  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.
