Decomposition of the population attributable fraction for two exposures

The population attributable fraction (AF) is frequently used to quantify disease burden attributable to exposures. AF is interpreted as the fractional reduction of disease events that would occur if exposures were eliminated. This article aims to provide a decomposition of the overall AF for two exposures into AFs for each of two exposures and AF for their interaction, using potential outcomes framework.

We provide the decomposition formula with and without confounders. We discuss an estimation method using standard regression models. We also show that these AFs without confounders can be effectively visualized.

By a numerical comparison, we show that our decomposition is different from a previous decomposition, which does not have a causal interpretation if confounding exists. We illustrate the proposed decomposition using a large prospective cohort study data.

When the primary exposure cannot be modifiable, the interventional interpretation of AF is difficult. Even then, if there exists an interaction between the exposure and another modifiable exposure, our decomposition can show what extent of the effect of the primary exposure can be eliminated by intervening on the modifiable exposure.