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Li X, Hu F. Sample size re-estimation for response-adaptive randomized clinical trials. Pharm Stat 2022; 21:1058-1073. [PMID: 35191605 DOI: 10.1002/pst.2199] [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: 01/13/2020] [Revised: 01/23/2022] [Accepted: 02/02/2022] [Indexed: 11/10/2022]
Abstract
Clinical trials usually take a period of time to recruit volunteers, and they become a steady accumulation of data. Traditionally, the sample size of a trial is determined in advance and data is collected before analysis proceeds. Over the past decades, many strategies have been proposed and rigorous theoretical groundings have been provided to conduct sample size re-estimation. However, the application of these methodologies has not been well extended to take care of trials with adaptive designs. Therefore, we aim to fill the gap by proposing a sample size re-estimation procedure on response-adaptive randomized trial. For ethical and economical concerns, we use multiple stopping criteria with the allowance of early termination. Statistical inference is studied for the hypothesis testing under doubly-adaptive biased coin design. We also prove that the test statistics for each stage are asymptotic independently normally distributed, though dependency exists between the two stages. We find that under our methods, compared to fixed sample size design and other commonly used randomization procedures: (1) power is increased for all scenarios with adjusted sample size; (2) sample size is reduced up to 40% when underestimating the treatment effect; (3) the duration of trials is shortened. These advantages are evidenced by numerical studies and real examples.
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Affiliation(s)
- Xin Li
- Department of Statistics, George Washington University, Washington, District of Columbia, USA
| | - Feifang Hu
- Department of Statistics, George Washington University, Washington, District of Columbia, USA
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2
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Gao L, Zhu H, Zhang L. Sequential monitoring of response-adaptive randomized clinical trials with sample size re-estimation. J Stat Plan Inference 2020. [DOI: 10.1016/j.jspi.2019.06.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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3
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Williamson SF, Villar SS. A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes. Biometrics 2019; 76:197-209. [PMID: 31322732 PMCID: PMC7078926 DOI: 10.1111/biom.13119] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Accepted: 06/24/2019] [Indexed: 12/21/2022]
Abstract
We propose a novel response‐adaptive randomization procedure for multi‐armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non‐myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response‐adaptive algorithm based on the Gittins index for the multi‐armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969‐978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi‐armed setting, there are efficiency and patient benefit gains of using a response‐adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response‐adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi‐armed trial context.
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Affiliation(s)
- S Faye Williamson
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.,MRC Biostatistics Unit, School of Clinical Medicine, University of Cambridge, Cambridge, UK
| | - Sofía S Villar
- MRC Biostatistics Unit, School of Clinical Medicine, University of Cambridge, Cambridge, UK
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Aletti G, Ghiglietti A, Rosenberger WF. Nonparametric covariate-adjusted response-adaptive design based on a functional urn model. Ann Stat 2018. [DOI: 10.1214/17-aos1677] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Liu Z, Hu F, Zhang LX. Nonparametric response-adaptive randomization for continuous responses. Pharm Stat 2018; 17:781-796. [PMID: 30152167 DOI: 10.1002/pst.1900] [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: 01/11/2018] [Revised: 06/08/2018] [Accepted: 07/24/2018] [Indexed: 11/06/2022]
Abstract
Many response-adaptive randomization procedures have been proposed and studied over the past few decades. However, most of these procedures are based on parametric structure and do not directly apply to nonparametric models. In this paper, we propose a response-adaptive randomization procedure based on Mann-Whitney U test statistic. Under widely satisfied conditions, we derive asymptotic properties of the randomization procedure and further obtain power functions in form under Mann-Whitney U test. Simulations show the proposed procedure is more robust and more ethical than classical response-adaptive randomization procedures in some circumstances. Advantages of the procedure are also illustrated in a redesigned real clinical trial.
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Affiliation(s)
- Zhongqiang Liu
- School of Mathematical Sciences, Zhejiang University, Hangzhou, China.,School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China
| | - Feifang Hu
- Department of Statistics, George Washington University, Washington, DC, USA
| | - Li-Xin Zhang
- School of Mathematical Sciences, Zhejiang University, Hangzhou, China
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Ghiglietti A, Vidyashankar AN, Rosenberger WF. Central limit theorem for an adaptive randomly reinforced urn model. ANN APPL PROBAB 2017. [DOI: 10.1214/16-aap1274] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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7
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Zhang LX. Central limit theorems of a recursive stochastic algorithm with applications to adaptive designs. ANN APPL PROBAB 2016. [DOI: 10.1214/16-aap1187] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Abstract
Abstract
In their recent paper Velleman and Warrington (2013) analyzed the expected values of some of the parameters in a memory game; namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively. We also make a connection between the memory game and one of the models of preferential attachment graphs. In particular, as a by-product of our methods, we obtain the joint asymptotic normality of the degree counts in the preferential attachment graphs. Furthermore, we obtain simpler proofs (although without rate of convergence) of some of the results of Peköz et al. (2014) on the joint limiting distributions of the degrees of the first few vertices in preferential attachment graphs. In order to prove that the length of the game is asymptotically normal, our main technical tool is a limit result for the joint distribution of the number of balls in a multitype generalized Pólya urn model.
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Peköz EA, Röllin A, Ross N. Generalized gamma approximation with rates for urns, walks and trees. ANN PROBAB 2016. [DOI: 10.1214/15-aop1010] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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10
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Abstract
The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obtain important asymptotic properties for multicolor reinforced urn models. We derive results for the rate of convergence of the number of patients assigned to each treatment under a set of minimum required conditions and provide the distributions of the limits. Furthermore, we study the asymptotic behavior for the nonhomogeneous case.
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Zhang LX, Hu F, Cheung SH, Chan WS. Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns. ADV APPL PROBAB 2016. [DOI: 10.1239/aap/1401369708] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obtain important asymptotic properties for multicolor reinforced urn models. We derive results for the rate of convergence of the number of patients assigned to each treatment under a set of minimum required conditions and provide the distributions of the limits. Furthermore, we study the asymptotic behavior for the nonhomogeneous case.
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Ghiglietti A, Paganoni AM. An urn model to construct an efficient test procedure for response adaptive designs. STAT METHOD APPL-GER 2015. [DOI: 10.1007/s10260-015-0314-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Statistical inference of adaptive randomized clinical trials for personalized medicine. ACTA ACUST UNITED AC 2015. [DOI: 10.4155/cli.15.15] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Ivanova A, Hoberman S. Higher order response adaptive urn designs for clinical trials with highly successful treatments. J R Stat Soc Ser C Appl Stat 2015; 64:175-189. [PMID: 25641991 DOI: 10.1111/rssc.12066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We consider a problem of reducing the expected number of treatment failures in trials where the probability of response to treatment is close to 1 and treatments are compared based on log odds ratio. We propose a new class of urn designs for randomization of patients in a clinical trial. The new urn designs target a number of allocation proportions including the allocation proportion that yields the same power as equal allocation but significantly less expected treatment failures. The new design is compared with the doubly adaptively biased coin design, the efficient randomized adaptive design and with equal allocation. The properties of the new class of designs are studied by embedding them into a family of continuous time stochastic processes.
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Affiliation(s)
- Anastasia Ivanova
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, U.S.A
| | - Steven Hoberman
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, U.S.A
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Galbete A, Moler JA, Plo F. Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design. Seq Anal 2015. [DOI: 10.1080/07474946.2015.995979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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16
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Sverdlov O, Wong WK. Novel Statistical Designs for Phase I/II and Phase II Clinical Trials With Dose-Finding Objectives. Ther Innov Regul Sci 2014; 48:601-612. [DOI: 10.1177/2168479014523765] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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17
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Azriel D, Feigin PD. Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments. Seq Anal 2014. [DOI: 10.1080/07474946.2014.856637] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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18
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Zhang L. A Gaussian process approximation for two-color randomly reinforced urns. ELECTRON J PROBAB 2014. [DOI: 10.1214/ejp.v19-3432] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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19
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Ghiglietti A, Paganoni AM. Statistical properties of two-color randomly reinforced urn design targeting fixed allocations. Electron J Stat 2014. [DOI: 10.1214/14-ejs899] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Sverdlov O, Rosenberger WF. On Recent Advances in Optimal Allocation Designs in Clinical Trials. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2013. [DOI: 10.1080/15598608.2013.783726] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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22
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Flournoy N, Haines LM, Rosenberger WF. A Graphical Comparison of Response-Adaptive Randomization Procedures. Stat Biopharm Res 2013. [DOI: 10.1080/19466315.2013.782822] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Abstract
In February 2010, the U.S. Food and Drug Administration (FDA, 2010 ) drafted guidance that discusses the statistical, clinical, and regulatory aspects of various adaptive designs for clinical trials. An important class of adaptive designs is adaptive randomization, which is considered very briefly in subsection VI.B of the guidance. The objective of this paper is to review several important new classes of adaptive randomization procedures and convey information on the recent developments in the literature on this topic. Much of this literature has been focused on the development of methodology to address past criticisms and concerns that have hindered the broader use of adaptive randomization. We conclude that adaptive randomization is a very broad area of experimental design that has important application in modern clinical trials.
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