Under the three-treatment three-period crossover design with simple carry-over effects, we derive the least-squares estimators for period effects, treatment effects and carry-over effects, as well as their covariance matrix in closed and explicit expressions. Using Monte Carlo simulation, we compare the test procedure adjusting carry-over with that ignoring carry-over with respect to Type I error and power. We further compare interval estimators adjusting carry-over with those ignoring carry-over with respect to the coverage probability and the average length. When the variation of responses within patients is small, the test procedure and interval estimators ignoring carry-over can lose accuracy in the presence of carry-over effects. When the variation of responses within patients is large, this loss of accuracy may become small or even minimal. We note that the loss of efficiency due to the adjustment of carry-over under the simple carry-over three-period crossover design is moderate, and is much less than that found for a two-period crossover design. We use the double-blind three-period crossover trial comparing formoterol solution aerosol and salbutamol suspension aerosol with a placebo for patients suffering from exercise-induced asthma on the forced expiratory volume in one second (FEV1) to illustrate the use of test procedures and interval estimators discussed here.

中文翻译：

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简单结转三期模型下三种处理比较试验和估计的注意事项。

在具有简单结转效应的三处理三期交叉设计下，我们推导出周期效应、处理效应和结转效应的最小二乘估计量，以及它们在封闭表达式和显式表达式中的协方差矩阵。使用 Monte Carlo 模拟，我们将调整结转的测试程序与忽略 I 类错误和功效的结转的测试程序进行了比较。我们进一步比较了调整结转的区间估计与忽略覆盖概率和平均长度的结转。当患者体内反应的变化很小时，忽略结转的测试程序和间隔估计器可能会在存在结转效应的情况下失去准确性。当患者内部的反应差异很大时，这种准确性损失可能会变小甚至最小。我们注意到，在简单结转三周期交叉设计下由于结转调整而导致的效率损失是适度的，并且远小于两周期交叉设计所发现的效率损失。我们使用双盲三期交叉试验比较福莫特罗溶液气雾剂和沙丁胺醇混悬气雾剂与安慰剂对患有运动性哮喘患者的一秒用力呼气容积 (FEV1) 的影响，以说明测试程序和间隔时间的使用这里讨论的估算器。