Early stopping for sequential restricted tests of binomial distributions

In applications of restricted sequential procedures, the accumulating data can provide a strong indication that rejection of the null hypothesis is very unlikely if sampling is continued; however, trial termination with acceptance of the null hypothesis can require a large number of additional observations. Modifications of restricted sequential plans, based on the conditional probability of an inference contrary to that suggested by the data, are presented for trials with binary responses. The derived tests provide the potential for early stopping with acceptance of the null hypothesis and reduction of the expected stopping times. Properties of the stopping-time distributions are obtained exactly by considering the absorption probabilities of a binomial random walk on the lattice determined by the restricted sequential design. Relative efficiencies of the derived tests to the corresponding sequential probability ratio tests are presented, along with an example based on data from a clinical trial.