Exact Methods for Multistage Estimation of a Binomial Proportion
This work addresses the need for efficient and reliable estimation methods in fields like clinical trials, though it appears incremental as it builds on existing sequential methods.
The authors tackled the problem of estimating a binomial proportion with specified margin of error and confidence level by proposing a new family of group sequential sampling schemes, establishing uniform controllability of coverage probability and asymptotic optimality to guarantee confidence with minimal sample waste.
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.