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Zhang YY, Rong TZ, Li MM. Analytical calculations of various powers assuming normality. Seq Anal 2021. [DOI: 10.1080/07474946.2021.2010411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Ying-Ying Zhang
- Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China
- Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, China
| | - Teng-Zhong Rong
- Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China
- Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, China
| | - Man-Man Li
- Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China
- Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, China
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2
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Hu J, Blatchford PJ, Goldenberg NA, Kittelson JM. Group sequential designs for clinical trials with bivariate endpoints. Stat Med 2020; 39:3823-3839. [PMID: 33048360 DOI: 10.1002/sim.8696] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Revised: 06/17/2020] [Accepted: 06/20/2020] [Indexed: 11/06/2022]
Abstract
Although all clinical trials are designed and monitored using more than one endpoint, methods are needed to assure that decision criteria are chosen to reflect the clinically relevant tradeoffs that assure the trial's scientific integrity. This article presents a framework for the design and monitoring clinical trials in a bivariate outcome space. The framework uses a rectangular hyperbola to define a bivariate null curve that divides outcome space into regions of benefit and lack of benefit. The curve is shown to be a flexible mapping of bivariate space that allows a continuous tradeoff between the two endpoints in a manner that captures many previous bivariate designs. The curve is extended to a distance function in bivariate space that allows different decisions in each of the four quadrants that comprise bivariate space. The distance function forms a statistic ( δ ); the distribution of its estimate is derived and used as a basis for trial design and group sequential monitoring plans in bivariate space. A recursive form of the bivariate group sequential density is used to evaluate and control operating characteristics for the proposed design. The bivariate designs are shown to meet or exceed the usual standards for size and power. The proposed design is illustrated in the ongoing NHLBI-sponsored Kids-DOTT multinational randomized controlled trial comparing shortened versus conventional anticoagulation for the treatment of venous thromboembolism in patients less than 21 years of age. The proposed methods are broadly applicable to a wide range of clinical settings and trial designs.
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Affiliation(s)
- Junxiao Hu
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, Colorado, USA
| | - Patrick J Blatchford
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, Colorado, USA
| | - Neil A Goldenberg
- Departments of Pediatrics and Medicine, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.,Thrombosis Program, Johns Hopkins All Children's Cancer and Blood Disorders Institute, Johns Hopkins All Children's Hospital, St. Petersburg, Florida, USA.,Johns Hopkins All Children's Institute for Clinical and Translational Research, Johns Hopkins All Children's Hospital, St. Petersburg, Florida, USA
| | - John M Kittelson
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Anschutz Medical Campus, Aurora, Colorado, USA
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3
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Asakura K, Evans SR, Hamasaki T. Interim Monitoring for Futility in Clinical Trials with Two Co-primary Endpoints Using Prediction. Stat Biopharm Res 2019; 12:164-175. [PMID: 33042476 DOI: 10.1080/19466315.2019.1677494] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
We discuss using prediction as a flexible and practical approach for monitoring futility in clinical trials with two co-primary endpoints. This approach is appealing in that it provides quantitative evaluation of potential effect sizes and associated precision, and can be combined with flexible error-spending strategies. We extend prediction of effect size estimates and the construction of predicted intervals to the two co-primary endpoints case, and illustrate interim futility monitoring of treatment effects using prediction with an example. We also discuss alternative approaches based on the conditional and predictive powers, compare these methods and provide some guidance on the use of prediction for better decision in clinical trials with co-primary endpoints.
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Affiliation(s)
- Koko Asakura
- Department of Data Science, National Cerebral and Cardiovascular Center, Osaka, Japan.,Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Osaka, Japan
| | - Scott R Evans
- The Biostatistics Center and the Department of Biostatistics and Bioinformatics, George Washington University, Maryland, USA
| | - Toshimitsu Hamasaki
- Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Osaka, Japan.,The Biostatistics Center and the Department of Biostatistics and Bioinformatics, George Washington University, Maryland, USA
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4
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Sinha AK, Moye L, Piller LB, Yamal J, Barcenas CH, Lin J, Davis BR. Adaptive group‐sequential design with population enrichment in phase 3 randomized controlled trials with two binary co‐primary endpoints. Stat Med 2019; 38:3985-3996. [DOI: 10.1002/sim.8216] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2018] [Revised: 04/28/2019] [Accepted: 05/09/2019] [Indexed: 11/11/2022]
Affiliation(s)
- Arup K. Sinha
- Department of Biostatistics, School of Public HealthYale University New Haven Connecticut
| | - Lemuel Moye
- Department of Biostatistics, School of Public HealthThe University of Texas Health Science Center at Houston Houston Texas
| | - Linda B. Piller
- Department of Epidemiology, Human Genetics, and Environmental Sciences, School of Public HealthThe University of Texas Health Science Center at Houston Houston Texas
| | - Jose‐Miguel Yamal
- Department of Biostatistics, School of Public HealthThe University of Texas Health Science Center at Houston Houston Texas
| | - Carlos H. Barcenas
- Department of Breast Medical Oncology, Division of Cancer MedicineThe University of Texas MD Anderson Cancer Center Houston Texas
| | | | - Barry R. Davis
- Department of Biostatistics, School of Public HealthThe University of Texas Health Science Center at Houston Houston Texas
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5
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Hamasaki T, Evans SR, Asakura K. Design, data monitoring, and analysis of clinical trials with co-primary endpoints: A review. J Biopharm Stat 2017; 28:28-51. [PMID: 29083951 DOI: 10.1080/10543406.2017.1378668] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
We review the design, data monitoring, and analyses of clinical trials with co-primary endpoints. Recently developed methods for fixed-sample and group-sequential settings are described. Practical considerations are discussed, and guidance for the application of these methods is provided.
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Affiliation(s)
- Toshimitsu Hamasaki
- a Department of Data Science , National Cerebral and Cardiovascular Center , Osaka , Japan.,b Department of Innovative Clinical Trials and Data Science , Osaka University Graduate School of Medicine , Osaka , Japan
| | - Scott R Evans
- c Department of Biostatistics and the Center for Biostatistics in AIDS Research , Harvard T.H. Chan School of Public Heath , MA , USA
| | - Koko Asakura
- a Department of Data Science , National Cerebral and Cardiovascular Center , Osaka , Japan.,b Department of Innovative Clinical Trials and Data Science , Osaka University Graduate School of Medicine , Osaka , Japan
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6
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Schüler S, Kieser M, Rauch G. Choice of futility boundaries for group sequential designs with two endpoints. BMC Med Res Methodol 2017; 17:119. [PMID: 28789615 PMCID: PMC5549398 DOI: 10.1186/s12874-017-0387-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2017] [Accepted: 06/30/2017] [Indexed: 12/20/2022] Open
Abstract
BACKGROUND In clinical trials, the opportunity for an early stop during an interim analysis (either for efficacy or for futility) may relevantly save time and financial resources. This is especially important, if the planning assumptions required for power calculation are based on a low level of evidence. For example, when including two primary endpoints in the confirmatory analysis, the power of the trial depends on the effects of both endpoints and on their correlation. Assessing the feasibility of such a trial is therefore difficult, as the number of parameter assumptions to be correctly specified is large. For this reason, so-called 'group sequential designs' are of particular importance in this setting. Whereas the choice of adequate boundaries to stop a trial early for efficacy has been broadly discussed in the literature, the choice of optimal futility boundaries has not been investigated so far, although this may have serious consequences with respect to performance characteristics. METHODS In this work, we propose a general method to construct 'optimal' futility boundaries according to predefined criteria. Further, we present three different group sequential designs for two endpoints applying these futility boundaries. Our methods are illustrated by a real clinical trial example and by Monte-Carlo simulations. RESULTS By construction, the provided method of choosing futility boundaries maximizes the probability to correctly stop in case of small or opposite effects while limiting the power loss and the probability of stopping the study 'wrongly'. Our results clearly demonstrate the benefit of using such 'optimal' futility boundaries, especially compared to futility boundaries commonly applied in practice. CONCLUSIONS As the properties of futility boundaries are often not considered in practice and unfavorably chosen futility boundaries may imply bad properties of the study design, we recommend assessing the performance of these boundaries according to the criteria proposed in here.
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Affiliation(s)
- Svenja Schüler
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, Heidelberg, 69120, Germany.
| | - Meinhard Kieser
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, Heidelberg, 69120, Germany
| | - Geraldine Rauch
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, Heidelberg, 69120, Germany
- Institute of Medical Biometry and Epidemiology, University Medical Center Hamburg Eppendorf, Martinistr. 52, Hamburg, 20246, Germany
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7
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Asakura K, Hamasaki T, Evans SR. Interim evaluation of efficacy or futility in group-sequential trials with multiple co-primary endpoints. Biom J 2016; 59:703-731. [PMID: 27757980 DOI: 10.1002/bimj.201600026] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Revised: 07/07/2016] [Accepted: 07/12/2016] [Indexed: 11/08/2022]
Abstract
We discuss group-sequential designs in superiority clinical trials with multiple co-primary endpoints, that is, when trials are designed to evaluate if the test intervention is superior to the control on all primary endpoints. We consider several decision-making frameworks for evaluating efficacy or futility, based on boundaries using group-sequential methodology. We incorporate the correlations among the endpoints into the calculations for futility boundaries and sample sizes as a function of other design parameters, including mean differences, the number of analyses, and efficacy boundaries. We investigate the operating characteristics of the proposed decision-making frameworks in terms of efficacy/futility boundaries, power, the Type I error rate, and sample sizes, while varying the number of analyses, the correlations among the endpoints, and the mean differences. We provide an example to illustrate the methods and discuss practical considerations when designing efficient group-sequential designs in clinical trials with co-primary endpoints.
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Affiliation(s)
- Koko Asakura
- Department of Data Science, National Cerebral and Cardiovascular Center, Suita, Osaka, 565-8565, Japan.,Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Suita, Osaka, Japan
| | - Toshimitsu Hamasaki
- Department of Data Science, National Cerebral and Cardiovascular Center, Suita, Osaka, 565-8565, Japan.,Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Suita, Osaka, Japan
| | - Scott R Evans
- Center for Biostatistics in AIDS Research, Department of Biostatistics, Harvard T. H. Chan School of Public Heath, Boston, MA, 02115, USA
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8
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Hamasaki T, Asakura K, Evans SR, Sugimoto T, Sozu T. Group-Sequential Strategies in Clinical Trials with Multiple Co-Primary Outcomes. Stat Biopharm Res 2015; 7:36-54. [PMID: 25844122 DOI: 10.1080/19466315.2014.1003090] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
We discuss the decision-making frameworks for clinical trials with multiple co-primary endpoints in a group-sequential setting. The decision-making frameworks can account for flexibilities such as a varying number of analyses, equally or unequally spaced increments of information and fixed or adaptive Type I error allocation among endpoints. The frameworks can provide efficiency, i.e., potentially fewer trial participants, than the fixed sample size designs. We investigate the operating characteristics of the decision-making frameworks and provide guidance on constructing efficient group-sequential strategies in clinical trials with multiple co-primary endpoints.
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Affiliation(s)
- Toshimitsu Hamasaki
- Office of Biostatistics and Data Management, National Cerebral and Cardiovascular Center, Japan ; Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Japan
| | - Koko Asakura
- Office of Biostatistics and Data Management, National Cerebral and Cardiovascular Center, Japan ; Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Japan
| | - Scott R Evans
- Department of Biostatistics and the Center for Biostatistics in AIDS Research, Harvard School of Public Health, USA
| | - Tomoyuki Sugimoto
- Department of Mathematical Sciences, Hirosaki University Graduate School of Science and Technology, Japan
| | - Takashi Sozu
- Department of Biostatistics, Kyoto University School of Public Health, Japan
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