Adaptive designs(AD) are a broad class of trial designs that allow preplanned modifications based on patient data providing improved efficiency and flexibility. However, a delay in observing the primary outcome variable can harm this added efficiency. In this paper, we aim to ascertain the size of such outcome delay that results in the realised efficiency gains of ADs becoming negligible compared to classical fixed sample RCTs. We measure the impact of delay by developing formulae for the no. of overruns in 2 arm GSDs with normal data, assuming different recruitment models. The efficiency of a GSD is usually measured in terms of the expected sample size (ESS), with GSDs generally reducing the ESS compared to a standard RCT. Our formulae measures the efficiency gain from a GSD in terms of ESS reduction that is lost due to delay. We assess whether careful choice of design (e.g., altering the spacing of the IAs) can help recover the benefits of GSDs in presence of delay. We also analyse the efficiency of GSDs with respect to time to complete the trial. Comparing the expected efficiency gains, with and without consideration of delay, it is evident GSDs suffer considerable losses due to delay. Even a small delay can have a significant impact on the trial's efficiency. In contrast, even in the presence of substantial delay, a GSD will have a smaller expected time to trial completion in comparison to a simple RCT. Although the no. of stages have little influence on the efficiency losses, the timing of IAs can impact the efficiency of a GSDs with delay. Particularly, for unequally spaced IAs, pushing IAs towards latter end of the trial can be harmful for the design with delay.

翻译：自适应设计（AD）是一类广泛的试验设计方法，允许基于患者数据进行预先计划的修改，从而提高效率和灵活性。然而，主要结局变量的观测延迟可能会削弱这种附加效率。本文旨在确定这种结果延迟的幅度，当延迟达到该幅度时，AD 相对于经典固定样本随机对照试验（RCT）所实现的效率增益变得微不足道。我们通过开发适用于正态数据双臂组序贯设计（GSD）中超额受试者数量的公式来衡量延迟的影响，并假设不同的招募模型。GSD 的效率通常以期望样本量（ESS）来衡量，与标准 RCT 相比，GSD 通常会降低 ESS。我们的公式从因延迟而损失的 ESS 减少量角度衡量 GSD 的效率增益。我们评估了精心选择设计（例如，改变中期分析的时间间隔）是否有助于在存在延迟的情况下恢复 GSD 的优势。我们还分析了 GSD 在完成试验时间方面的效率。比较考虑延迟和不考虑延迟情况下的期望效率增益，可以明显看出 GSD 因延迟而遭受显著损失。即使是很小的延迟也可能对试验效率产生重大影响。相比之下，即使存在较大延迟，相比简单 RCT，GSD 完成试验的期望时间也更短。虽然阶段数对效率损失影响很小，但中期分析的时间安排会影响存在延迟的 GSD 的效率。特别是，对于不等间隔的中期分析，将中期分析推向试验后期可能对有延迟的设计不利。