Berglund Lars, Garmo Hans, Lindbäck Johan, Zethelius Björn
Department of Public Health/Geriatrics, Uppsala University, Uppsala, Sweden.
Stat Med. 2007 May 10;26(10):2246-57. doi: 10.1002/sim.2698.
The least squares estimator of the slope in a simple linear regression model will be biased towards zero when the predictor is measured with random error, i.e. intra-individual variation or technical measurement error. A correction factor can be estimated from a reliability study where one replicate is available on a subset of subjects from the main study. Previous work in this field has assumed that the reliability study constitutes a random subsample from the main study. We propose that a more efficient design is to collect replicates for subjects with extreme values on their first measurement. A variance formula for this estimator of the correction factor is presented. The variance for the corrected estimated regression coefficient for the extreme selection technique is also derived and compared with random subsampling. Results show that variances for corrected regression coefficients can be markedly reduced with extreme selection. The variance gain can be estimated from the main study data. The results are illustrated using Monte Carlo simulations and an application on the relation between insulin sensitivity and fasting insulin using data from the population-based ULSAM study. In conclusion, an investigator faced with the planning of a reliability study may wish to consider an extreme selection design in order to improve precision at a given number of subjects or alternatively decrease the number of subjects at a given precision.
在简单线性回归模型中，当预测变量存在随机误差（即个体内部变异或技术测量误差）时，斜率的最小二乘估计值会向零偏倚。校正因子可通过可靠性研究来估计，在主要研究的一部分受试者中，有一个重复测量值可供使用。该领域以前的研究假设可靠性研究是主要研究的随机子样本。我们提出一种更有效的设计方法，即对首次测量值处于极端值的受试者收集重复测量数据。给出了该校正因子估计值的方差公式。还推导了极端选择技术下校正估计回归系数的方差，并与随机子抽样进行了比较。结果表明，采用极端选择法可显著降低校正回归系数的方差。方差增益可根据主要研究数据进行估计。通过蒙特卡罗模拟以及利用基于人群的ULSAM研究数据对胰岛素敏感性与空腹胰岛素之间关系的应用，对结果进行了说明。总之，面临可靠性研究规划的研究者可能希望考虑采用极端选择设计，以便在给定的受试者数量下提高精度，或者在给定精度下减少受试者数量。
