Test-Based Exact Confidence Intervals for the Difference of Two Binomial Proportions
Article first published online: 25 MAY 2004
Volume 55, Issue 4, pages 1202–1209, December 1999
How to Cite
Chan, I. S. F. and Zhang, Z. (1999), Test-Based Exact Confidence Intervals for the Difference of Two Binomial Proportions. Biometrics, 55: 1202–1209. doi: 10.1111/j.0006-341X.1999.01202.x
- Issue published online: 25 MAY 2004
- Article first published online: 25 MAY 2004
- Received February 1998. Revised January 1999. Accepted January 1999.
- Constrained MLE;
- Exact test;
- Two-by-two table;
- Unconditional distribution
Summary. Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.