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Biostatistics. 2010 Jul;11(3):572-82. doi: 10.1093/biostatistics/kxq007. Epub 2010 Mar 4.

On quantifying the magnitude of confounding.

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  • 1Vaccine 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.


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.

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