Rosner B, Willett W C
Channing Laboratory, Department of Preventive Medicine, Harvard Medical School, Boston, MA.
Am J Epidemiol. 1988 Feb;127(2):377-86. doi: 10.1093/oxfordjournals.aje.a114811.
It is well known that random measurement error can attenuate the correlation coefficient between two variables. One possible solution to this problem is to estimate the correlation coefficient based on an average of a large number of replicates for each individual. As an alternative, several authors have proposed an unattenuated (or corrected) correlation coefficient which is an estimate of the true correlation between two variables after removing the effect of random measurement error. In this paper, the authors obtain an estimate of the standard error for the corrected correlation coefficient and an associated 100% x (1-alpha) confidence interval. The standard error takes into account the variability of the observed correlation coefficient as well as the estimated intraclass correlation coefficient between replicates for one or both variables. The standard error is useful in hypothesis testing for comparisons of correlation coefficients based on data with different degrees of random error. In addition, the standard error can be used to evaluate the relative efficiency of different study designs. Specifically, an investigator often has the option of obtaining either a few replicates on a large number of individuals, or many replicates on a small number of individuals. If one establishes the criterion of minimizing the standard error of the corrected coefficient while fixing the total number of measurements obtained, in almost all instances it is optimal to obtain no more than five replicates per individual. If the intraclass correlation is greater than or equal to 0.5, it is usually optimal to obtain no more than two replicates per individual.
众所周知，随机测量误差会削弱两个变量之间的相关系数。解决这个问题的一种可能方法是基于每个个体大量重复测量的平均值来估计相关系数。作为一种替代方法，几位作者提出了一种无衰减（或校正）的相关系数，它是去除随机测量误差影响后两个变量之间真实相关性的估计值。在本文中，作者获得了校正相关系数的标准误差估计值以及相关的100%×(1 - α)置信区间。该标准误差考虑了观察到的相关系数的变异性以及一个或两个变量重复测量之间估计的组内相关系数。该标准误差在基于具有不同程度随机误差的数据进行相关系数比较的假设检验中很有用。此外，该标准误差可用于评估不同研究设计的相对效率。具体而言，研究者通常可以选择对大量个体进行少量重复测量，或者对少量个体进行大量重复测量。如果在固定获得的测量总数的同时，以最小化校正系数的标准误差为标准，那么在几乎所有情况下，每个个体获得不超过五次重复测量是最优的。如果组内相关系数大于或等于0.5，通常每个个体获得不超过两次重复测量是最优的。
