A crossover trial is an efficient trial design when there is no carry-over effect. To reduce the impact of the biological carry-over effect, a wash-out period is often designed. However, the carry-over effect remains an outstanding concern when a wash-out period is unethical or cannot sufficiently diminish the impact of the carry-over effect. The latter can occur in comparative effectiveness research where the carry-over effect is often non-biological but behavioral. In this paper, we investigate the crossover design under a potential outcomes framework with and without the carry-over effect. We find that when the carry-over effect exists and satisfies a sign condition, the basic estimator underestimates the treatment effect, which does not inflate the type I error of one-sided tests but negatively impacts the power. This leads to a power trade-off between the crossover design and the parallel-group design, and we derive the condition under which the crossover design does not lead to type I error inflation and is still more powerful than the parallel-group design. We also develop covariate adjustment methods for crossover trials. We illustrate the performance of cross-over design and covariate adjustment using simulations based on resampling data from an HIV prevention trial.

翻译：交叉试验是一种高效的研究设计，前提是不存在延续效应。为减少生物学延续效应的影响，通常会设计洗脱期。然而，当设置洗脱期违反伦理或无法充分减弱延续效应的影响时，延续效应仍是值得关注的难题。后者常见于比较效果研究中，此时的延续效应往往非生物性，而属于行为学范畴。本文在潜在结果框架下探讨了有无延续效应时交叉设计的特性。研究发现：当延续效应存在且满足符号条件时，基础估计量会低估处理效应，这虽不会增加单侧检验的I类错误率，但会降低统计功效。由此引出了交叉设计与平行组设计之间的功效权衡问题，我们推导出了交叉设计既不导致I类错误膨胀、且功效仍优于平行组设计的适用条件。此外，我们发展了适用于交叉试验的协变量调整方法。通过基于HIV预防试验重抽样数据的模拟研究，我们展示了交叉设计与协变量调整的实际表现。