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 washout period is often designed. However, the carry-over effect remains an outstanding concern when a washout 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 evaluate the performance of cross-over design and covariate adjustment using data from the MTN-034/REACH study.

翻译：交叉试验是一种在无延滞效应时高效的试验设计。为减少生物学延滞效应的影响，通常设计洗脱期。然而，当洗脱期不符合伦理或无法充分减弱延滞效应影响时，延滞效应仍是突出难题。后者常见于比较效果研究中，此时的延滞效应通常非生物学性质，而是行为性的。本文在潜在结果框架下，研究存在与不存在延滞效应时的交叉设计。我们发现，当延滞效应存在且满足符号条件时，基本估计量会低估处理效应，这不仅不会膨胀单侧检验的I类错误，反而会降低检验功效。这导致交叉设计与平行组设计之间存在功效权衡，我们推导出交叉设计既不导致I类错误膨胀、同时仍比平行组设计更有效的条件。此外，我们还开发了适用于交叉试验的协变量调整方法。通过MTN-034/REACH研究数据，评估了交叉设计与协变量调整的性能。