Analysis of case‐control data with covariate measurement error: Application to diet and colon cancer

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Abstract
We propose a method for estimating odds ratios from case‐control data in which covariates are subject to measurement error. The measurement error may contain both a random component and a systematic difference between cases and controls (recall bias). A multivariate normal discriminant analysis model is assumed. If the distribution of measurement error is known, then a simple correction to naive (biased) estimates of odds ratios from logistic regression of disease on fallible measurements of covariates removes bias. The same correction yields confidence intervals and significance tests. We apply the proposed methods to data from a case‐control study of colon cancer and diet.