Group Sequential Clinical Trials Research Articles

Wilcoxon rank-sum tests to detect one-sided mixture alternatives in group sequential clinical trials.

Traditional methods based on the assumption that the treatment distribution is a pure shift of the control distribution may not always hold. The possibility that an individual from the treatment group may not respond to the treatment motivates the use of a mixture distribution for the treatment group. This paper considers two test procedures based on the Wilcoxon rank-sum statistic for a group sequential design to detect the one-sided mixture alternative. Error spending functions are used for the allocation of error rates at each stage. The two tests are evaluated individually in determination of critical values and arm sizes and asymptotic multivariate normality is shown to hold for both. Upon comparison, the tests are presented to be asymptotically equivalent. Both test statistics maintain the Type I error rate even if is misspecified in the design alternative. A more general definition of the treatment effect is used with the mixture distribution. Method of moments estimators and constrained -means estimators for the treatment effect are evaluated.

Optimal Enrollment in Late-Stage New Drug Development with Learning of Drug’s Efficacy for Group-Sequential Clinical Trials

Problem definition: The cost for developing a new drug ranged from $1 billion to more than $2 billion between 2010 and 2019. In addition to high development costs, the efficacy of the candidate drug, patient enrollment, the market exclusivity period (MEP), and the planning horizon are uncertain. Moreover, slow enrollment leads to increased costs, canceled clinical trials, and lost potential revenue. Many firms, hoping to detect efficacy versus futility of the candidate drug early to save development costs, plan interim analyses of patient-response data in their clinical trials. Academic/practical relevance: The problem for optimizing patient-enrollment rates has an uncertain planning horizon. We developed a continuous-time dynamic programming (DP) model with learning of a drug’s efficacy and MEP to assist firms in developing optimal enrollment policies in their clinical trials. We also established the optimality equation for this DP model. Through a clinical trial for testing a cancer drug developed by a leading pharmaceutical firm, we demonstrate that our DP model can help firms effectively manage their trials with a sizable profit gain (as large as $270 million per drug). Firms can also use our model in simulation to select their trial design parameters (e.g., the sample sizes of interim analyses). Methodology: We update a drug’s efficacy by Bayes’ rules. Using the stochastic order and the likelihood-ratio order of distribution functions, we prove the monotonic properties of the value function and an optimal policy. Results: We established that the value of the drug-development project increases as the average response from patients using the candidate drug increases. For drugs having low annual revenue or a strong market brand or treating rare diseases, we also established that the optimal enrollment policy is monotonic in the average patient response. Moreover, the optimal enrollment rate increases as the variance of the MEP decreases. Managerial implications: Firms can use the properties of the value function to select late-stage clinical trials for their drug-development project portfolios. Firms can also use our optimal policy to guide patient recruitment in their clinical trials considering competition from other drugs in the marketplace. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1162 .

An alternative metric for evaluating the potential patient benefit of response-adaptive randomization procedures.

When planning a two-arm group sequential clinical trial with a binary primary outcome that has severe implications for quality of life (e.g., mortality), investigators may strive to find the design that maximizes in-trial patient benefit. In such cases, Bayesian response-adaptive randomization (BRAR) is often considered because it can alter the allocation ratio throughout the trial in favor of the treatment that is currently performing better. Although previous studies have recommended using fixed randomization over BRAR based on patient benefit metrics calculated from the realized trial sample size, these previous comparisons have been limited by failures to hold type I and II error rates constant across designs or consider the impacts on all individuals directly affected by the design choice. In this paper, we propose a metric for comparing designs with the same type I and II error rates that reflects expected outcomes among individuals who would participate in the trial if enrollment is open when they become eligible. We demonstrate how to use the proposed metric to guide the choice of design in the context of two recent trials in persons suffering out of hospital cardiac arrest. Using computer simulation, we demonstrate that various implementations of group sequential BRAR offer modest improvements with respect to the proposed metric relative to conventional group sequential monitoringalone.

Personalized Risk-Based Screening Design for Comparative Two-Arm Group Sequential Clinical Trials.

Personalized medicine has been emerging to take into account individual variability in genes and environment. In the era of personalized medicine, it is critical to incorporate the patients’ characteristics and improve the clinical benefit for patients. The patients’ characteristics are incorporated in adaptive randomization to identify patients who are expected to get more benefit from the treatment and optimize the treatment allocation. However, it is challenging to control potential selection bias from using observed efficacy data and the effect of prognostic covariates in adaptive randomization. This paper proposes a personalized risk-based screening design using Bayesian covariate-adjusted response-adaptive randomization that compares the experimental screening method to a standard screening method based on indicators of having a disease. Personalized risk-based allocation probability is built for adaptive randomization, and Bayesian adaptive decision rules are calibrated to preserve error rates. A simulation study shows that the proposed design controls error rates and yields a much smaller number of failures and a larger number of patients allocated to a better intervention compared to existing randomized controlled trial designs. Therefore, the proposed design performs well for randomized controlled clinical trials under personalized medicine.

Design and analysis of group-sequential clinical trials based on a modestly weighted log-rank test in anticipation of a delayed separation of survival curves: A practical guidance.

A common feature of many recent trials evaluating the effects of immunotherapy on survival is that non-proportional hazards can be anticipated at the design stage. This raises the possibility to use a statistical method tailored towards testing the purported long-term benefit, rather than applying the more standard log-rank test and/or Cox model. Many such proposals have been made in recent years, but there remains a lack of practical guidance on implementation, particularly in the context of group-sequential designs. In this article, we aim to fill this gap. We illustrate how the POPLAR trial, which compared immunotherapy versus chemotherapy in non-small-cell lung cancer, might have been re-designed to be more robust to the presence of a delayed effect using the modestly-weighted log-rank test in a group-sequential setting. We provide step-by-step instructions on how to analyse a hypothetical realization of the trial, based on this new design. Basic theory on weighted log-rank tests and group-sequential methods is covered, and an accompanying R package (including vignette) is provided.

Optimal adaptive promising zone designs.

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 with good power, but not sufficient to detect the smallest clinically meaningful treatment effect . Moreover it is difficult for the sponsors of such trials to make the up-front commitment needed to adequately power a study to detect . 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 we propose a Bayesian option whereby a prior distribution is assigned to the unknown treatment effect , which is then integrated out of the objective function with respect to its posterior distribution at the interim analysis.

A simulation-based comparison of estimation methods for adaptive and classical group sequential clinical trials.

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 , or the backward image confidence interval (BWCI), which provides exact coverage of 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 . 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.

Expected Value of Sample Information to Guide the Design of Group Sequential Clinical Trials.

IntroductionAdaptive designs allow changes to an ongoing trial based on prespecified early examinations of accrued data. Opportunities are potentially being missed to incorporate health economic considerations into the design of these studies.MethodsWe describe how to estimate the expected value of sample information for group sequential design adaptive trials. We operationalize this approach in a hypothetical case study using data from a pilot trial. We report the expected value of sample information and expected net benefit of sampling results for 5 design options for the future full-scale trial including the fixed-sample-size design and the group sequential design using either the Pocock stopping rule or the O’Brien-Fleming stopping rule with 2 or 5 analyses. We considered 2 scenarios relating to 1) using the cost-effectiveness model with a traditional approach to the health economic analysis and 2) adjusting the cost-effectiveness analysis to incorporate the bias-adjusted maximum likelihood estimates of trial outcomes to account for the bias that can be generated in adaptive trials.ResultsThe case study demonstrated that the methods developed could be successfully applied in practice. The results showed that the O’Brien-Fleming stopping rule with 2 analyses was the most efficient design with the highest expected net benefit of sampling in the case study.ConclusionsCost-effectiveness considerations are unavoidable in budget-constrained, publicly funded health care systems, and adaptive designs can provide an alternative to costly fixed-sample-size designs. We recommend that when planning a clinical trial, expected value of sample information methods be used to compare possible adaptive and nonadaptive trial designs, with appropriate adjustment, to help justify the choice of design characteristics and ensure the cost-effective use of research funding.HighlightsOpportunities are potentially being missed to incorporate health economic considerations into the design of adaptive clinical trials.Existing expected value of sample information analysis methods can be extended to compare possible group sequential and nonadaptive trial designs when planning a clinical trial.We recommend that adjusted analyses be presented to control for the potential impact of the adaptive designs and to maintain the accuracy of the calculations.This approach can help to justify the choice of design characteristics and ensure the cost-effective use of limited research funding.

Early treatment with inhaled budesonide to prevent clinical deterioration in patients with COVID-19

Early treatment with inhaled budesonide to prevent clinical deterioration in patients with COVID-19

On information fraction for Fleming‐Harrington type weighted log‐rank tests in a group‐sequential clinical trial design

When comparing survival times of treatment and control groups under a more realistic nonproportional hazards scenario, the standard log-rank (SLR) test may be replaced by a more efficient weighted log-rank (WLR) test, such as the Fleming-Harrington (FH) test. Designing a group-sequential clinical trial with one or more interim looks during which a FH test will be performed, necessitates correctly quantifying the information fraction (IF). For SLR test, IF is defined simply as the ratio of interim to final numbers of events; but for FH test, it can deviate substantially from this ratio. In this article, we separate the effect of weight function (of FH test) alone on IF from the effect of censoring. We have shown that, without considering the effect of censoring, IF can be derived analytically for FH test using information available at the design stage and the additional effect due to censoring is relatively smaller. This article intends to serve two major purposes: first, to emphasize and rationalize the deviation of IF in weighted log-rank test from that of SLR test which is often overlooked (Jiménez, Stalbovskaya, and Jones); second, although it is impossible to predict IF for a weighted log-rank test at the design stage, our decomposition of effects on IF provides a reasonable and practically feasible range of IF to work with. We illustrate our approach with an example and provide simulation results to evaluate operating characteristics.

On selecting the critical boundary functions in group-sequential trials with two time-to-event outcomes

We investigate selection of critical boundary functions for testing the hypotheses of two time-to-event outcomes as both primary endpoints or a primary and a secondary endpoint in group-sequential clinical trials, where (1) the effect sizes of endpoints are unequal, or (2) one endpoint is for short-term evaluation and the other for long-term evaluation. Bonferroni-Holm and fixed-sequence procedures are considered. We assess the effects of the magnitudes of the hazard ratios and the correlation between the endpoints on statistical powers and provide guidance for consideration.

Embedding a COVID-19 group sequential clinical trial within an ongoing trial: lessons from an unusual experience

The Cape-Covid trial is an embedded clinical trial within the ongoing Cape-Cod trial. The Covid-19 pandemic appeared while we were conducting a randomized trial assessing the effectiveness of corticosteroids in severe community-acquired pneumonia. We took advantage of this ongoing trial to embed a sub-trial assessing hydrocortisone in SARS-CoV-2 infected patients. In this manuscript, we wish to share our experience when we needed to make fast and robust methodological decisions during the Covid-19 pandemic in a two weeks period of time.

Exact critical values for group sequential designs with small sample sizes

ABSTRACT Group sequential clinical trial designs allow the sequential hypothesis testing as data is accumulated over time, while ensuring the control of type-1 error rate. These designs vary in how they split the overall type-1 error among analyses, but practically, all assume that: 1. The underlying data is normal or approximately so, and 2. the sample sizes are large, so the individual test statistics are sufficiently normal rather than Student’s t. These two assumptions lead to the reliance on the multivariate normal distribution for calculation of the critical values. Several publications have pointed out that for small sample sizes, such an approach leads to an inflated type-1 error and proposed different sets of critical values from either simulations or by an ad-hoc adjustment to the asymptotic critical values. In this paper, we develop the exact joint distribution of the test statistics for any sample size. We show how to calculate exact critical values that conform to some well-known alpha-spending functions, such as the O’Brien-Fleming and Pocock critical values. We also compare the resulting type-1 error of these critical values with the asymptotic, as well as with other methods that have been proposed for small sample sizes.

Comparison of Bayesian and frequentist group-sequential clinical trial designs

BackgroundThere is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs.MethodsThis paper presents a practical comparison of Bayesian and frequentist group-sequential tests. Focussing on the setting in which data can be summarised by normally distributed test statistics, we evaluate and compare boundary values and operating characteristics.ResultsAlthough Bayesian and frequentist group-sequential approaches are based on fundamentally different paradigms, in a single arm trial or two-arm comparative trial with a prior distribution specified for the treatment difference, Bayesian and frequentist group-sequential tests can have identical stopping rules if particular critical values with which the posterior probability is compared or particular spending function values are chosen. If the Bayesian critical values at different looks are restricted to be equal, O’Brien and Fleming’s design corresponds to a Bayesian design with an exceptionally informative negative prior, Pocock’s design to a Bayesian design with a non-informative prior and frequentist designs with a linear alpha spending function are very similar to Bayesian designs with slightly informative priors.This contrasts with the setting of a comparative trial with independent prior distributions specified for treatment effects in different groups. In this case Bayesian and frequentist group-sequential tests cannot have the same stopping rule as the Bayesian stopping rule depends on the observed means in the two groups and not just on their difference. In this setting the Bayesian test can only be guaranteed to control the type I error for a specified range of values of the control group treatment effect.ConclusionsComparison of frequentist and Bayesian designs can encourage careful thought about design parameters and help to ensure appropriate design choices are made.

The Inspire Study in Higher-Risk Myelodysplastic Syndrome (HR-MDS): A Novel Phase 3 Study Adaptive Design for Hematological Malignancies in Adults

Background: Patients with HR-MDS have a dismal prognosis after failure of hypomethylating agents (HMAs) (Zeidan 2014), with median overall survival (OS) of less than 6 months (Prebet 2011) and currently no approved second-line therapy (Garcia-Manero 2016). Targeted therapies with novel mechanisms of action, combination strategies, as well as innovative study designs, are all needed to expedite and address the high unmet medical need in patients with HMA refractory HR-MDS. Rigosertib is a unique targeted therapy that inhibits PI3K and PLK signaling pathways by binding directly to the Ras-binding domain (Athuluri-Divakar 2016) and in vitro cytotoxicity studies have demonstrated synergy with azacitidine (Cosenza 2015). INSPIRE study is an example of a study with a novel compound and unique mechanism of action as well as an innovative study design. Methods: INSPIRE (NCT02562443) is a global randomized Phase 3 trial in patients with HR-MDS after HMA failure. Patients are randomized in a 2:1 fashion to rigosertib or physician's choice of treatment. Key inclusion criteria: age <82 years; MDS classified as RAEB-1, RAEB-2 or RAEB-t; ≥1 cytopenia; patient must demonstrate one of the following: progression any time after initiation of HMA treatment, intolerance to HMA, failure to achieve complete remission (CR), partial remission (PR), or hematologic improvement (HI) after six 4-week cycles of AZA or either four 4-week or four 6-week cycles of DAC, or relapse after initial CR, PR or HI; duration of prior HMA ≤9 cycles within 12 months; last dose of HMA ≤6 months before enrollment; and ECOG score 0-2. The primary endpoint of overall survival (OS) will be tested in a sequential fashion in the intention to treat (ITT) population and the IPSS-R very high risk (VHR) subgroup. Secondary endpoints include OS in patients with monosomy 7 or trisomy 8, overall response, quality-of-life, and HI. The initial sample size was 225 patients with a pre-planned interim analysis (IA) after 88 deaths. INSPIRE featured an adaptive trial design with a pre-planned Sample Size Re-estimation (Cui 1999) to 360 patients and 288 OS events as one option that the Independent Data Monitoring Committee (IDMC) could implement at IA. The adaptive sample size modification of an on-going two-arm, group sequential clinical trial is used to categorize the results for each population into three zones of Unfavorable, Promising, and Favorable. This adaptive design is advantageous as it allows study sample size to be adjusted when there is high variance in estimating the true effect of the drug under investigation which could otherwise result in underpowering of the study. The IDMC had several options following the interim analysis, including continuation of the study as initially planned, discontinuation for futility or safety, trial expansion using pre-planned sample size re-estimation, and continuation for only the pre-defined VHR subgroup. The investigators remain blinded to the specific interim analysis results. Enrollment in the trial is ongoing with topline data expected in 2020. Conclusions: Based on the results of interim analysis, the IDMC recommended continuation of the trial based on ITT result in promising zone with one-time expansion in enrollment, using a pre-planned sample size re-estimation, the sample size for the study was increased from 225 to 360 with unchanged eligibility criteria. The Adaptive Design used real time data from the IA to modify sample size and mitigate the risk of underpowering without undermining its validity and integrity, while preserving type-1 error. The study design used in INSPIRE may be advantageous for other novel agents in rare hematological diseases during the transition from phase 2 to phase 3 studies. Clinical trial information: (NCT02562443). Disclosures Luger: Agios: Honoraria; Ariad: Research Funding; Biosight: Research Funding; Celgene: Research Funding; Cyslacel: Research Funding; Daichi Sankyo: Honoraria; Genetech: Research Funding; Jazz: Honoraria; Kura: Research Funding; Onconova: Research Funding; Pfizer: Honoraria; Seattle Genetics: Research Funding. Al-Kali:Astex Pharmaceuticals, Inc.: Research Funding. Woodman:Onconova Therapeutics, Inc.: Employment. Adesanya:Onconova Therapeutics, Inc.: Employment. Azarnia:Onconova Therapeutics, Inc.: Employment. Parris:Onconova Therapeutics, Inc.: Employment. Jedrzejczak:Roche: Other: travel support for hematology meetings (ASH, EBMT, EHA) ; Novartis: Research Funding; Takeda: Consultancy; Amgen: Consultancy, Other: travel support for hematology meetings (ASH, EBMT, EHA) ; Celgene: Other: travel support for hematology meetings (ASH, EBMT, EHA) . Díez-Campelo:Celgene Corporation: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; Novartis: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding. Garcia-Manero:Amphivena: Consultancy, Research Funding; Helsinn: Research Funding; Novartis: Research Funding; AbbVie: Research Funding; Celgene: Consultancy, Research Funding; Astex: Consultancy, Research Funding; Onconova: Research Funding; H3 Biomedicine: Research Funding; Merck: Research Funding.

A useful design utilizing the information fraction in a group sequential clinical trial with censored survival data.

Lan and DeMets (1983) proposed the alpha spending function for group sequential trials to permit the use of unspecified frequencies and timings of interim analyses in the trial design. Regarding a trial with censored time to endpoint, Lan and DeMets (1989) later defined information time at an interim analysis in a maximum duration trial. To compare two survival curves utilizing such a design, information times for group sequential logrank and Wilcoxon-type statistics have been developed by assuming that the survival time follows an exponential distribution or a Weibull distribution without considering the censoring distribution. To better address the practical concerns inherent in clinical trials with survival endpoints, we present a new approach to adequately design a group sequential trial using the Harrington-Fleming (1982) test based on our proposed information fractions by assuming the censoring distribution depends on the patient's accrual time according to various entry distributions and by extending the underlying survival distribution to the generalized gamma distribution. We also determine associated sample sizes, expected number of events and expected stopping time. Two phase III trials of non-small-cell lung cancer originally designed using fixed-sample tests are utilized to illustrate the potential advantages of using a group sequential design with the proposed approach. This enhanced method facilitates the design and analysis of group sequential clinical trials studying survival endpoints by increasing implemental flexibility.

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.

Designing one-sided group sequential clinical trials to detect a mixture alternative

We consider the construction of one-sided group sequential designs where the stopping rule includes boundaries for early stopping to accept for futility and to reject for efficacy. The traditional assumption that all patients have the same likelihood of benefiting from the treatment is sometimes unrealistic and can underestimate the required sample size. This motivates us to power the design for an alternative where the treatment group observations come from a mixture of normal distributions. For the proposed setting, we use standardized test statistics based on sample means, and the test turns out to be an L-optimal similar test. Stopping boundaries and arm size for the design are determined by Type I and Type II error spending equations. We demonstrate the need for larger arm sizes when trying to detect a mixture alternative compared to trying to detect a pure shift alternative. The unknown variance case is discussed. With the mixture model, we discuss a more general definition of treatment effect. The maximum likelihood estimator for the treatment effect is discussed.

Defining information fractions in group sequential clinical trials with multiple endpoints

The group sequential design has been well understood and widely applied in designs of late phase clinical trial to enable potentially early stopping for efficacy or futility. The information fraction (IF) is one of the key elements to determine the decision boundary at the interim analyses. The family-wise error rate (FWER) control is highly critical for clinical trials with multiple endpoints to be tested. In this article, we illustrate the importance of properly defining the information fraction for each individual endpoint regarding the FWER control through the numerical evaluation and a case study.

Multi-arm group sequential designs with a simultaneous stopping rule.

Multi‐arm group sequential clinical trials are efficient designs to compare multiple treatments to a control. They allow one to test for treatment effects already in interim analyses and can have a lower average sample number than fixed sample designs. Their operating characteristics depend on the stopping rule: We consider simultaneous stopping, where the whole trial is stopped as soon as for any of the arms the null hypothesis of no treatment effect can be rejected, and separate stopping, where only recruitment to arms for which a significant treatment effect could be demonstrated is stopped, but the other arms are continued. For both stopping rules, the family‐wise error rate can be controlled by the closed testing procedure applied to group sequential tests of intersection and elementary hypotheses. The group sequential boundaries for the separate stopping rule also control the family‐wise error rate if the simultaneous stopping rule is applied. However, we show that for the simultaneous stopping rule, one can apply improved, less conservative stopping boundaries for local tests of elementary hypotheses. We derive corresponding improved Pocock and O'Brien type boundaries as well as optimized boundaries to maximize the power or average sample number and investigate the operating characteristics and small sample properties of the resulting designs. To control the power to reject at least one null hypothesis, the simultaneous stopping rule requires a lower average sample number than the separate stopping rule. This comes at the cost of a lower power to reject all null hypotheses. Some of this loss in power can be regained by applying the improved stopping boundaries for the simultaneous stopping rule. The procedures are illustrated with clinical trials in systemic sclerosis and narcolepsy. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.