Results on differential and dependent measurement error of the exposure and the outcome using signed directed acyclic graphs.

Measurement error in both the exposure and the outcome is a common problem in epidemiologic studies. Measurement errors in the exposure and the outcome are said to be independent of each other if the measured exposure and the measured outcome are statistically independent conditional on the true exposure and true outcome (and dependent otherwise). Measurement error is said to be nondifferential if measurement of the exposure does not depend on the true outcome conditional on the true exposure and vice versa; otherwise it is said to be differential. Few results on differential and dependent measurement error are available in the literature. Here the authors use formal rules governing associations on signed directed acyclic graphs (DAGs) to draw conclusions about the presence and sign of causal effects under differential and dependent measurement error. The authors apply these rules to 4 forms of measurement error: independent nondifferential, dependent nondifferential, independent differential, and dependent differential. For a binary exposure and outcome, the authors generalize Weinberg et al.'s (Am J Epidemiol. 1994;140(6):565-571) result for nondifferential measurement error on preserving the direction of a trend to settings which also allow measurement error in the outcome and to cases involving dependent and/or differential error.