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On quantifying the magnitude of confounding. (English) Zbl 1437.62504
Summary: 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 [S. Greenland et al., Stat. Sci. 14, No. 1, 29–46 (1999; Zbl 1059.62506)]; 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.
##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis
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