Document Type


Journal/Book Title

Population Health Metrics

Publication Date



BioMed Central Ltd.



First Page


Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Last Page



Background: This paper discusses best practices for estimating fractions of mortality attributable to health exposures in survey data that are biased by observed confounders and unobserved endogenous selection. Extant research has shown that estimates of population attributable fractions (PAF) from the formula using the proportion of deceased that is exposed (PAFpd) can attend to confounders, whereas the formula using the proportion of the entire sample exposed (PAFpe) is biased by confounders. Research has not explored how PAFpd and PAFpe equations perform when both confounding and selection bias are present.

Methods: We review equations for calculating PAF based on either the proportion of deceased (pd) or the proportion of the entire sample (pe) that receives the exposure. We explore how estimates from each equation are affected by confounding bias and selection bias using hypothetical data and real-world survey data from the National Health Interview Survey–Linked Mortality Files, 1987–2011. We examine the association between cigarette smoking and all-cause mortality risk in the US adult population as an example.

Results: We show that both PAFpd and PAFpe calculate the true PAF in the presence of confounding bias if one uses the “weighted-sum” approach. We further show that both the PAFpd and PAFpe calculate biased PAFs in the presence of collider bias, but that the bias is more severe in the PAFpd formula.

Conclusion: We recommend that researchers use the PAFpe formula with the weighted-sum approach when estimates of the exposure-outcome relationship are biased by endogenous selection.