A birth and death urn for ternary outcomes: Stochastic processes applied to Urn models

Probability and Statistical Models with Applications

Volumn , Issue , 2000, Pages 583-600

  Ivanova, Anastasia ^a   Flournoy, Nancy ^b  

^a IL   (United States)

^b AMERICAN UNIVERSITY   (United States)

Author keywords

Adaptive designs; Birth and death process with immigration; Clinical trials; Experimental design

Indexed keywords

EID: 17444372869     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (11)

1. Anderson, W. J. (1991). Continuous-Time Markov Chains. Springer Verlag, New York.
2. Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer Verlag, Berlin.
3. Cox, D. R. and Miller, H. D. (1965). The Theory of Stochastic Processes. John Wiley & Sons, New York.
4. Durham, S. D., Flournoy, N., and Li, W. (1998). A sequential design for maximizing the probability of a favorable response. Canadian Journal of Statistics 26, 479-495.
5. Ivanova, A. (1998). A birth and death urn for randomized clinical trials. Unpublished Doctoral Dissertation, University of Maryland Graduate School, Baltimore.
6. Ivanova, A. and Rosenberger, W. F. (2000). A comparison of urn designs for randomized clinical trials of K > 2 treatments. Journal of Biophanriaceutical Statistics 10 93-107.
7. Ivanova, A., Rosenberger, W. F., Durham, S. D., and Flournoy, N. (2000). A birth and death urn for randomized clinical trials: Asymptotic methods. Sankhya, Series B (to appear).
8. Karlin, S. and Taylor, H. M. (1974). A First Course in Stochastic Processes. Academic Press, New York.
9. Kotz, S. and Balakrishnan, N. (1997). Advances in urn models during the past two decades. In Advances in Combinatorial Methods and Applications to Probability and Statistics (Ed., N. Balakrishnan), pp. 203-257. Birkhaiiser, Boston.
10. Wei, L. J. (1979). The generalized Polyak urn design for sequential medical trials. Annals of Statistics 7, 291-296.
11. Wei, L. J. and Durham, S. D. (1978). The randomized play-the-winner rule in medical trials. Journal of the American Statistical Association 73, 840-843.