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. Greater efficiency is lost with increase in the no. of stages. The timing of IAs also can impact the efficiency of a GSDs with delay. Particularly, for unequally spaced IAs, conducting IAs too early in the trial can be harmful for the design with delay.

翻译：适应性设计是一类广泛的试验设计，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，观察主要结局变量的延迟可能会损害这种额外的效率。本文旨在确定导致适应性设计相较于经典固定样本随机对照试验实现的效率增益变得可忽略不计的结局延迟大小。我们通过为具有正态数据的双臂组序贯设计中超限数量建立公式来衡量延迟的影响，假设了不同的招募模型。组序贯设计的效率通常以期望样本量来衡量，组序贯设计通常能降低期望样本量，相较于标准随机对照试验。我们的公式从因延迟而损失的期望样本量减少方面衡量组序贯设计的效率增益。我们评估了精心选择设计（例如，改变期中分析的时间间隔）是否有助于在存在延迟的情况下恢复组序贯设计的优势。我们还分析了组序贯设计在完成试验所需时间方面的效率。比较考虑延迟与不考虑延迟时的期望效率增益，显然组序贯设计因延迟而遭受相当大的损失。即使很小的延迟也可能对试验效率产生显著影响。相比之下，即使在存在显著延迟的情况下，组序贯设计相较于简单随机对照试验仍具有更短的期望试验完成时间。阶段数量增加会导致更大的效率损失。期中分析的时间安排也会影响存在延迟的组序贯设计的效率。特别是对于不等间隔的期中分析，在试验中过早进行期中分析可能对存在延迟的设计有害。