IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v85y2022i4d10.1007_s00184-021-00839-w.html
   My bibliography  Save this article

Most powerful test sequences with early stopping options

Author

Listed:
  • Sergey Tarima

    (Institute for Health and Equity, Medical College of Wisconsin)

  • Nancy Flournoy

    (University of Missouri, 600 S State St.)

Abstract

We extended the application of uniformly most powerful tests to sequential tests with different stage-specific sample sizes and critical regions. In the one parameter exponential family, likelihood ratio sequential tests are shown to be uniformly most powerful for any predetermined $$\alpha $$ α -spending function and stage-specific sample sizes. To obtain this result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into components determined by the stopping stage. These components are the sub-densities of interim test statistics first described by Armitage et al. (J R Stat Soc: Ser A 132:235–244, 1969) that are commonly used to create stopping boundaries given an $$\alpha $$ α -spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics that are typically normal, are not. Rather they are derived from mixtures of truncated multivariate normal distributions.

Suggested Citation

  • Sergey Tarima & Nancy Flournoy, 2022. "Most powerful test sequences with early stopping options," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 491-513, May.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:4:d:10.1007_s00184-021-00839-w
    DOI: 10.1007/s00184-021-00839-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-021-00839-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-021-00839-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. HaiYing Wang & Nancy Flournoy & Eloi Kpamegan, 2014. "A new bounded log-linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 695-720, July.
    2. Christopher Jennison & Bruce W. Turnbull, 2006. "Adaptive and nonadaptive group sequential tests," Biometrika, Biometrika Trust, vol. 93(1), pages 1-21, March.
    3. Sergey Tarima & Nancy Flournoy, 2019. "Asymptotic properties of maximum likelihood estimators with sample size recalculation," Statistical Papers, Springer, vol. 60(2), pages 373-394, April.
    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. Sergey Tarima & Nancy Flournoy, 2023. "Group sequential tests: beyond exponential family models," Statistical Papers, Springer, vol. 64(4), pages 1361-1372, August.
    2. Alessandro Baldi Antognini & Rosamarie Frieri & Maroussa Zagoraiou, 2023. "New insights into adaptive enrichment designs," Statistical Papers, Springer, vol. 64(4), pages 1305-1328, August.

    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. Jay Bartroff & Jinlin Song, 2016. "A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 3-19, March.
    2. Sergey Tarima & Nancy Flournoy, 2019. "Asymptotic properties of maximum likelihood estimators with sample size recalculation," Statistical Papers, Springer, vol. 60(2), pages 373-394, April.
    3. Carl-Fredrik Burman & Christian Sonesson, 2006. "Rejoinder," Biometrics, The International Biometric Society, vol. 62(3), pages 680-683, September.
    4. Gregory P. Levin & Sarah C. Emerson & Scott S. Emerson, 2014. "An evaluation of inferential procedures for adaptive clinical trial designs with pre-specified rules for modifying the sample size," Biometrics, The International Biometric Society, vol. 70(3), pages 556-567, September.
    5. Christopher Jennison & Bruce W. Turnbull, 2006. "Discussions," Biometrics, The International Biometric Society, vol. 62(3), pages 670-673, September.
    6. Nancy Flournoy & Sergey Tarima, 2023. "Discussion on “Adaptive enrichment designs with a continuous biomarker” by Nigel Stallard," Biometrics, The International Biometric Society, vol. 79(1), pages 31-35, March.
    7. André Scherag & Johannes Hebebrand & Helmut Schäfer & Hans-Helge Müller, 2009. "Flexible Designs for Genomewide Association Studies," Biometrics, The International Biometric Society, vol. 65(3), pages 815-821, September.
    8. Dejian Lai, 2010. "Group sequential tests under fractional Brownian motion in monitoring clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 277-286, June.
    9. Oke Gerke & Sören Möller, 2021. "Bland–Altman Limits of Agreement from a Bayesian and Frequentist Perspective," Stats, MDPI, vol. 4(4), pages 1-11, December.

    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:spr:metrik:v:85:y:2022:i:4:d:10.1007_s00184-021-00839-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.