Knuiman M W, Divitini M L, Buzas J S, Fitzgerald P E
Department of Public Health, University of Western Australia, Nedlands, Australia.
Ann Epidemiol. 1998 Jan;8(1):56-63. doi: 10.1016/s1047-2797(97)00107-5.
The term "regression dilution" describes the dilution/attenuation in a regression coefficient that occurs when a single measured value of a covariate is used instead of the usual or average value over a period of time. This paper reviews the current knowledge concerning a simple method of adjusting for regression dilution in single and multiple covariate situations and illustrates the adjustment procedure.
Formulation of the regression dilution problem as a measurement error problem allows existing measurement error theory to be applied to developing methods of adjustment for regression dilution. This theory leads to a precise method of adjustment for linear regression and approximate methods for logistic and Cox proportional hazards regression. The method involves obtaining the naive estimates of coefficients by assuming that covariates are not measured with error, and then adjusting these coefficients using reliability estimates for the covariates. Methods for estimating the reliability of covariates from the reliability and main study data and a method for the calculation of standard errors and confidence intervals for adjusted coefficients are described.
An illustration involving logistic regression analysis of risk factors for death from cardiovascular disease based on cohort and reliability data from the Busselton Health Study shows that the different methods for estimating the adjustment factors give very similar adjusted estimates of coefficients, that univariate adjustment procedures may lead to inappropriate adjustments in multiple covariate situations, whether or not other covariates have intra-individual variation, and when the reliability study is moderate to large, the precision of the estimates of reliability coefficients has little impact on the standard errors of adjusted regression coefficients.
The simple method of adjusting regression coefficients for "regression dilution" that arises out of measurement error theory is applicable to many epidemiological settings and is easily implemented. The choice of method to estimate the reliability coefficient has little impact on the results. The practice of applying univariate adjustments in multiple covariate situations is not recommended.
“回归稀释”一词描述的是，当使用协变量的单个测量值而非一段时间内的常规值或平均值时，回归系数出现的稀释/衰减情况。本文回顾了关于在单协变量和多协变量情况下调整回归稀释的一种简单方法的现有知识，并说明了调整过程。
将回归稀释问题表述为测量误差问题，使得现有的测量误差理论可应用于开发回归稀释的调整方法。该理论引出了线性回归的精确调整方法以及逻辑回归和Cox比例风险回归的近似方法。该方法包括通过假设协变量无测量误差来获得系数的朴素估计值，然后使用协变量的可靠性估计值对这些系数进行调整。描述了从可靠性和主要研究数据估计协变量可靠性的方法，以及计算调整后系数的标准误差和置信区间的方法。
基于巴瑟尔顿健康研究的队列和可靠性数据，对心血管疾病死亡风险因素进行逻辑回归分析的一个示例表明，估计调整因子的不同方法给出的系数调整估计值非常相似；单变量调整程序在多协变量情况下可能导致不适当的调整，无论其他协变量是否存在个体内变异；并且当可靠性研究为中度至大型时，可靠性系数估计值的精度对调整后回归系数的标准误差影响很小。
基于测量误差理论对“回归稀释”进行回归系数调整的简单方法适用于许多流行病学场景且易于实施。估计可靠性系数的方法选择对结果影响很小。不建议在多协变量情况下应用单变量调整的做法。
