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Journal of Probability and Statistics
Volume 2013, Article ID 603297, 24 pages
http://dx.doi.org/10.1155/2013/603297
Research Article

Exact Group Sequential Methods for Estimating a Binomial Proportion

1Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA 30322, USA
2Department of Electrical Engineering, Southern University and A&M College, Baton Rouge, LA 70813, USA

Received 23 May 2012; Revised 1 October 2012; Accepted 9 October 2012

Academic Editor: Xuelin Huang

Copyright © 2013 Zhengjia Chen and Xinjia Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.