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.

Residual Disease After Primary Surgical Treatment for Advanced Epithelial Ovarian Cancer, Part 2: Network Meta-analysis Incorporating Expert Elicitation to Adjust for Publication Bias.

BACKGROUND: Previous work has identified a strong association between the achievements of macroscopic cytoreduction and improved overall survival (OS) after primary surgical treatment of advanced epithelial ovarian cancer. Despite the use of contemporary methodology, resulting in the most comprehensive currently available evidence to date in this area, opponents remain skeptical. AREAS OF UNCERTAINTY: We aimed to conduct sensitivity analyses to adjust for potential publication bias, to confirm or refute existing conclusions and recommendations, leveraging elicitation to incorporate expert opinion. We recommend our approach as an exemplar that should be adopted in other areas of research. DATA SOURCES: We conducted random-effects network meta-analyses in frequentist and Bayesian (using Markov Chain Montel Carlo simulation) frameworks comparing OS across residual disease thresholds in women with advanced epithelial ovarian cancer after primary cytoreductive surgery. Elicitation methods among experts in gynecology were used to derive priors for an extension to a previously reported Copas selection model and a novel approach using effect estimates calculated from the elicitation exercise, to attempt to adjust for publication bias and increase confidence in the certainty of the evidence. THERAPEUTIC ADVANCES: Analyses using data from 25 studies (n = 20,927 women) all showed the prognostic importance of complete cytoreduction (0 cm) in both frameworks. Experts accepted publication bias was likely, but after adjustment for their opinions, published results overpowered the informative priors incorporated into the Bayesian sensitivity analyses. Effect estimates were attenuated but conclusions were robust in all analyses. CONCLUSIONS: There remains a strong association between the achievement of complete cytoreduction and improved OS even after adjustment for publication bias using strong informative priors formed from an expert elicitation exercise. The concepts of the elicitation survey should be strongly considered for utilization in other meta-analyses.

Residual Disease Threshold After Primary Surgical Treatment for Advanced Epithelial Ovarian Cancer, Part 1: A Systematic Review and Network Meta-Analysis.

BACKGROUND: We present a systematic review and network meta-analysis (NMA) that is the precursor underpinning the Bayesian analyses that adjust for publication bias, presented in the same edition in AJT. The review assesses optimal cytoreduction for women undergoing primary advanced epithelial ovarian cancer (EOC) surgery. AREAS OF UNCERTAINTY: To assess the impact of residual disease (RD) after primary debulking surgery in women with advanced EOC. This review explores the impact of leaving varying levels of primary debulking surgery. DATA SOURCES: We conducted a systematic review and random-effects NMA for overall survival (OS) to incorporate direct and indirect estimates of RD thresholds, including concurrent comparative, retrospective studies of ≥100 adult women (18+ years) with surgically staged advanced EOC (FIGO stage III/IV) who had confirmed histological diagnoses of ovarian cancer. Pairwise meta-analyses of all directly compared RD thresholds was previously performed before conducting this NMA, and the statistical heterogeneity of studies within each comparison was evaluated using recommended methods. THERAPEUTIC ADVANCES: Twenty-five studies (n = 20,927) were included. Analyses demonstrated the prognostic importance of complete cytoreduction to no macroscopic residual disease (NMRD), with a hazard ratio for OS of 2.0 (95% confidence interval, 1.8-2.2) for <1 cm RD threshold versus NMRD. NMRD was associated with prolonged survival across all RD thresholds. Leaving NMRD was predicted to provide longest survival (probability of being best = 99%). The results were robust to sensitivity analysis including only those studies that adjusted for extent of disease at primary surgery (hazard ratio 2.3, 95% confidence interval, 1.9-2.6). The overall certainty of evidence was moderate and statistical adjustment of effect estimates in included studies minimized bias. CONCLUSIONS: The results confirm a strong association between complete cytoreduction to NMRD and improved OS. The NMA approach forms part of the methods guidance underpinning policy making in many jurisdictions. Our analyses present an extension to the previous work in this area.

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.

The Infant KIdney Dialysis and Utrafiltration (I-KID) Study: A Stepped-Wedge Cluster-Randomized Study in Infants, Comparing Peritoneal Dialysis, Continuous Venovenous Hemofiltration, and Newcastle Infant Dialysis Ultrafiltration System, a Novel Infant Hemodialysis Device.

OBJECTIVES: Renal replacement therapy (RRT) options are limited for small babies because of lack of available technology. We investigated the precision of ultrafiltration, biochemical clearances, clinical efficacy, outcomes, and safety profile for a novel non-Conformité Européenne-marked hemodialysis device for babies under 8 kg, the Newcastle Infant Dialysis Ultrafiltration System (NIDUS), compared with the current options of peritoneal dialysis (PD) or continuous venovenous hemofiltration (CVVH). DESIGN: Nonblinded cluster-randomized cross-sectional stepped-wedge design with four periods, three sequences, and two clusters per sequence. SETTING: Clusters were six U.K. PICUs. PATIENTS: Babies less than 8 kg requiring RRT for fluid overload or biochemical disturbance. INTERVENTIONS: In controls, RRT was delivered by PD or CVVH, and in interventions, NIDUS was used. The primary outcome was precision of ultrafiltration compared with prescription; secondary outcomes included biochemical clearances. MEASUREMENTS AND MAIN RESULTS: At closure, 97 participants were recruited from the six PICUs (62 control and 35 intervention). The primary outcome, obtained from 62 control and 21 intervention patients, showed that ultrafiltration with NIDUS was closer to that prescribed than with control: sd controls, 18.75, intervention, 2.95 (mL/hr); adjusted ratio, 0.13; 95% CI, 0.03-0.71; p = 0.018. Creatinine clearance was smallest and least variable for PD (mean, sd ) = (0.08, 0.03) mL/min/kg, larger for NIDUS (0.46, 0.30), and largest for CVVH (1.20, 0.72). Adverse events were reported in all groups. In this critically ill population with multiple organ failure, mortality was lowest for PD and highest for CVVH, with NIDUS in between. CONCLUSIONS: NIDUS delivers accurate, controllable fluid removal and adequate clearances, indicating that it has important potential alongside other modalities for infant RRT.

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.

Mind the gap: covariate constrained randomisation can protect against substantial power loss in parallel cluster randomised trials.

BACKGROUND: Cluster randomised trials often randomise a small number of units, putting them at risk of poor balance of covariates across treatment arms. Covariate constrained randomisation aims to reduce this risk by removing the worst balanced allocations from consideration. This is known to provide only a small gain in power over that averaged under simple randomisation and is likely influenced by the number and prognostic effect of the covariates. We investigated the performance of covariate constrained randomisation in comparison to the worst balanced allocations, and considered the impact on the power of the prognostic effect and number of covariates adjusted for in the analysis. METHODS: Using simulation, we examined the Monte Carlo type I error rate and power of cross-sectional, two-arm parallel cluster-randomised trials with a continuous outcome and four binary cluster-level covariates, using either simple or covariate constrained randomisation. Data were analysed using a small sample corrected linear mixed-effects model, adjusted for some or all of the binary covariates. We varied the number of clusters, intra-cluster correlation, number and prognostic effect of covariates balanced in the randomisation and adjusted in the analysis, and the size of the candidate set from which the allocation was selected. For each scenario, 20,000 simulations were conducted. RESULTS: When compared to the worst balanced allocations, covariate constrained randomisation with an adjusted analysis provided gains in power of up to 20 percentage points. Even with analysis-based adjustment for those covariates balanced in the randomisation, the type I error rate was not maintained when the intracluster correlation is very small (0.001). Generally, greater power was achieved when more prognostic covariates are restricted in the randomisation and as the size of the candidate set decreases. However, adjustment for weakly prognostic covariates lead to a loss in power of up to 20 percentage points. CONCLUSIONS: When compared to the worst balanced allocations, covariate constrained randomisation provides moderate to substantial improvements in power. However, the prognostic effect of the covariates should be carefully considered when selecting them for inclusion in the randomisation.

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.

A review of available software for adaptive clinical trial design.

BACKGROUND/AIMS: The increasing cost of the drug development process has seen interest in the use of adaptive trial designs grow substantially. Accordingly, much research has been conducted to identify barriers to increasing the use of adaptive designs in practice. Several articles have argued that the availability of user-friendly software will be an important step in making adaptive designs easier to implement. Therefore, we present a review of the current state of software availability for adaptive trial design. METHODS: We review articles from 31 journals published in 2013-2017 that relate to methodology for adaptive trials to assess how often code and software for implementing novel adaptive designs is made available at the time of publication. We contrast our findings against these journals' policies on code distribution. We also search popular code repositories, such as Comprehensive R Archive Network and GitHub, to identify further existing user-contributed software for adaptive designs. From this, we are able to direct interested parties toward solutions for their problem of interest. RESULTS: Only 30% of included articles made their code available in some form. In many instances, articles published in journals that had mandatory requirements on code provision still did not make code available. There are several areas in which available software is currently limited or saturated. In particular, many packages are available to address group sequential design, but comparatively little code is present in the public domain to determine biomarker-guided adaptive designs. CONCLUSIONS: There is much room for improvement in the provision of software alongside adaptive design publications. In addition, while progress has been made, well-established software for various types of trial adaptation remains sparsely available.

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.