IDEAS home Printed from
   My bibliography  Save this article

Simultaneous score confidence bounds for risk differences in multiple comparisons to a control


  • Klingenberg, Bernhard


Asymptotic simultaneous lower (upper) confidence bounds for risk differences arising from comparing several treatments to a common control are constructed by inverting the maximum (minimum) of score statistics. With a few exceptions, these bounds perform better in terms of simultaneous coverage probability than procedures based on adjusted Wald methods (e.g., adding pseudo-observations), especially over relevant parts of the parameter space in superiority or inferiority studies. A further improvement is realized by using an appropriate multiplicity adjusted critical value that takes advantage of the correlation information in the score statistics estimated under the null instead of a regular plug-in estimate. Simulation results and a worked example show a gain in terms of the precision of the lower bounds and their power; however, not too much is lost when using the straightforward Sidak multiplicity adjustment when the number of comparisons is small. All methods discussed are implemented and reproducible with general and publicly available R code.

Suggested Citation

  • Klingenberg, Bernhard, 2012. "Simultaneous score confidence bounds for risk differences in multiple comparisons to a control," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1079-1089.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1079-1089 DOI: 10.1016/j.csda.2011.01.025

    Download full text from publisher

    File URL:
    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

    1. Zou, Guang Yong & Huang, Wenyi & Zhang, Xiaohe, 2009. "A note on confidence interval estimation for a linear function of binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1080-1085, February.
    2. Santner, Thomas J. & Pradhan, Vivek & Senchaudhuri, Pralay & Mehta, Cyrus R. & Tamhane, Ajit, 2007. "Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5791-5799, August.
    3. Andersson, Per Gösta, 2009. "A Simple Correlation Adjustment Procedure Applied to Confidence Interval Construction," The American Statistician, American Statistical Association, vol. 63(3), pages 258-262.
    4. Pan, Wei, 2002. "Approximate confidence intervals for one proportion and difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 143-157, July.
    5. Alan Agresti & Matilde Bini & Bruno Bertaccini & Euijung Ryu, 2008. "Simultaneous Confidence Intervals for Comparing Binomial Parameters," Biometrics, The International Biometric Society, vol. 64(4), pages 1270-1275, December.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:eee:csdana:v:56:y:2012:i:12:p:3865-3875 is not listed on IDEAS
    2. Klingenberg, Bernhard & Satopää, Ville, 2013. "Simultaneous confidence intervals for comparing margins of multivariate binary data," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 87-98.


    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:csdana:v:56:y:2012:i:5:p:1079-1089. 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: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.