A Variational Approach to Optimal Two-Treatment Crossover Designs: Application to Carryover-Effect Models
提出一种变分方法，为重复测量模型中的双治疗p期交叉设计找到最优条件，最小化治疗差异估计量的方差，并应用于包含残留效应的模型。
Abstract A variational method is used to obtain sufficient conditions for an optimal two-treatment, p-period design, given a repeated-measures model with arbitrary within-subject covariance. The design minimizes the variance of the estimator of treatment differences over all possible allocations of N subjects to the 2 p possible treatment sequences. The method is applied to a model that includes carryover effects. When subject effects are random with equicorrelated observations, designs are optimal if they are (a) strongly balanced; (b) uniform on the rows; and (c) either uniform on the subjects p is even and greater than 2, or uniform on the first p — 1 periods if p is odd. For two periods the optimal design is AB, BA, AA, BB. The same designs are optimal when baseline measurements are obtained in each period. Baseline observations improve efficiency considerably for p = 2, only slightly for p odd, and are of no help for p even and greater than 2. A second model of errors in which a subject's response has an autoregressive covariance matrix is also considered. Key Words: Carryover balanced designRandom subject effects