Conditioning in 2 × 2 Tables

  1. Michael A. Proschan,
  2. Martha Nason

Article first published online: 23 MAY 2008

DOI: 10.1111/j.1541-0420.2008.01053.x

Issue

Biometrics

Biometrics

Volume 65, Issue 1, pages 316–322, March 2009

Additional Information

How to Cite

Proschan, M. A. and Nason, M. (2009), Conditioning in 2 × 2 Tables. Biometrics, 65: 316–322. doi: 10.1111/j.1541-0420.2008.01053.x

Author Information

  1. Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 6700B Rockledge Drive, MSC 7609, Bethesda, Maryland 20892-7609, U.S.A. email: ProschaM@niaid.nih.gov and mnason@niaid.nih.gov

Publication History

  1. Issue published online: 17 MAR 2009
  2. Article first published online: 23 MAY 2008
  3. Received July 2007. Revised December 2007. Accepted January 2008.

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Keywords:

  • Adaptive sample size;
  • Conditional inference;
  • Contingency table;
  • Fisher's exact test;
  • Nuisance parameter;
  • Test of proportions

Summary Two-by-two tables arise in a number of diverse settings in biomedical research, including analysis of data from a clinical trial with a binary outcome and gating methods in flow cytometry to separate antigen-specific immune responses from general immune responses. These applications offer interesting challenges concerning what we should really be conditioning on—the total number of events, the number of events in the control condition, etc. We give several biostatistics examples to illustrate the complexities of analyzing what appear to be simple data.

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