Correlated errors in biased surrogates: study designs and methods for measurement error correction

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Abstract
A measurement error model proposed previously allows for correlations between subject‐specific biases and between random within‐subject errors in the surrogates obtained from two modes of measurement. However, most of these model parameters are not identifiable from the standard validation study design, including, importantly, the attenuation factor needed to correct for bias in relative risk estimates due to measurement error. We propose validation study designs that permit estimation and inference for the attenuation factor and other parameters of interest when these correlations are present. We use an estimating equations framework to develop semi‐parametric estimators for these parameters, exploiting instrumental variables techniques. The methods are illustrated through application to data from the Nurses' Health Study and Health Professionals' Follow‐up Study, and comparisons are made to more restrictive models. Copyright © 2005 John Wiley & Sons, Ltd.