A new method for dealing with measurement error in explanatory variables of regression models
A new method for dealing with measurement error in explanatory variables of regression models
复制标题
DOI：
10.1111/j.0006-341x.2004.00164.x
复制
发表时间：
2004-03-01
期刊：
影响因子：
1.9
通讯作者：
Carroll, RJ
中科院分区：
文献类型：
--
作者：
Freedman, LS;Fainberg, V;Carroll, RJ
本文介绍了一种新的修正回归模型中协变量测量误差的方法--矩重构法。其中心思想类似于回归校准，因为测量误差的协变量值被“调整”值取代。在回归校准中，调整值是以测量值为条件的真值的期望值。在矩重构中，调整值是以结果变量为条件的真值的方差保持经验贝叶斯估计。因此，调整后的值具有与未观察到的“真实”协变量值相同的前两个矩和与结果变量相同的协方差。我们表明，矩重建是等效的回归校准的情况下，线性回归，但导致不同的结果为逻辑回归。对于病例对照研究，logistic回归和协变量在病例和对照组内呈正态分布，我们表明回归系数的估计值是一致的。在模拟中，我们证明了logistic回归，矩重建进行更少的偏差比回归校准，并为病例对照研究是上级的均方误差的标准回归校准方法。最后，我们给出了一个例子，使用矩重建线性判别分析和一个非标准的问题，我们希望调整分类树的测量误差的解释变量。
We introduce a new method, moment reconstruction, of correcting for measurement error in covariates in regression models. The central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by "adjusted" values. In regression calibration the adjusted value is the expectation of the true value conditional on the measured value. In moment reconstruction the adjusted value is the variance-preserving empirical Bayes estimate of the true value conditional on the outcome variable. The adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved "true" covariate values. We show that moment reconstruction is equivalent to regression calibration in the case of linear regression, but leads to different results for logistic regression. For case-control studies with logistic regression and covariates that are normally distributed within cases and controls, we show that the resulting estimates of the regression coefficients are consistent. In simulations we demonstrate that for logistic regression, moment reconstruction carries less bias than regression calibration, and for case-control studies is superior in mean-square error to the standard regression calibration approach. Finally, we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables.