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  • Volume 10, Number 3 (2004), 447-463.

Asymptotic normality of urn models for clinical trials with delayed response

Feifang Hu and Li-Xin Zhang

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Abstract

For response-adaptive clinical trials using a generalized Friedman's urn design, we derive the asymptotic normality of the sample fraction assigned to each treatment under staggered entry and delayed response. The rate of convergence and the law of the iterated logarithm are obtained for both the urn composition and the sample fraction. Some applications are also discussed.

Article information

Source
Bernoulli, Volume 10, Number 3 (2004), 447-463.

Dates
First available in Project Euclid: 7 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1089206406

Digital Object Identifier
doi:10.3150/bj/1089206406

Mathematical Reviews number (MathSciNet)
MR2061440

Zentralblatt MATH identifier
1054.62083

Keywords
Gaussian process generalized Friedman's urn staggered entry treatment allocation urn models

Citation

Hu, Feifang; Zhang, Li-Xin. Asymptotic normality of urn models for clinical trials with delayed response. Bernoulli 10 (2004), no. 3, 447--463. doi:10.3150/bj/1089206406. https://projecteuclid.org/euclid.bj/1089206406


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References

  • [1] Athreya, K.B. and Karlin, S. (1968) Embedding of urn schemes into continuous time branching processes and related limit theorems. Ann. Math. Statist., 39, 1801-1817.
    Mathematical Reviews (MathSciNet): MR232455
    Zentralblatt MATH: 0185.46103
    Digital Object Identifier: doi:10.1214/aoms/1177698013
    Project Euclid: euclid.aoms/1177698013
  • [2] Bai, Z.D. and Hu, F. (1999) Asymptotic theorem for urn models with nonhomogeneous generating matrices. Stochastic Process. Appl., 80, 87-101. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1670107
    Zentralblatt MATH: 0954.62014
    Digital Object Identifier: doi:10.1016/S0304-4149(98)00094-5
  • [3] Bai, Z.D., Hu, F. and Rosenberger, W.F. (2002) Asymptotic properties of adaptive designs for clinical trials with delayed response. Ann. Statist., 30, 122-139. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1892658
    Zentralblatt MATH: 1012.62087
    Digital Object Identifier: doi:10.1214/aos/1015362187
    Project Euclid: euclid.aos/1015362187
  • [4] Bandyopadhyay, U. and Biswas, A. (1996) Delayed response in randomized play-the-winner rule: a decision theoretic approach. Calcutta Statist. Assoc. Bull., 46, 69-88. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1416890
    Zentralblatt MATH: 0907.62009
  • [5] Durham, S.D., Flournoy, N. and Li, W. (1998) A sequential design for maximizing the probability of a favourable response. Canad. J. Statist., 26, 479-495. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1646698
    Digital Object Identifier: doi:10.2307/3315771
    JSTOR: links.jstor.org
  • [6] Flournoy, N. and Rosenberger, W.F. (eds.) (1995) Adaptive Designs. Hayward, CA: Institute of Mathematical Statistics.
    Mathematical Reviews (MathSciNet): MR1477667
  • [7] Hu, F. (2003) Sample size and power of randomized design. Submitted for publication.
  • [8] Hu, F. and Ivanova, A. (2004) Adaptive designs. In S.-C. Chow (ed.), Encyclopedia of Biopharmaceutical Statistics. New York: Marcel Dekker.
  • [9] Hu, F. and Rosenberger, W.F. (2003) Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc., 98, 671-678.
    Mathematical Reviews (MathSciNet): MR2011680
    Zentralblatt MATH: 1040.62102
    Digital Object Identifier: doi:10.1198/016214503000000576
  • [10] Monrad, D. and Philipp, W. (1991) Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales. Probab. Theory Related Fields, 88, 381-404. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1100898
    Zentralblatt MATH: 0722.60006
    Digital Object Identifier: doi:10.1007/BF01418867
  • [11] Rosenberger, W.F. (1996) New directions in adaptive designs. Statist. Sci., 11, 137-149. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Digital Object Identifier: doi:10.1214/ss/1038425657
  • [12] Rosenberger, W.F. (2002) Randomized urn models and sequential design (with discussions). Sequential Anal., 21, 1-28. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1903097
  • [13] Smythe, R.T. (1996) Central limit theorems for urn models. Stochastic Process. Appl., 65, 115-137. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR1422883
    Zentralblatt MATH: 0889.60013
    Digital Object Identifier: doi:10.1016/S0304-4149(96)00094-4
  • [14] Tamura, R.N., Faries, D.E., Andersen, J.S. and Heiligenstein, J.H. (1994) A case study of an adaptive clinical trial in the treatment of out-patients with depressive disorder. J. Amer. Statist. Assoc., 89, 768-776. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Digital Object Identifier: doi:10.2307/2290902
  • [15] Wei, L.J. (1988) Exact two-sample permutation tests based on the randomized play-the-winner rule. Biometrika, 75, 603-606. Abstract can also be found in the ISI/STMA publication
    URL: Link to item
    Mathematical Reviews (MathSciNet): MR967604
    Zentralblatt MATH: 0657.62086
    Digital Object Identifier: doi:10.1093/biomet/75.3.603
    JSTOR: links.jstor.org

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