Exact interval estimation for the linear combination of binomial proportions.

The weighted sum of binomial proportions and the interaction effect are two important cases of the linear combination of binomial proportions. Existing confidence intervals for these two parameters are approximate. We apply the -function method to a given approximate interval and obtain an exact interval.

Optimal confidence intervals for the relative risk and odds ratio.

The relative risk and odds ratio are widely used in many fields, including biomedical research, to compare two treatments. Extensive research has been done to infer the two parameters through approximate or exact confidence intervals. However, these intervals may be liberal or conservative.