An improved method for deriving optimal one-sided group sequential tests

SUMMARY. We derive one-sided group sequential tests for normal responses which minimize expected sample size; minimization is at a single value of the normal mean or integrated with respect to a normal density. The methods employed are much faster and also numerically more stable than those of Jennison (1987). They provide solutions for cases with as many as 200 groups and, for small numbers of groups, facilitate optimization over the choice of group sizes. We present a new method for constructing near-optimal tests when group sizes are unpredictable, based on interpolating the error spending function of an optimal test with a large number of groups.