IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Probabilistic Foundation of Confirmatory Adaptive Designs

  • W. Brannath
  • G. Gutjahr
  • P. Bauer
Registered author(s):

    Adaptive designs allow the investigator of a confirmatory trial to react to unforeseen developments by changing the design. This broad flexibility comes at the price of a complex statistical model where important components, such as the adaptation rule, remain unspecified. It has thus been doubted whether Type I error control can be guaranteed in general adaptive designs. This criticism is fully justified as long as the probabilistic framework on which an adaptive design is based remains vague and implicit. Therefore, an indispensable step lies in the clarification of the probabilistic fundamentals of adaptive testing. We demonstrate that the two main principles of adaptive designs, namely the conditional Type I error rate and the conditional invariance principle, will provide Type I error rate control, if the conditional distribution of the second-stage data, given the first-stage data, can be described in terms of a regression model. A similar assumption is required for regression analysis where the distribution of the covariates is a nuisance parameter and the model needs to be identifiable independently from the covariate distribution. We further show that under the assumption of a regression model, the events of an arbitrary adaptive design can be embedded into a formal probability space without the need of posing any restrictions on the adaptation rule. As a consequence of our results, artificial constraints that had to be imposed on the investigator only for mathematical tractability of the model are no longer necessary.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://hdl.handle.net/10.1080/01621459.2012.682540
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2011)
    Issue (Month): 498 (June)
    Pages: 824-832

    as
    in new window

    Handle: RePEc:taf:jnlasa:v:107:y:2011:i:498:p:824-832
    Contact details of provider: Web page: http://www.tandfonline.com/UASA20

    Order Information: Web: http://www.tandfonline.com/pricing/journal/UASA20

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2011:i:498:p:824-832. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.