On quantifying the magnitude of confounding

In studying the association between an exposure and an 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 recognized as flawed due to a phenomenon called non-collapsibility. With a non-linear measure of association, there can be a difference between the adjusted and unadjusted associations even in the absence of confounding.

We explore a new approach to quantifying confounding which separates confounding bias from non-collapsibility bias. The relative performances of the two approaches to quantifying confounding are assessed in simulations and in a data example, where we quantify confounding due to age in the smoking-lung cancer association. We conclude that the simple approach to quantifying confounding is adequate in most settings.