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.

中文翻译：

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使用二项式数据进行顺序分析的最佳Alpha支出

对于顺序分析假设检验，已提出了各种alpha支出函数。给定预先指定的总体alpha水平和功率，我们得出了最佳的alpha消耗函数，该函数可以最大程度地减少连续和小组顺序分析发出信号的预期时间。如果最大样本量或预期样本量也受到限制，我们可以这样做。或者，对于固定的总Alpha，功率和预期的信号发送时间，我们得出了最佳的Alpha支出函数，该函数使预期的样本大小最小化。该方法构造的alpha支出函数要比其他任何方法（例如经典的Wald，Pocock或O'Brien-Fleming方法）统一更好。结果是基于使用线性编程的精确计算得出的。所有数值示例均使用R Sequential程序包运行。