IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i10p1014-1020.html
   My bibliography  Save this article

Goodness-of-fit test for response adaptive clinical trials

Author

Listed:
  • Yi, Yanqing
  • Wang, Xikui

Abstract

Much attention has been given in recent years to adaptive designs of clinical trials as ethical alternatives when the traditional randomization becomes ethically infeasible. But such designs create dependency among the collected data, and hence statistical methods for adaptive clinical trials are more complex than those for traditional randomized clinical trials. In this paper, we examine some extensions of common statistical methods for independent data. Under regularity conditions, the logarithm of likelihood ratio statistic 2ln[lambda] for dependent data is shown to be asymptotically chi-square distributed, providing a foundation for asymptotic analysis of adaptive clinical trials with k treatments. We also discuss both the consistency and the asymptotic normality of the maximum likelihood estimators for a wide class of adaptive designs.

Suggested Citation

  • Yi, Yanqing & Wang, Xikui, 2007. "Goodness-of-fit test for response adaptive clinical trials," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1014-1020, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:1014-1020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00041-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kiyoshi Inoue & Sigeo Aki, 2005. "A generalized Pólya urn model and related multivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 49-59, March.
    2. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
    3. William F. Rosenberger & Nigel Stallard & Anastasia Ivanova & Cherice N. Harper & Michelle L. Ricks, 2001. "Optimal Adaptive Designs for Binary Response Trials," Biometrics, The International Biometric Society, vol. 57(3), pages 909-913, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yi, Yanqing, 2013. "Exact statistical power for response adaptive designs," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 201-209.
    2. Tolusso, David & Wang, Xikui, 2011. "Interval estimation for response adaptive clinical trials," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 725-730, January.
    3. Yi, Yanqing & Wang, Xikui, 2023. "A Markov decision process for response adaptive designs," Econometrics and Statistics, Elsevier, vol. 25(C), pages 125-133.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li-Xin, Zhang, 2006. "Asymptotic results on a class of adaptive multi-treatment designs," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 586-605, March.
    2. Uttam Bandyopadhyay & Atanu Biswas & Shirsendu Mukherjee, 2009. "Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 13-33, March.
    3. Biswas, Atanu & Bhattacharya, Rahul, 2011. "Optimal response-adaptive allocation designs in phase III clinical trials: Incorporating ethics in optimality," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1155-1160, August.
    4. Hengtao Zhang & Guosheng Yin, 2021. "Response‐adaptive rerandomization," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1281-1298, November.
    5. Uttam Bandyopadhyay & Atanu Biswas, 2018. "Fixed-width confidence interval for covariate-adjusted response-adaptive designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 353-371, April.
    6. Alessandro Baldi Antognini & Marco Novelli & Maroussa Zagoraiou, 2022. "A simple solution to the inadequacy of asymptotic likelihood-based inference for response-adaptive clinical trials," Statistical Papers, Springer, vol. 63(1), pages 157-180, February.
    7. Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
    8. Bai, Z. D. & Hu, Feifang, 1999. "Asymptotic theorems for urn models with nonhomogeneous generating matrices," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 87-101, March.
    9. Atkinson, Anthony C. & Biswas, Atanu, 2017. "Optimal response and covariate-adaptive biased-coin designs for clinical trials with continuous multivariate or longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 297-310.
    10. Soumaya Idriss & Hosam Mahmoud, 2023. "Exact Covariances and Refined Asymptotics in Dichromatic Tenable Balanced Pólya Urn Schemes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    11. Sofía S. Villar & William F. Rosenberger, 2018. "Covariate†adjusted response†adaptive randomization for multi†arm clinical trials using a modified forward looking Gittins index rule," Biometrics, The International Biometric Society, vol. 74(1), pages 49-57, March.
    12. Chambaz Antoine & van der Laan Mark J., 2011. "Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Simulation Study," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-30, January.
    13. Hanan Hammouri & Marwan Alquran & Ruwa Abdel Muhsen & Jaser Altahat, 2022. "Optimal Weighted Multiple-Testing Procedure for Clinical Trials," Mathematics, MDPI, vol. 10(12), pages 1-19, June.
    14. Feng, Yarong & Mahmoud, Hosam M., 2021. "Dynamic Pólya–Eggenberger urns," Statistics & Probability Letters, Elsevier, vol. 174(C).
    15. Yanqing Yi & Yuan Yuan, 2013. "An optimal allocation for response-adaptive designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1996-2008, September.
    16. Ruicheng Ao & Hongyu Chen & David Simchi-Levi, 2024. "Prediction-Guided Active Experiments," Papers 2411.12036, arXiv.org, revised Nov 2024.
    17. Biswas, Atanu & Bhattacharya, Rahul, 2010. "An optimal response-adaptive design with dual constraints," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 177-185, February.
    18. Atkinson, Anthony C. & Biswas, Atanu, 2017. "Optimal response and covariate-adaptive biased-coin designs for clinical trials with continuous multivariate or longitudinal responses," LSE Research Online Documents on Economics 66761, London School of Economics and Political Science, LSE Library.
    19. Jennifer Proper & Thomas A. Murray, 2023. "An alternative metric for evaluating the potential patient benefit of response‐adaptive randomization procedures," Biometrics, The International Biometric Society, vol. 79(2), pages 1433-1445, June.
    20. Anupam Kundu & Nabaneet Das & Sayantan Chakraborty & Subir Kumar Bhandari, 2017. "Optimal Test Statistics for Minimising not Cured Proportion in Adaptive Clinical Trial," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 156-169, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:1014-1020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.