial. Reference priors, reflecting the opinions of 'sceptical' and 'enthusiastic' investigators, are used to quantify and guide the suitability of single-arm trials in this setting. We observe that the explored development plans incorporating single-arm trials are often non-optimal. Moreover, even the most pessimistic reference priors have a considerable probability in favour of alternative plans. Analysis suggests expected sample size savings of up to 25% could have been made, and the issues associated with single-arm trials avoided, for the non-small-cell lung cancer treatment through direct progression to a group sequential randomised two-arm trial. Careful consideration should thus be given to the use of single-arm trials in oncological drug development when a randomised trial will follow.

Point estimation following a two-stage group sequential trial.

Repeated testing in a group sequential trial can result in bias in the maximum likelihood estimate of the unknown parameter of interest. Many authors have therefore proposed adjusted point estimation procedures, which attempt to reduce such bias. Here, we describe nine possible point estimators within a common general framework for a two-stage group sequential trial. We then contrast their performance in five example trial settings, examining their conditional and marginal biases and residual mean square error. By focusing on the case of a trial with a single interim analysis, additional new results aiding the determination of the estimators are given. Our findings demonstrate that the uniform minimum variance unbiased estimator, whilst being marginally unbiased, often has large conditional bias and residual mean square error. If one is concerned solely about inference on progression to the second trial stage, the conditional uniform minimum variance unbiased estimator may be preferred. Two estimators, termed mean adjusted estimators, which attempt to reduce the marginal bias, arguably perform best in terms of the marginal residual mean square error. In all, one should choose an estimator accounting for its conditional and marginal biases and residual mean square error; the most suitable estimator will depend on relative desires to minimise each of these factors. If one cares solely about the conditional and marginal biases, the conditional maximum likelihood estimate may be preferred provided lower and upper stopping boundaries are included. If the conditional and marginal residual mean square error are also of concern, two mean adjusted estimators perform well.