Stratification Issues with Binary Endpoints


This note addresses four interrelated issues for a stratified comparative trial with a binary endpoint: 1. How to define the true overall treatment effect parameter, 2. How the strata should be weighted when conducting inference and estimation involving the overall treatment effect, 3. How to (and how not to) test for a treatment by stratum (T × S) interaction, and 4. When, why, and how the outcome of the T × S test should influence the weights assigned to each stratum. Numerical examples are provided to reinforce the key points.

This is a preview of subscription content, access via your institution.


  1. 1.

    Mehrotra DV, Railkar R. Minimum risk weights for comparing treatments in stratified binomial trials. Stat Med. 2000;19:811–825.

    CAS  Article  Google Scholar 

  2. 2.

    Radhakrishna S. Combination of results from several 2x2 contingency tables. Biometrics. 1965;21:86–98.

    Article  Google Scholar 

  3. 3.

    Breslow NE, Day NE. The analysis of case-control studies. In Statistical Methods in Cancer Research, Vol. 1. Lyon, France: International Agency for Research on Cancer; 1980.

    Google Scholar 

  4. 4.

    Gail M, Simon R. Testing for qualitative interactions between treatment effects and patient subsets. Biometrics. 1985;41:361–372.

    CAS  Article  Google Scholar 

  5. 5.

    DerSimonian R, Laird NM. Meta-analysis in clinical trials. Control Clin Trials. 1986;7:177–188.

    Article  Google Scholar 

  6. 6.

    Tarone RE. Homogeneity score tests with nuisance parameters. Commun Stat, Series A. 1988;17:1549–1556.

    Article  Google Scholar 

  7. 7.

    Gart JJ, Nam J. Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to multiple tables. Biometrics. 1990;46:637–643.

    CAS  Article  Google Scholar 

  8. 8.

    Lipsitz SR, Dear KBG, Laird NM, Molenberghs G. Tests for homogeneity of the risk difference when data are sparse. Biometrics. 1998;54:148–160.

    CAS  Article  Google Scholar 

  9. 9.

    Lui KJ, Kelly C. A revisit on tests for homogeneity of the risk difference. Biometrics. 2000;56:309–315.

    CAS  Article  Google Scholar 

  10. 10.

    Brown MB, Forsythe AB. The small sample behavior of some statistics which test the equality of several means. Technometrics. 1974;16:129–132.

    Article  Google Scholar 

  11. 11.

    Mehrotra DV. Improving the Brown-Forsythe solution to the Generalized Behrens-Fisher problem. Commun Stat, Series B. 1997;23:1139–1145.

    Article  Google Scholar 

  12. 12.

    Senn S. Statistical Issues in Drug Development. Chichester: Wiley; 1997.

    Google Scholar 

  13. 13.

    Fleiss JL. Analysis of data from multicenter trials. Control Clin Trials. 1986;10:237–243.

    Article  Google Scholar 

  14. 14.

    Pocock SJ. Clinical Trials: A Practical Approach. New York, NY: Wiley; 1983.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Devan V. Mehrotra PhD.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mehrotra, D.V. Stratification Issues with Binary Endpoints. Ther Innov Regul Sci 35, 1343–1350 (2001).

Download citation

Key Words

  • Binomial
  • Independent proportions
  • Interaction
  • Scale
  • Weighting