Exact optimum coin bias in Efron's randomization procedure
Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which...
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| Published in | Statistics in medicine Vol. 34; no. 28; pp. 3760 - 3768 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
10.12.2015
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 |
| DOI | 10.1002/sim.6576 |
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| Abstract | Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples. Copyright © 2015 John Wiley & Sons, Ltd. |
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| AbstractList | Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples. Copyright © 2015 John Wiley & Sons, Ltd. Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized , in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples. Copyright © 2015 John Wiley & Sons, Ltd. Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efron's coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples. |
| Author | Wang, Yang Antognini, Alessandro Baldi Rosenberger, William F. Zagoraiou, Maroussa |
| Author_xml | – sequence: 1 givenname: Alessandro Baldi surname: Antognini fullname: Antognini, Alessandro Baldi email: Correspondence to: Alessandro Baldi Antognini, Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, 40127, Bologna, Italy., a.baldi@unibo.it organization: Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, 40127, Bologna, Italy – sequence: 2 givenname: William F. surname: Rosenberger fullname: Rosenberger, William F. organization: Department of Statistics, George Mason University, 4400 University Drive MS 4A7, VA, Fairfax, U.S.A – sequence: 3 givenname: Yang surname: Wang fullname: Wang, Yang organization: Department of Statistics, George Mason University, 4400 University Drive MS 4A7, VA, Fairfax, U.S.A – sequence: 4 givenname: Maroussa surname: Zagoraiou fullname: Zagoraiou, Maroussa organization: Department of Business Administration and Law, University of Calabria, 87036, Arcavacata di Rende (CS), Italy |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/26123177$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1111/j.2517-6161.1988.tb01717.x 10.1214/12-AOS1007 10.1111/j.1467-9876.2004.00436.x 10.1136/bmj.325.7358.249 10.2307/2529712 10.1093/biomet/asr021 10.1093/biomet/asr077 10.1002/0471722103 10.1016/j.jspi.2007.06.033 10.1002/sim.4780142406 10.1016/S0197-2456(99)00014-8 10.1214/09-AOS758 10.1016/j.cct.2011.08.004 10.1002/pst.493 10.1111/1467-9868.00056 10.1016/j.jspi.2014.11.002 10.1093/biomet/58.3.403 10.1214/aos/1176344068 10.1002/sim.3014 10.1002/sim.1538 10.1201/b18306 10.2174/157488706775246139 10.1214/aoms/1177706973 10.1002/(SICI)1097-0258(19990815)18:15<1903::AID-SIM188>3.0.CO;2-F 10.1016/j.jspi.2005.08.012 10.1214/13-STS449 10.1093/biomet/asq055 |
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| Keywords | selection bias compound optimality biased coin design accidental bias restricted randomization |
| Language | English |
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| References | Pocock SJ, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 1975; 31:103-115. Azriel D, Mandel M, Rinott Y. Optimal allocation to maximize power of two-sample tests for binary response. Biometrika 2012; 99:101-113. Kjaegard LL, Als-Nielsen B. Association between competing interests and author's conclusions: epidemiological study of randomized clinical trials published in the BMJ. British Medical Journal 2002; 325:249-252. Baldi Antognini A, Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika 2011; 98:519-535. Berger VW, Exner DV. Detecting selection bias in randomized clinical trials. Controlled Clinical Trials 1999; 20:319-327. Senn S. A personal view of some controversies in allocating treatment to patients in clinical trials. Statistics in Medicine 1995; 14:2661-2674. Wei LJ. The adaptive biased coin design for sequential experiments. The Annals of Statistics 1978; 6:92-100. Berger VW, Ivanova A, Knoll MD. Minimizing predictability while retaining balance through the use of less restrictive randomization procedures. Statistics in Medicine 2003; 22:3017-3028. Atkinson AC, Biswas A. Randomised Response-Adaptive Designs In Clinical Trials. Boca Raton: Chapman & Hall/CRC Press, 2014. Efron B. Forcing sequential experiments to be balanced. Biometrika 1971; 58:403-417. Salama I, Ivanova A, Qaqish B. Efficient generation of constrained block allocation sequences. Statistics in Medicine 2008; 27:1421-1428. Rosenberger WF, Lachin JL. Randomization in Clinical Trials: Theory and Practice. John Wiley & Sons: New York, 2002. Berger VW. A review of methods for ensuring the comparability of comparison groups in randomized clinical trials. Reviews on Recent Clinical Trials 2006; 1:81-86. Baldi Antognini A, Giovagnoli A. Compound optimal allocation for individual and collective ethics in binary clinical trials. Biometrika 2010; 97:935-946. Lewis JA. Statistical principles for clinical trials (ICH e9): an introductory note on an international guideline. Statistics in Medicine 1999; 18:1903-1942. Azriel D. Power efficiency of Efron's biased coin design. Journal of Statistical Planning and Inference 2015; 159:15-27. Dette H. Designing experiments with respect to standardized optimality criteria. Journal of the Royal Statistical Society Series B 1997; 59:97-110. Baldi Antognini A, Giovagnoli A. Adaptive Designs for Sequential Treatment allocation. Boca Raton: Chapman & Hall/CRC Press, 2015. Zhao W, Weng Y. Block urn designs. a new randomization algorithm for sequential trials with two or more treatments and balanced or unbalanced allocation. Contemporary Clinical Trials 2011; 32:953-996. Cumberland WG, Royall RM. Does simple random sampling provide adequate balance? Journal of Royal Statistical Society Series B 1988; 50:118-124. Markaryan T, Rosenberger WF. Exact properties of Efron's biased coin randomization procedure. The Annals of Statistics 2010; 38:1546-1567. Baldi Antognini A, Giovagnoli A. A new "biased coin design" for the sequential allocation of two treatments. Journal of the Royal Statistical Society Series C 2004; 53:651-664. Baldi Antognini A, Zagoraiou M. Multi-objective optimal designs in comparative clinical trials with covariates: the reinforced doubly-adaptive biased coin design. The Annals of Statistics 2012; 40:1315-1345. Burman CF. On sequential treatment allocations in clinical trials. PhD Dissertation. Department of Mathematics. Goteborg University, 1996. Baldi Antognini A. A theoretical analysis of the power of biased coin designs. Journal of Statistical Planning and Inference 2008; 138:1792-1798. Atkinson AC. Selecting a biased-coin design. Statistical Science 2014; 29:144-163. Zhao W, Weng Y, Wu Q, Palesch Y. Quantitative comparison of randomization designs in sequential clinical trials based on treatment balance and allocation randomness. Pharmaceutical Statistics 2012; 11:39-48. Geraldes M, Melfi V, Page C, Zhang H. The doubly adaptive weighted difference design. Journal of Statistical Planning and Inference 2006; 136:1923-1939. Blackwell DH, Hodges JL. Design for the control of selection bias. 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| References_xml | – reference: Kjaegard LL, Als-Nielsen B. Association between competing interests and author's conclusions: epidemiological study of randomized clinical trials published in the BMJ. British Medical Journal 2002; 325:249-252. – reference: Pocock SJ, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 1975; 31:103-115. – reference: Baldi Antognini A, Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika 2011; 98:519-535. – reference: Dette H. Designing experiments with respect to standardized optimality criteria. Journal of the Royal Statistical Society Series B 1997; 59:97-110. – reference: Lewis JA. Statistical principles for clinical trials (ICH e9): an introductory note on an international guideline. Statistics in Medicine 1999; 18:1903-1942. – reference: Baldi Antognini A, Giovagnoli A. Adaptive Designs for Sequential Treatment allocation. Boca Raton: Chapman & Hall/CRC Press, 2015. – reference: Salama I, Ivanova A, Qaqish B. Efficient generation of constrained block allocation sequences. Statistics in Medicine 2008; 27:1421-1428. – reference: Atkinson AC. Selecting a biased-coin design. Statistical Science 2014; 29:144-163. – reference: Azriel D. Power efficiency of Efron's biased coin design. Journal of Statistical Planning and Inference 2015; 159:15-27. – reference: Efron B. Forcing sequential experiments to be balanced. Biometrika 1971; 58:403-417. – reference: Baldi Antognini A, Zagoraiou M. Multi-objective optimal designs in comparative clinical trials with covariates: the reinforced doubly-adaptive biased coin design. The Annals of Statistics 2012; 40:1315-1345. – reference: Wei LJ. The adaptive biased coin design for sequential experiments. The Annals of Statistics 1978; 6:92-100. – reference: Baldi Antognini A, Giovagnoli A. Compound optimal allocation for individual and collective ethics in binary clinical trials. Biometrika 2010; 97:935-946. – reference: Zhao W, Weng Y. Block urn designs. a new randomization algorithm for sequential trials with two or more treatments and balanced or unbalanced allocation. Contemporary Clinical Trials 2011; 32:953-996. – reference: Berger VW, Ivanova A, Knoll MD. Minimizing predictability while retaining balance through the use of less restrictive randomization procedures. Statistics in Medicine 2003; 22:3017-3028. – reference: Baldi Antognini A. A theoretical analysis of the power of biased coin designs. Journal of Statistical Planning and Inference 2008; 138:1792-1798. – reference: Atkinson AC, Biswas A. Randomised Response-Adaptive Designs In Clinical Trials. Boca Raton: Chapman & Hall/CRC Press, 2014. – reference: Blackwell DH, Hodges JL. Design for the control of selection bias. Annals of Mathematical Statistics 1957; 28:449-460. – reference: Rosenberger WF, Lachin JL. Randomization in Clinical Trials: Theory and Practice. John Wiley & Sons: New York, 2002. – reference: Cumberland WG, Royall RM. Does simple random sampling provide adequate balance? Journal of Royal Statistical Society Series B 1988; 50:118-124. – reference: Burman CF. On sequential treatment allocations in clinical trials. PhD Dissertation. Department of Mathematics. Goteborg University, 1996. – reference: Berger VW, Exner DV. Detecting selection bias in randomized clinical trials. Controlled Clinical Trials 1999; 20:319-327. – reference: Senn S. A personal view of some controversies in allocating treatment to patients in clinical trials. Statistics in Medicine 1995; 14:2661-2674. – reference: Markaryan T, Rosenberger WF. Exact properties of Efron's biased coin randomization procedure. The Annals of Statistics 2010; 38:1546-1567. – reference: Berger VW. A review of methods for ensuring the comparability of comparison groups in randomized clinical trials. Reviews on Recent Clinical Trials 2006; 1:81-86. – reference: Geraldes M, Melfi V, Page C, Zhang H. The doubly adaptive weighted difference design. Journal of Statistical Planning and Inference 2006; 136:1923-1939. – reference: Azriel D, Mandel M, Rinott Y. Optimal allocation to maximize power of two-sample tests for binary response. Biometrika 2012; 99:101-113. – reference: Baldi Antognini A, Giovagnoli A. A new "biased coin design" for the sequential allocation of two treatments. Journal of the Royal Statistical Society Series C 2004; 53:651-664. – reference: Zhao W, Weng Y, Wu Q, Palesch Y. Quantitative comparison of randomization designs in sequential clinical trials based on treatment balance and allocation randomness. 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note on an international guideline publication-title: Statistics in Medicine – volume: 28 start-page: 449 year: 1957 end-page: 460 article-title: Design for the control of selection bias publication-title: Annals of Mathematical Statistics – volume: 27 start-page: 1421 year: 2008 end-page: 1428 article-title: Efficient generation of constrained block allocation sequences publication-title: Statistics in Medicine – volume: 1 start-page: 81 year: 2006 end-page: 86 article-title: A review of methods for ensuring the comparability of comparison groups in randomized clinical trials publication-title: Reviews on Recent Clinical Trials – volume: 29 start-page: 144 year: 2014 end-page: 163 article-title: Selecting a biased‐coin design publication-title: Statistical Science – volume: 6 start-page: 92 year: 1978 end-page: 100 article-title: The adaptive biased coin design for sequential experiments publication-title: The Annals of Statistics – year: 2014 – volume: 22 start-page: 3017 year: 2003 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article-title: Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial publication-title: Biometrics – volume: 40 start-page: 1315 year: 2012 end-page: 1345 article-title: Multi‐objective optimal designs in comparative clinical trials with covariates: the reinforced doubly‐adaptive biased coin design publication-title: The Annals of Statistics – volume: 58 start-page: 403 year: 1971 end-page: 417 article-title: Forcing sequential experiments to be balanced publication-title: Biometrika – volume: 325 start-page: 249 year: 2002 end-page: 252 article-title: Association between competing interests and author's conclusions: epidemiological study of randomized clinical trials published in the BMJ publication-title: British Medical Journal – year: 2002 – volume: 138 start-page: 1792 year: 2008 end-page: 1798 article-title: A theoretical analysis of the power of biased coin designs publication-title: Journal of Statistical Planning and Inference – 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| Snippet | Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects... Efron's biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized , in that subjects... |
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| SubjectTerms | accidental bias Asymptotic methods biased coin design Clinical Trials as Topic - statistics & numerical data compound optimality Humans Medical statistics Medical treatment Optimization techniques Probability distribution Random Allocation Research Design restricted randomization Selection Bias |
| Title | Exact optimum coin bias in Efron's randomization procedure |
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