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We develop optimal decision rules for sample size re-estimation in two-stage adaptive group sequential clinical trials. It is usual for the initial sample size specification of such trials to be adequate to detect a realistic treatment effect δ a with good power, but not sufficient to detect the smallest clinically meaningful treatment effect δ min . Moreover it is difficult for the sponsors of such trials to make the up-front commitment needed to adequately power a study to detect δ min . It is easier to justify increasing the sample size if the interim data enter a so-called "promising zone" that ensures with high probability that the trial will succeed. We have considered promising zone designs that optimize unconditional power and promising zone designs that optimize conditional power and have discussed the tension that exists between these two objectives. Where there is reluctance to base the sample size re-estimation rule on the parameter δ min we propose a Bayesian option whereby a prior distribution is assigned to the unknown treatment effect δ , which is then integrated out of the objective function with respect to its posterior distribution at the interim analysis., (© 2022 John Wiley & Sons Ltd.)

Statistical methods for controlling the type-I error of hypothesis tests in adaptive group sequential clinical trials are well established and well understood. However, methods for obtaining statistically valid point estimates and confidence intervals for adaptive designs are not as well established or as well understood. At the end of an adaptive trial, one may calculate the repeated confidence interval (RCI), which provides conservative coverage of δ , or the backward image confidence interval (BWCI), which provides exact coverage of δ and is an extension of the stagewise adjusted confidence interval (SWCI, used in classical group sequential designs). The BWCI can also provide a median unbiased estimate (MUE) of δ . There is a need to better understand the coverage and possible biases associated with these methods. We conducted a simulation study exploring parameter estimation following sample size reestimation based on testing methods with strong control of type-I error. Generally, the BWCI provided exact coverage, the naïve CI provided inconsistent coverage, and the RCI provided conservative coverage. Additionally, we note considerable asymmetry in the coverage from above/from below for the RCI, although we did not see any instance where the 95% RCI excluded the true parameter more than 2.5% on either side. At the end of an adaptive group sequential trial, we strongly recommend the use of the BWCI (and associated MUE), with the RCI computed during interim looks; the naïve CI should be avoided. These results and conclusions also hold true for classical group sequential designs., (© 2021 John Wiley & Sons Ltd.)

Two methods for designing adaptive multiarm multistage (MAMS) clinical trials, originating from conceptually different group sequential frameworks are presented, and their operating characteristics are compared. In both methods pairwise comparisons are made, stage-by-stage, between each treatment arm and a common control arm with the goal of identifying active treatments and dropping inactive ones. At any stage one may alter the future course of the trial through adaptive changes to the prespecified decision rules for treatment selection and sample size reestimation, and notwithstanding such changes, both methods guarantee strong control of the family-wise error rate. The stage-wise MAMS approach was historically the first to be developed and remains the standard method for designing inferentially seamless phase 2-3 clinical trials. In this approach, at each stage, the data from each treatment comparison are summarized by a single multiplicity adjusted P-value. These stage-wise P-values are combined by a prespecified combination function and the resultant test statistic is monitored with respect to the classical two-arm group sequential efficacy boundaries. The cumulative MAMS approach is a more recent development in which a separate test statistic is constructed for each treatment comparison from the cumulative data at each stage. These statistics are then monitored with respect to multiplicity adjusted group sequential efficacy boundaries. We compared the powers of the two methods for designs with two and three active treatment arms, under commonly utilized decision rules for treatment selection, sample size reestimation and early stopping. In our investigations, which were carried out over a reasonably exhaustive exploration of the parameter space, the cumulative MAMS designs were more powerful than the stage-wise MAMS designs, except for the homogeneous case of equal treatment effects, where a small power advantage was discernable for the stage-wise MAMS designs., (© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

With few notable exceptions, drug development for heart failure (HF) has become progressively more challenging, and there remain no definitively proven therapies for patients with acute HF or HF with preserved ejection fraction. Inspection of temporal trends suggests an increasing rate of disagreement between early-phase and phase III trial end points. Preliminary results from phase II HF trials are frequently promising, but increasingly followed by disappointing phase III results. Given this potential disconnect, it is reasonable to carefully re-evaluate the purpose, design, and execution of phase II HF trials, with particular attention directed toward the surrogate end points commonly used by these studies. In this review, we offer a critical reappraisal of the role of phase II HF trials and surrogate end points, highlighting challenges in their use and interpretation, lessons learned from past experiences, and specific strengths and weaknesses of various surrogate outcomes. We conclude by proposing a series of approaches that should be considered for the goal of optimizing the efficiency of HF drug development. This review is based on discussions between scientists, clinical trialists, industry and government sponsors, and regulators that took place at the Cardiovascular Clinical Trialists Forum in Washington, DC, on December 2, 2016.

Two-arm group sequential designs have been widely used for over 40 years, especially for studies with mortality endpoints. The natural generalization of such designs to trials with multiple treatment arms and a common control (MAMS designs) has, however, been implemented rarely. While the statistical methodology for this extension is clear, the main limitation has been an efficient way to perform the computations. Past efforts were hampered by algorithms that were computationally explosive. With the increasing interest in adaptive designs, platform designs, and other innovative designs that involve multiple comparisons over multiple stages, the importance of MAMS designs is growing rapidly. This article provides break-through algorithms that can compute MAMS boundaries rapidly thereby making such designs practical. For designs with efficacy-only boundaries the computational effort increases linearly with number of arms and number of stages. For designs with both efficacy and futility boundaries the computational effort doubles with successive increases in number of stages., (© 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.)

Over the past 25 years, adaptive designs have gradually gained acceptance and are being used with increasing frequency in confirmatory clinical trials. Recent surveys of submissions to the regulatory agencies reveal that the most popular type of adaptation is unblinded sample size re-estimation. Concerns have nevertheless been raised that this type of adaptation is inefficient.We intend to show in our discussion that such concerns are greatly exaggerated in any practical setting and that the advantages of adaptive sample size re-estimation usually outweigh any minor loss of efficiency., (Copyright © 2016 John Wiley & Sons, Ltd.)

The development of molecularly targeted therapies for certain types of cancers has led to the consideration of population enrichment designs that explicitly factor in the possibility that the experimental compound might differentially benefit different biomarker subgroups. In such designs, enrollment would initially be open to a broad patient population with the option to restrict future enrollment, following an interim analysis, to only those biomarker subgroups that appeared to be benefiting from the experimental therapy. While this strategy could greatly improve the chances of success for the trial, it poses several statistical and logistical design challenges. Because late-stage oncology trials are typically event driven, one faces a complex trade-off between power, sample size, number of events, and study duration. This trade-off is further compounded by the importance of maintaining statistical independence of the data before and after the interim analysis and of optimizing the timing of the interim analysis. This paper presents statistical methodology that ensures strong control of type 1 error for such population enrichment designs, based on generalizations of the conditional error rate approach. The special difficulties encountered with time-to-event endpoints are addressed by our methods. The crucial role of simulation for guiding the choice of design parameters is emphasized. Although motivated by oncology, the methods are applicable as well to population enrichment designs in other therapeutic areas., (Copyright © 2014 John Wiley & Sons, Ltd.)

Proof-of-concept (POC) clinical trials play an important role in developing novel treatments and determining whether existing treatments may be efficacious in broader populations of patients. The goal of most POC trials is to determine whether a treatment is likely to be efficacious for a given indication and thus whether it is worth investing the financial resources and participant exposure necessary for a confirmatory trial of that intervention. A challenge in designing POC trials is obtaining sufficient information to make this important go/no-go decision in a cost-effective manner. An IMMPACT consensus meeting was convened to discuss design considerations for POC trials in analgesia, with a focus on maximizing power with limited resources and participants. We present general design aspects to consider including patient population, active comparators and placebos, study power, pharmacokinetic-pharmacodynamic relationships, and minimization of missing data. Efficiency of single-dose studies for treatments with rapid onset is discussed. The trade-off between parallel-group and crossover designs with respect to overall sample sizes, trial duration, and applicability is summarized. The advantages and disadvantages of more recent trial designs, including N-of-1 designs, enriched designs, adaptive designs, and sequential parallel comparison designs, are summarized, and recommendations for consideration are provided. More attention to identifying efficient yet powerful designs for POC clinical trials of chronic pain treatments may increase the percentage of truly efficacious pain treatments that are advanced to confirmatory trials while decreasing the percentage of ineffective treatments that continue to be evaluated rather than abandoned., (Copyright © 2014 International Association for the Study of Pain. Published by Elsevier B.V. All rights reserved.)

We propose a Markov process theory-based adaptive sequential testing procedure for multiple comparisons. The procedure can be used for confirmative trials involving multi-comparisons, including dose selection or population enrichment. Dose or subpopulation selection and sample size modification can be made at any interim analysis. Type I error control is exact.

Methods for controlling the type-1 error of an adaptive group sequential trial were developed in seminal papers by Cui, Hung, and Wang (Biometrics, 1999), Lehmacher and Wassmer (Biometrics, 1999), and Müller and Schäfer (Biometrics, 2001). However, corresponding solutions for the equally important and related problem of parameter estimation at the end of the adaptive trial have not been completely satisfactory. In this paper, a method is provided for computing a two-sided confidence interval having exact coverage, along with a point estimate that is median unbiased for the primary efficacy parameter in a two-arm adaptive group sequential design. The possible adaptations are not only confined to sample size alterations but also include data-dependent changes in the number and spacing of interim looks and changes in the error spending function. The procedure is based on mapping the final test statistic obtained in the modified trial into a corresponding backward image in the original trial. This is an advance on previously available methods, which either produced conservative coverage and no point estimates or provided exact coverage for one-sided intervals only., (Copyright © 2013 John Wiley & Sons, Ltd.)

Ordered categorical data occur frequently in biomedical research. The linear by linear association test for ordered R x C tables permits the investigator to specify row and column scores for analysis. When an investigator believes that there may be more than one set of reasonable scores or when more than one investigator proposes scores, we need a method to decide upon a single procedure to use. We show how to use efficiency robustness principles to combine tests from two or more sets of scores into one robust test for analysis. This test minimizes the worst possible efficiency loss over all the sets of scores. We illustrate the methodology for the R x C case and, in detail, for the important special 2 x C case.

We develop an algorithm for computing sample sizes, equal or unequal, for categorical data. We illustrate its use in the two-sample setting using the Wilcoxon rank-sum statistic, but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well. The sample size determinations can be based on either exact power or on a very precise Monte Carlo estimate of it. To reduce the computations further, power can be computed as a function of asymptotic critical values when the number of categories is not too small. For the Wilcoxon statistic we show that this approximation works well if there are more than five response categories.