Winkens Bjorn, Schouten Hubert J A, van Breukelen Gerard J P, Berger Martijn P F
Department of Methodology and Statistics, University of Maastricht, Maastricht, The Netherlands.
Stat Methods Med Res. 2007 Dec;16(6):523-37. doi: 10.1177/0962280206071847. Epub 2007 Aug 14.
The effect of adding intermediate measures on the efficiency of treatment effect estimation is considered for a second-order polynomial treatment effect, equidistant time-points, different covariance structures and two optimality criteria, assuming either a fixed sample size or a fixed budget. The benefit of adding intermediate measures (at the expense of subjects) depends strongly on the assumed covariance structure and is hardly affected by the two used optimality criteria (Ds or c). For a fixed sample size, the increase in efficiency by adding intermediate measures is large for a compound symmetric structure and small for a first-order auto-regressive structure. For a first-order auto-regressive structure with measurement error, the results depend on the covariance parameter values. For a fixed budget and linear cost function, the design with only three measures per subject is often highly efficient. If the structure resembles compound symmetry and the cost per subject is eight or more times larger than the cost per repeated measure, however, more than three measures are required to obtain highly efficient treatment effect estimators. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. Given a design with three repeated measures and a second-order polynomial treatment effect, equidistant time-points are either optimal (Ds-) or highly efficient (c-optimality criterion). The results are illustrated by a practical example.
对于二阶多项式治疗效果、等距时间点、不同协方差结构以及两个最优性标准，在假设固定样本量或固定预算的情况下，考虑添加中间测量对治疗效果估计效率的影响。添加中间测量（以牺牲受试者数量为代价）的益处很大程度上取决于假设的协方差结构，并且几乎不受所使用的两个最优性标准（Ds 或 c）的影响。对于固定样本量，对于复合对称结构，添加中间测量带来的效率提升很大，而对于一阶自回归结构则很小。对于存在测量误差的一阶自回归结构，结果取决于协方差参数值。对于固定预算和线性成本函数，每个受试者仅进行三次测量的设计通常效率很高。然而，如果结构类似于复合对称，并且每个受试者的成本比每次重复测量的成本大八倍或更多倍，则需要进行三次以上的测量才能获得高效的治疗效果估计量。如果协方差结构未知，就协方差结构错误指定的稳健性而言，基于存在测量误差的一阶自回归结构的最优设计更可取。对于具有三次重复测量和二阶多项式治疗效果的设计，等距时间点要么是最优的（Ds -），要么是高效的（c - 最优性标准）。通过一个实际例子对结果进行了说明。
