Exact Methods for Multistage Estimation of a Binomial Proportion

TL;DR

This paper introduces a new family of group sequential sampling schemes for estimating a binomial proportion, ensuring prescribed confidence levels with minimal sample waste, supported by theoretical analysis and numerical experiments.

Contribution

It proposes a novel family of sampling schemes with proven coverage control and asymptotic optimality, enhancing estimation efficiency in binomial proportion studies.

Findings

Established uniform controllability of coverage probability.

Derived analytic bounds for distribution functions and sample expectations.

Demonstrated efficiency through numerical experiments and clinical trial examples.

Abstract

We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.