Winkens Bjorn, Schouten Hubert J A, van Breukelen Gerard J P, Berger Martijn P F
Department of Methodology and Statistics, University of Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands.
Stat Med. 2005 Dec 30;24(24):3743-56. doi: 10.1002/sim.2385.
In repeated measures studies, equidistant time-points do not always yield efficient treatment effect estimators. In the present paper, the optimal allocation of time-points is calculated for a small number of repeated measures, different covariance structures and linearly divergent treatment effects. The gain in efficiency of the treatment effect estimator by using optimally allocated time-points instead of equidistant time-points or by adding optimally spaced measures (at the expense of patients) is then computed. The assumed covariance structure is crucial for the results. For a compound symmetric covariance structure, a large gain in efficiency is obtained by adding repeated measures at the end of the study. For a first-order auto-regressive covariance structure, highly efficient treatment effect estimators are obtained with only two repeated measures, i.e. at the start and at the end of the study. For a first-order auto-regressive covariance structure including measurement error, the gain in efficiency by adding optimally spaced measures depends on the covariance parameter values. The gain in efficiency is similar with or without a random intercept. For a fixed study budget, the commonly used design with more than two equally spaced measures was never optimal for the linear cost function and covariance structures that were used. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive covariance structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. The numerical results are illustrated by two examples.
在重复测量研究中，等距时间点并不总是能产生有效的治疗效果估计量。在本文中，针对少量重复测量、不同协方差结构和线性发散的治疗效果，计算了时间点的最优分配。然后计算通过使用最优分配的时间点而非等距时间点，或者通过添加最优间隔的测量（以患者为代价），治疗效果估计量在效率上的提升。假定的协方差结构对结果至关重要。对于复合对称协方差结构，在研究结束时添加重复测量可大幅提高效率。对于一阶自回归协方差结构，仅通过在研究开始和结束时进行两次重复测量就能获得高效的治疗效果估计量。对于包含测量误差的一阶自回归协方差结构，添加最优间隔测量所带来的效率提升取决于协方差参数值。有无随机截距时效率提升情况相似。对于固定的研究预算，对于所使用的线性成本函数和协方差结构，常用的具有两个以上等距测量的设计绝非最优。如果协方差结构未知，基于包含测量误差的一阶自回归协方差结构的最优设计在抵御协方差结构误设方面更具稳健性。通过两个例子说明了数值结果。
