On construction of the smallest one-sided confidence interval for the difference of two proportions

TL;DR

This paper develops the smallest one-sided confidence interval for the difference of two proportions, providing a method for dose-response analysis and multiple testing control in binary data, with extensions to other discrete spaces.

Contribution

It introduces a novel construction of the smallest one-sided confidence interval for two proportions and applies it to dose-response studies and multiple testing procedures.

Findings

Constructed the smallest confidence interval based on coverage probability analysis.

Applied the interval to identify minimum effective dose in binary dose-response data.

Developed a multiple test procedure controlling familywise error rate at level α.

Abstract

For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at level $\alpha$ is obtained. A generalization of constructing the smallest one-sided confidence interval to other discrete sample spaces is discussed in the presence of nuisance parameters.