Which design is better? Ehrenfest urn versus biased coin

Advances in Applied Probability

Volumn 32, Issue 3, 2000, Pages 738-749

  Chen, Yung Pin ^a  

^a SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT TRANSFER; RANDOM PROCESSES; STATISTICAL METHODS;

EHRENFEST URN DESIGN; SEQUENTIAL CLINICAL TRIAL;

PROBABILITY;

EID: 0034266679     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800010235     Document Type: Article

References (33)

1. ATKINSON, A. C. (1982). Optimum biased coin design for sequential clinical trials with prognostic factors. Biometrika 69, 61-67.
2. BINGHAM, N. H. (1991). Fluctuation theory for the Ehrenfest urn. Adv. Appl. Prob. 23, 598-611.
3. BLACKWELL, D. AND HODGES, J. L., JR. (1957). Design for the control of selection bias. Ann. Math. Statist. 28, 449-460.
4. BLOM, G. (1989). Mean transition times for the Ehrenfest urn model. Adv. Appl. Prob. 21, 479-480.
5. CHEN, Y. (1994). A study of the trade-offs between balance and randomness in various sequential sampling procedures. Ph.D. Thesis, Department of Statistics, Purdue University.
6. CHEN, Y. (1999). Biased coin design with imbalance tolerance. Commun. Statist. Stoch. Models 15, 953-975.
7. DIACONIS, P. (1988). Group Representations in Probability and Statistics. Lecture Notes - Monographs 11, Institute of Mathematical Statistics, Hayward.
8. EFRON, B. (1971). Forcing a sequential experiment to be balanced. Biometrika 58, 403-417.
9. FELLER, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. John Wiley, New York.
10. FRIEDMAN, B. (1949). A simple urn model. Commun. Pure Appl. Math. 2, 59-70.
11. HESS, F. G. (1954). Alternative solution to the Ehrenfest problem. Amer. Math. Monthly 61, 323-327.
12. KAC, M. (1947). Random walk and the theory of Brownian motion. Amer. Math. Monthly 54, 369-391.
13. KAC, M. (1959). Probability and Related Topics in Physical Sciences. Interscience, London.
14. KARLIN, S. AND TAYLOR, M. H. (1975). A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.
15. KARLIN, S. AND TAYLOR, M. H. (1981). A Second Course in Stochastic Processes. Academic Press, New York.
16. MELFI, V. F. (1992). Nonlinear Markov renewal theory with statistical applications. Ann. Prob. 20, 753-771.
17. PALACIOS, J. L. (1993). Fluctuation theory for the Ehrenfest urn via electric networks. Adv. Appl. Prob. 25, 472-476.
18. PALACIOS, J. L. (1994). Another look at the Ehrenfest urn via electric networks. Adv. Appl. Prob. 26, 820-824.
19. POCOCK, S. J. AND SIMON, R. (1975). Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trials. Biometrics 31, 103-115.
20. POCOCK, S. J. (1979). Allocation of patients to treatment in clinical trials. Biometrics 35, 183-197.
21. POCOCK, S. J. (1983). Clinical Trials: A Practical Approach. John Wiley, New York.
22. SHAPIRO, S. H. AND LOUIS, T. A. (1983). Clinical Trials: Issues and Approaches. Marcel Dekker, New York.
23. SIEGERT, A. J. F. (1949). On the approach to statistical equilibrium. Phys. Rev. 76, 1708-1714.
24. SIMON, R. (1977). Adaptive treatment assignment methods and clinical trials. Biometrics 33, 743-749.
25. SIMON, R. (1979). Restricted randomization designs in clinical trials. Biometrics 35, 503-512.
26. SMITH, R. L. (1984a). Properties of biased coin designs in sequential clinical trials. Ann. Statist. 12, 1018-1034.
27. SMITH, R. L. (1984b). Sequential treatment allocation using biased coin designs. J. R. Statist. Soc. B 46, 519-543.
28. SOARES, J. F. AND WU, C. F. J. (1983). Some restricted randomization rules in sequential designs. Commun. Statist. Theory Meth. 12, 2017-2034.
29. TAKÁCS, L. (1979). On an urn problem of Paul and Tatiana Ehrenfest. Math. Proc. Camb. Phil. Soc. 86, 127-130.
30. WEI, L. J. (1978a). A class of designs for sequential clinical trials. J. Amer. Statist. Assoc. 72, 382-386.
31. WEI, L. J. (1978b). The adaptive biased coin designs for sequential experiments. Ann. Statist. 6, 92-99.
32. WEI, L. J. (1978c). An application of an urn model to the design of sequential controlled clinical trials. J. Amer. Statist. Assoc. 73, 559-563.
33. WEI, L. J., SMYTHE, R. T. AND SMITH, R. L. (1986). K-treatment comparisons with restricted randomization rules in clinical trials. Ann. Statist. 14, 265-274.