TY - JOUR

T1 - A New Method for Dealing with Measurement Error in Explanatory Variables of Regression Models

AU - Freedman, Laurence S.

AU - Fainberg, Vitaly

AU - Kipnis, Victor

AU - Midthune, Douglas

AU - Carroll, Raymond J.

PY - 2004/3

Y1 - 2004/3

N2 - 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.

AB - 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.

KW - Case-control study

KW - Classification trees

KW - Cohort study

KW - Errors-in-variables

KW - Linear discriminant analysis

KW - Logistic regression

KW - Measurement error

KW - Regression calibration

UR - http://www.scopus.com/inward/record.url?scp=1642312761&partnerID=8YFLogxK

U2 - 10.1111/j.0006-341x.2004.00164.x

DO - 10.1111/j.0006-341x.2004.00164.x

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C2 - 15032787

AN - SCOPUS:1642312761

SN - 0006-341X

VL - 60

SP - 172

EP - 181

JO - Biometrics

JF - Biometrics

IS - 1

ER -