Review Articles

Power analysis, sample size calculation for testing the largest binomial probability

Thuan Nguyen ,

a Oregon Health and Science University, Portland, OR, USA;b University of California, Davis, CA, USA

Jiming Jiang

a Oregon Health and Science University, Portland, OR, USA;b University of California, Davis, CA, USA

Pages 78-83 | Received 31 Oct. 2018, Accepted 20 Feb. 2019, Published online: 15 Mar. 2019,
  • Abstract
  • Full Article
  • References
  • Citations


A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments. It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameter-free, but χ21χ12 is a conservative asymptotic null distribution. A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability. An example from an animal clinical trial is discussed.


  1. Alam, M. K., Rao, M. B., & Cheng, F.-C. (2010). Sample size determination in logistic regression. Sankhyā B72, 58–75. doi: 10.1007/s13571-010-0004-6 [Crossref], [Google Scholar]
  2. Borenstein, M., Rothstein, H., & Cohen, J. (2001). Power and precision. Englewood, US: Biostat Inc. [Google Scholar]
  3. Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in Medicine26, 3385–3397. doi: 10.1002/sim.2771 [Crossref][Web of Science ®], [Google Scholar]
  4. Hsieh, F. Y., Bloch, D. A., & Larsen, M. D. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine17, 1623–1634. doi: 10.1002/(SICI)1097-0258(19980730)17:14<1623::AID-SIM871>3.0.CO;2-S [Crossref][Web of Science ®], [Google Scholar]
  5. Jiang, J. (2000). A nonlinear Gauss-Seidel algorithm for inference about GLMM. Computational Statistics15, 229–241. doi: 10.1007/s001800000030 [Crossref][Web of Science ®], [Google Scholar]
  6. Jiang, J. (2010). Large sample techniques for statistics. New York: Springer. [Crossref], [Google Scholar]
  7. Novikov, I., Fund, N., & Freedman, L. S. (2010). A modified approach to estimating sample size for simple logistic regression with one continuous covariate. Statistics in Medicine29, 97–105. [Crossref][Web of Science ®], [Google Scholar]
  8. White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica50, 1–25. doi: 10.2307/1912526 [Crossref][Web of Science ®], [Google Scholar]
  9. Whittemore, A. (1981). Sample size for logistic regression with small response probability. Journal of the American Statistical Association76, 27–32. doi: 10.1080/01621459.1981.10477597 [Taylor & Francis Online][Web of Science ®], [Google Scholar]