This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage designs where sample sizes are reassessed for a specific conditional power and the goal is to minimize the expected sample size. The previous theory can easily lead to a non-monotonous conditional error function which is highly undesirable for logical reasons and can harm type I error rate control for composite null hypotheses. The here presented method extends the existing theory by introducing intermediate monotonising steps that can easily be implemented.

翻译：本笔记提出了一种方法，可为一大类自适应两阶段设计提供最优单调条件错误函数。所提出的方法建立在先前发展的自适应两阶段设计通用最优理论之上，该理论针对特定条件功效重新评估样本量，并以最小化期望样本量为目标。先前的理论容易导致非单调的条件错误函数，这出于逻辑原因极不可取，并且可能损害复合零假设下的第一类错误率控制。本文提出的方法通过引入易于实现的中间单调化步骤，扩展了现有理论。