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Chen X, Nifong B, Alt EM, Psioda MA, Ibrahim JG. Bayesian design of clinical trials using the scale transformed power prior. J Biopharm Stat 2024:1-20. [PMID: 38639571 DOI: 10.1080/10543406.2024.2330205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 03/01/2024] [Indexed: 04/20/2024]
Abstract
There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint.
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Affiliation(s)
- Xinxin Chen
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
| | - Brady Nifong
- Non-Clinical and Translational Statistics, GSK, Collegeville, PA, USA
| | - Ethan M Alt
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
| | - Matthew A Psioda
- Statistics and Data Science Innovation Hub, GSK, Collegeville, PA, USA
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
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3
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Harun N, Liu C, Kim MO. Critical appraisal of Bayesian dynamic borrowing from an imperfectly commensurate historical control. Pharm Stat 2020; 19:613-625. [PMID: 32185886 DOI: 10.1002/pst.2018] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Revised: 10/15/2019] [Accepted: 03/06/2020] [Indexed: 11/10/2022]
Abstract
Bayesian dynamic borrowing designs facilitate borrowing information from historical studies. Historical data, when perfectly commensurate with current data, have been shown to reduce the trial duration and the sample size, while inflation in the type I error and reduction in the power have been reported, when imperfectly commensurate. These results, however, were obtained without considering that Bayesian designs are calibrated to meet regulatory requirements in practice and even no-borrowing designs may use information from historical data in the calibration. The implicit borrowing of historical data suggests that imperfectly commensurate historical data may similarly impact no-borrowing designs negatively. We will provide a fair appraiser of Bayesian dynamic borrowing and no-borrowing designs. We used a published selective adaptive randomization design and real clinical trial setting and conducted simulation studies under varying degrees of imperfectly commensurate historical control scenarios. The type I error was inflated under the null scenario of no intervention effect, while larger inflation was noted with borrowing. The larger inflation in type I error under the null setting can be offset by the greater probability to stop early correctly under the alternative. Response rates were estimated more precisely and the average sample size was smaller with borrowing. The expected increase in bias with borrowing was noted, but was negligible. Using Bayesian dynamic borrowing designs may improve trial efficiency by stopping trials early correctly and reducing trial length at the small cost of inflated type I error.
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Affiliation(s)
- Nusrat Harun
- Division of Biostatistics and Epidemiology, Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
| | - Chunyan Liu
- Division of Biostatistics and Epidemiology, Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
| | - Mi-Ok Kim
- Department of Epidemiology and Biostatistics, University of California, San Francisco, California, USA.,UCSF Helen Diller Family Comprehensive Cancer Center, University of California, San Francisco, California, USA
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4
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Psioda MA, Ibrahim JG. Bayesian clinical trial design using historical data that inform the treatment effect. Biostatistics 2020; 20:400-415. [PMID: 29547966 DOI: 10.1093/biostatistics/kxy009] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Accepted: 01/13/2018] [Indexed: 11/12/2022] Open
Abstract
We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma.
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Affiliation(s)
- Matthew A Psioda
- Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, CB#7420, Chapel Hill, NC, USA
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, CB#7420, Chapel Hill, NC, USA
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Psioda MA, Soukup M, Ibrahim JG. A practical Bayesian adaptive design incorporating data from historical controls. Stat Med 2018. [PMID: 30033617 DOI: 10.1002/sim.7897.] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
In this paper, we develop the fixed-borrowing adaptive design, a Bayesian adaptive design which facilitates information borrowing from a historical trial using subject-level control data while assuring a reasonable upper bound on the maximum type I error rate and lower bound on the minimum power. First, one constructs an informative power prior from the historical data to be used for design and analysis of the new trial. At an interim analysis opportunity, one evaluates the degree of prior-data conflict. If there is too much conflict between the new trial data and the historical control data, the prior information is discarded and the study proceeds to the final analysis opportunity at which time a noninformative prior is used for analysis. Otherwise, the trial is stopped early and the informative power prior is used for analysis. Simulation studies are used to calibrate the early stopping rule. The proposed design methodology seamlessly accommodates covariates in the statistical model, which the authors argue is necessary to justify borrowing information from historical controls. Implementation of the proposed methodology is straightforward for many common data models, including linear regression models, generalized linear regression models, and proportional hazards models. We demonstrate the methodology to design a cardiovascular outcomes trial for a hypothetical new therapy for treatment of type 2 diabetes mellitus and borrow information from the SAVOR trial, one of the earliest cardiovascular outcomes trials designed to assess cardiovascular risk in antidiabetic therapies.
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Affiliation(s)
- Matthew A Psioda
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina
| | - Mat Soukup
- Division of Biometrics VII, Office of Biostatistics, Center for Drug Evaluation and Research, US Food and Drug Administration, Silver Spring, Maryland
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina
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Kim MO, Harun N, Liu C, Khoury JC, Broderick JP. Bayesian selective response-adaptive design using the historical control. Stat Med 2018; 37:3709-3722. [PMID: 29900577 PMCID: PMC6221103 DOI: 10.1002/sim.7836] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2017] [Revised: 05/04/2018] [Accepted: 05/04/2018] [Indexed: 01/14/2023]
Abstract
High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior-data conflict. Motivated by well-publicized two-arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior-data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors.
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Affiliation(s)
- Mi-Ok Kim
- UCSF Helen Diller Family Comprehensive Cancer Center, San Francisco, California, USA.,Department of Epidemiology and Biostatistics, University of California San Francisco, San Francisco, California, USA
| | - Nusrat Harun
- UCSF Helen Diller Family Comprehensive Cancer Center, San Francisco, California, USA
| | - Chunyan Liu
- Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
| | - Jane C Khoury
- Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
| | - Joseph P Broderick
- Department of Neurology and Rehabilitation Medicine, University of Cincinnati College of Medicine, Cincinnati, Ohio, USA
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Psioda MA, Soukup M, Ibrahim JG. A practical Bayesian adaptive design incorporating data from historical controls. Stat Med 2018; 37:4054-4070. [PMID: 30033617 DOI: 10.1002/sim.7897] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2017] [Revised: 05/24/2018] [Accepted: 06/13/2018] [Indexed: 12/12/2022]
Abstract
In this paper, we develop the fixed-borrowing adaptive design, a Bayesian adaptive design which facilitates information borrowing from a historical trial using subject-level control data while assuring a reasonable upper bound on the maximum type I error rate and lower bound on the minimum power. First, one constructs an informative power prior from the historical data to be used for design and analysis of the new trial. At an interim analysis opportunity, one evaluates the degree of prior-data conflict. If there is too much conflict between the new trial data and the historical control data, the prior information is discarded and the study proceeds to the final analysis opportunity at which time a noninformative prior is used for analysis. Otherwise, the trial is stopped early and the informative power prior is used for analysis. Simulation studies are used to calibrate the early stopping rule. The proposed design methodology seamlessly accommodates covariates in the statistical model, which the authors argue is necessary to justify borrowing information from historical controls. Implementation of the proposed methodology is straightforward for many common data models, including linear regression models, generalized linear regression models, and proportional hazards models. We demonstrate the methodology to design a cardiovascular outcomes trial for a hypothetical new therapy for treatment of type 2 diabetes mellitus and borrow information from the SAVOR trial, one of the earliest cardiovascular outcomes trials designed to assess cardiovascular risk in antidiabetic therapies.
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Affiliation(s)
- Matthew A Psioda
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina
| | - Mat Soukup
- Division of Biometrics VII, Office of Biostatistics, Center for Drug Evaluation and Research, US Food and Drug Administration, Silver Spring, Maryland
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina
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Psioda MA, Ibrahim JG. Bayesian design of a survival trial with a cured fraction using historical data. Stat Med 2018; 37:3814-3831. [PMID: 29938817 DOI: 10.1002/sim.7846] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Revised: 02/14/2018] [Accepted: 05/12/2018] [Indexed: 11/06/2022]
Abstract
In this paper, we develop a general Bayesian clinical trial design methodology, tailored for time-to-event trials with a cured fraction in scenarios where a previously completed clinical trial is available to inform the design and analysis of the new trial. Our methodology provides a conceptually appealing and computationally feasible framework that allows one to construct a fixed, maximally informative prior a priori while simultaneously identifying the minimum sample size required for the new trial so that the design has high power and reasonable type I error control from a Bayesian perspective. This strategy is particularly well suited for scenarios where adaptive borrowing approaches are not practical due to the nature of the trial, complexity of the model, or the source of the prior information. Control of a Bayesian type I error rate offers a sensible balance between wanting to use high-quality information in the design and analysis of future trials while still controlling type I errors in an equitable way. Moreover, sample size determination based on our Bayesian view of power can lead to a more adequately sized trial by virtue of taking into account all the uncertainty in the treatment effect. We demonstrate our methodology by designing a cancer clinical trial in high-risk melanoma.
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Affiliation(s)
- Matthew A Psioda
- Department of Biostatistics, University of North Carolina, Chapel Hill, 27599, North Carolina, USA
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, Chapel Hill, 27599, North Carolina, USA
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Hsu YY, Zalkikar J, Tiwari RC. Hierarchical Bayes approach for subgroup analysis. Stat Methods Med Res 2017; 28:275-288. [DOI: 10.1177/0962280217721782] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In clinical data analysis, both treatment effect estimation and consistency assessment are important for a better understanding of the drug efficacy for the benefit of subjects in individual subgroups. The linear mixed-effects model has been used for subgroup analysis to describe treatment differences among subgroups with great flexibility. The hierarchical Bayes approach has been applied to linear mixed-effects model to derive the posterior distributions of overall and subgroup treatment effects. In this article, we discuss the prior selection for variance components in hierarchical Bayes, estimation and decision making of the overall treatment effect, as well as consistency assessment of the treatment effects across the subgroups based on the posterior predictive p-value. Decision procedures are suggested using either the posterior probability or the Bayes factor. These decision procedures and their properties are illustrated using a simulated example with normally distributed response and repeated measurements.
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Affiliation(s)
- Yu-Yi Hsu
- U.S. Food and Drug Administration, Silver Spring, USA
| | | | - Ram C Tiwari
- U.S. Food and Drug Administration, Silver Spring, USA
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Li W, Chen MH, Wangy X, Dey DK. Bayesian Design of Non-Inferiority Clinical Trials via the Bayes Factor. STATISTICS IN BIOSCIENCES 2017; 10:439-459. [PMID: 30344778 DOI: 10.1007/s12561-017-9200-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We developed a Bayes factor based approach for the design of non-inferiority clinical trials with a focus on controlling type I error and power. Historical data are incorporated in the Bayesian design via the power prior discussed in Ibrahim and Chen (2000). The properties of the proposed method are examined in detail. An efficient simulation-based computational algorithm is developed to calculate the Bayes factor, type I error and power. The proposed methodology is applied to the design of a non-inferiority medical device clinical trial.
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Affiliation(s)
- Wenqing Li
- Ventana Medical Systems, Inc., 1910 East Innovation Park Drive, Tucson, AZ 85755, USA
| | - Ming-Hui Chen
- Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, Connecticut 06269, USA
| | - Xiaojing Wangy
- Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, Connecticut 06269, USA
| | - Dipak K Dey
- Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, Connecticut 06269, USA
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Quan H, Zhang B, Chuang-Stein C, Jones B. Integrated Data Analysis for Assessing Treatment Effect through Combining Information from All Sources. Stat Biopharm Res 2017. [DOI: 10.1080/19466315.2016.1197150] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Hui Quan
- Biostatistics and Programming, Sanofi, Bridgewater, NJ
| | - Bingzhi Zhang
- Biostatistics and Programming, Sanofi, Bridgewater, NJ
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12
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Spence GT, Steinsaltz D, Fanshawe TR. A Bayesian approach to sequential meta‐analysis. Stat Med 2016; 35:5356-5375. [DOI: 10.1002/sim.7052] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2016] [Revised: 05/24/2016] [Accepted: 07/01/2016] [Indexed: 01/25/2023]
Affiliation(s)
- Graeme T. Spence
- Nuffield Department of Primary Care Health SciencesUniversity of Oxford Oxford U.K
| | | | - Thomas R. Fanshawe
- Nuffield Department of Primary Care Health SciencesUniversity of Oxford Oxford U.K
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Ibrahim JG, Chen MH, Gwon Y, Chen F. The power prior: theory and applications. Stat Med 2015; 34:3724-49. [PMID: 26346180 DOI: 10.1002/sim.6728] [Citation(s) in RCA: 149] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2014] [Revised: 06/27/2015] [Accepted: 08/13/2015] [Indexed: 01/21/2023]
Abstract
The power prior has been widely used in many applications covering a large number of disciplines. The power prior is intended to be an informative prior constructed from historical data. It has been used in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. It has also been applied for a wide variety of models and settings, both in the experimental design and analysis contexts. In this review article, we give an A-to-Z exposition of the power prior and its applications to date. We review its theoretical properties, variations in its formulation, statistical contexts for which it has been used, applications, and its advantages over other informative priors. We review models for which it has been used, including generalized linear models, survival models, and random effects models. Statistical areas where the power prior has been used include model selection, experimental design, hierarchical modeling, and conjugate priors. Frequentist properties of power priors in posterior inference are established, and a simulation study is conducted to further examine the empirical performance of the posterior estimates with power priors. Real data analyses are given illustrating the power prior as well as the use of the power prior in the Bayesian design of clinical trials.
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Affiliation(s)
- Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, Chapel Hill, 27599, NC, U.S.A
| | - Ming-Hui Chen
- Department of Statistics, University of Connecticut, Storrs, CT, 06269, U.S.A
| | - Yeongjin Gwon
- Department of Statistics, University of Connecticut, Storrs, CT, 06269, U.S.A
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