On group sequential designs comparing two binomial proportions.

Discussed is the problem of sample size determination for one- and two-stage hypothesis tests comparing two binomial proportions using two independent random samples. A FORTRAN compiled search algorithm identifies exact group sequential designs that allow early stopping only for futility or only for efficacy or for either futility or efficacy. The resulting designs yield a substantial savings in terms of total sample size in many practical cases, are seen to satisfy a number of desirable properties, and are compared to other exact one- and two-stage designs and to designs derived based upon asymptotic normal theory methods.