Optimal alpha spending for sequential analysis with binomial data

For sequential analysis hypothesis testing, various alpha spending functions have been proposed. Given a prespecified overall alpha level and power, we derive the optimal alpha spending function that minimizes the expected time to signal for continuous as well as group sequential analysis. If there is also a restriction on the maximum sample size or on the expected sample size, we do the same. Alternatively, for fixed overall alpha, power and expected time to signal, we derive the optimal alpha spending function that minimizes the expected sample size. The method constructs alpha spending functions that are uniformly better than any other method, such as the classical Wald, Pocock or O’Brien–Fleming methods. The results are based on exact calculations using linear programming. All numerical examples were run by using the R Sequential package.