A statistical model for measurement error that incorporates variation over time in the target measure, with application to nutritional epidemiology

Most statistical methods that adjust analyses for measurement error assume that the target exposure T is a fixed quantity for each individual. However, in many applications, the value of T for an individual varies with time. We develop a model that accounts for such variation, describing the model within the framework of a meta-analysis of validation studies of dietary self-report instruments, where the reference instruments are biomarkers. We demonstrate that in this application, the estimates of the attenuation factor and correlation with true intake, key parameters quantifying the accuracy of the self-report instrument, are sometimes substantially modified under the time-varying exposure model compared with estimates obtained under a traditional fixed-exposure model. We conclude that accounting for the time element in measurement error problems is potentially important.