title: On quantifying the magnitude of confounding.
abstract: When estimating the association between an exposure and outcome, a simple approach to quantifying the amount of confounding by a factor, Z, is to compare estimates of the exposure-outcome association with and without adjustment for Z. This approach is widely believed to be problematic due to the nonlinearity of some exposure-effect measures. When the expected value of the outcome is modeled as a nonlinear function of the exposure, the adjusted and unadjusted exposure effects can differ even in the absence of confounding (Greenland , Robins, and Pearl, 1999); we call this the nonlinearity effect. In this paper, we propose a corrected measure of confounding that does not include the nonlinearity effect. The performances of the simple and corrected estimates of confounding are assessed in simulations and illustrated using a study of risk factors for low birth-weight infants. We conclude that the simple estimate of confounding is adequate or even preferred in settings where the nonlinearity effect is very small. In settings with a sizable nonlinearity effect, the corrected estimate of confounding has improved performance.
authors.affiliation: Vaccine and Infectious Disease Institute and Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North M2-C200, Seattle, WA 98109, USA. hjanes@scharp.org
authors.forename: Holly
authors.initials: H
authors.lastname: Janes
authors.forename: Francesca
authors.initials: F
authors.lastname: Dominici
authors.forename: Scott
authors.initials: S
authors.lastname: Zeger
mesh_terms: D015331:Cohort Studies; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D007230:Infant, Low Birth Weight; D007231:Infant, Newborn; D008404:Massachusetts; D015233:Models, Statistical; D016017:Odds Ratio; D011247:Pregnancy; D012907:Smoking / Q000009:adverse effects; D014599:Uterus / Q000503:physiopathology