Selecting a biased-coin design

Statistical Science

Volumn 29, Issue 1, 2014, Pages 144-163

  Atkinson, Anthony C ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Clinical trial; Covariate balancing; Loss of information; Optimum experimental design; Random allocation; Selection bias

Indexed keywords

EID: 84901455700     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-STS449     Document Type: Article

References (47)

1. ATKINSON, A. C. (1982). Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika 69 61-67. MR0655670.
2. ATKINSON, A. C. (2002). The comparison of designs for sequential clinical trials with covariate information. J. Roy. Statist. Soc. Ser. A 165 349-373. MR1904822.
3. ATKINSON, A. C. (2003). The distribution of loss in two-treatment biased-coin designs. Biostatistics 4 179-193.
4. ATKINSON, A. C. (2004). Adaptive biased-coin designs for clinical trials with several treatments. Discuss. Math. Probab. Stat. 24 85-108. MR2118925.
5. ATKINSON, A. C. (2012). Bias and loss: The two sides of a biased coin. Stat. Med. 31 3494-3503. MR3041826.
6. ATKINSON, A. C. and BISWAS, A. (2005a). Bayesian adaptive biased-coin designs for clinical trials with normal responses. Biometrics 61 118-125. MR2135851.
7. ATKINSON, A. C. and BISWAS, A. (2005b). Adaptive biased-coin designs for skewing the allocation proportion in clinical trials with normal responses. Stat. Med. 24 2477-2492. MR2112377.
8. ATKINSON, A. C. and BISWAS, A. (2014). Randomised Response-Adaptive Designs in Clinical Trials. Chapman & Hall/CRC Press, Boca Raton.
9. ATKINSON, A. C., DONEV, A. N. and TOBIAS, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford Statistical Science Series 34. Oxford Univ. Press, Oxford. MR2323647.
10. BAILEY, R. A. and NELSON, P. R. (2003). Hadamard randomization: A valid restriction of random permuted blocks. Biom. J. 45 554-560. MR1998135.
11. BALDI ANTOGNINI, A. (2008). A theoretical analysis of the power of biased coin designs. J. Statist. Plann. Inference 138 1792-1798. MR2400479.
12. BALDI ANTOGNINI, A. and GIOVAGNOLI, A. (2004). A new "biased coin design" for the sequential allocation of two treatments. J. R. Stat. Soc. Ser. C Appl. Stat. 53 651-664. MR2087777.
13. BALDI ANTOGNINI, A. and ZAGORAIOU, M. (2011). The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika 98 519-535. MR2836404.
14. BALL, F. G., SMITH, A. F. M. and VERDINELLI, I. (1993). Biased coin designs with a Bayesian bias. J. Statist. Plann. Inference 34 403-421. MR1210443.
15. BEGG, C. B. and KALISH, L. A. (1984). Treatment allocation for nonlinear models in clinical trials: The logistic model. Biometrics 40 409-420.
16. BERGER, V. W. (2005). Selection Bias and Covariate Imbalances in Clinical Trials. Wiley, New York.
17. BISWAS, A. and BHATTACHARYA, R. (2011). Treatment adaptive allocations in randomized clinical trials: An overview. In Handbook of Adaptive Designs in Pharmaceutical and Clinical Development (A. Pong and S.-C. Chow, eds.) 17:1-17:19. Chapman & Hall/CRC Press, Boca Raton, FL.
18. BLACKWELL, D. and HODGES, J. L. JR. (1957). Design for the control of selection bias. Ann. Math. Statist. 28 449-460. MR0088849.
19. BURMAN, C. F. (1996). On Sequential Treatment Allocations in Clinical Trials. Dept. Mathematics, Göteborg.
20. CHEN, Y.-P. (1999). Biased coin design with imbalance tolerance. Comm. Statist. Stochastic Models 15 953-975. MR1721241.
21. COX, D. R. (1951). Some systematic experimental designs. Biometrika 38 312-323. MR0046013.
22. EFRON, B. (1971). Forcing a sequential experiment to be balanced. Biometrika 58 403-417. MR0312660.
23. EFRON, B. (1980). Randomizing and balancing a complicated sequential experiment. In Biostatistics Casebook (R. J. Miller, B. Efron, B. W. Brown and L. E. Moses, eds.) 19-30. Wiley, New York.
24. GWISE, T. E., HU, J. and HU, F. (2008). Optimal biased coins for two-arm clinical trials. Stat. Interface 1 125-135. MR2425350.
25. GWISE, T. E., ZHOU, J. and HU, F. (2011). An optimal response adaptive biased coin design with k heteroscedastic treatments. J. Statist. Plann. Inference 141 235-242. MR2719490.
26. HERITIER, S., GEBSKI, V. and PILLAI, A. (2005). Dynamic balancing randomization in controlled clinical trials. Stat. Med. 24 3729-3741. MR2221964.
27. HU, Y. and HU, F. (2012). Asymptotic properties of covariateadaptive randomization. Ann. Statist. 40 1794-1815. MR3015044.
28. HU, F. and ROSENBERGER, W. F. (2006). The Theory of Response-Adaptive Randomization in Clinical Trials. Wiley, Hoboken, NJ. MR2245329.
29. LAGAKOS, S. W. and POCOCK, S. J. (1984). Randomization and stratification in cancer clinical trials: An international survey. In Cancer Clinical Trials: Methods and Practice (M. E. Buyse, M. J. Staquet and R. J. Sylvester, eds.). Oxford Univ. Press, Oxford.
30. LIN, Y. and SU, Z. (2012). Balancing continuous and categorical baseline covariates in sequential clinical trials using the area between empirical cumulative distribution functions. Stat. Med. 31 1961-1971. MR2956029.
31. MARKARYAN, T. and ROSENBERGER, W. F. (2010). Exact properties of Efron's biased coin randomization procedure. Ann. Statist. 38 1546-1567. MR2662351.
32. MCENTEGART, D. (2003). The pursuit of balance using stratified and dynamic randomization techniques: An overview. Drug Information Journal 37 293-308.
33. POCOCK, S. J. (1983). Clinical Trials. Wiley, New York.
34. POCOCK, S. J. and SIMON, R. (1975). Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 31 103-115.
35. PROSCHAN, M., BRITTAIN, E. and KAMMERMAN, L. (2012). Letter to the editor. Biometrics 68 990-991.
36. ROSENBERGER, W. F. and LACHIN, J. M. (2002). Randomization in Clinical Trials: Theory and Practice. Wiley, New York. MR1914364.
37. ROSENBERGER, W. F. and SVERDLOV, O. (2008). Handling covariates in the design of clinical trials. Statist. Sci. 23 404-419. MR2483911.
38. ROSENBERGER, W. F., SVERDLOV, O. and HU, F. (2012). Adaptive randomization for clinical trials. J. Biopharm. Statist. 22 719-736. MR2931067.
39. SENN, S., ANISIMOV, V. V. and FEDOROV, V. V. (2010). Comparisons of minimization and Atkinson's algorithm. Stat. Med. 29 721-730. MR2752037.
40. SHAO, J., YU, X. and ZHONG, B. (2010). A theory for testing hypotheses under covariate-adaptive randomization. Biometrika 97 347-360. MR2650743.
41. SMITH, R. L. (1984a). Properties of biased coin designs in sequential clinical trials. Ann. Statist. 12 1018-1034. MR0751289.
42. SMITH, R. L. (1984b). Sequential treatment allocation using biased coin designs. J. R. Stat. Soc. Ser. B Stat. Methodol. 46 519-543. MR0790636.
43. SOARES, J. F. and WU, C. F. J. (1983). Some restricted randomization rules in sequential designs. Comm. Statist. Theory Methods 12 2017-2034. MR0714209.
44. SVERDLOV, O. and ROSENBERGER, W. F. (2013). Randomization in clinical trials: Can we eliminate bias? Clinical Trial Perspective 3 37-47.
45. WEI, L. J. (1978). The adaptive biased coin design for sequential experiments. Ann. Statist. 6 92-100. MR0471205.
46. ZHANG, L.-X., HU, F., CHEUNG, S. H. and CHAN, W. S. (2007). Asymptotic properties of covariate-adjusted response-adaptive designs. Ann. Statist. 35 1166-1182. MR2341702.
47. ZHAO, W., WENG, Y., WU, Q. and PALESCH, Y. (2012). Quantitative comparison of randomization designs in sequential clinical trials based on treatment balance and allocation randomness. Pharm. Stat. 11 39-48.