Defining the population attributable fraction for infectious diseases.

Background: The population attributable fraction (PAF) is used to quantify the contribution of a risk group to disease burden. For infectious diseases, high-risk individuals may increase disease risk for the wider population in addition to themselves; therefore methods are required to estimate the PAF for infectious diseases.
Methods: A mathematical model of disease transmission in a population with a high-risk group was used to compare existing approaches for calculating the PAF. We quantify when existing methods are consistent and when estimates diverge. We introduce a new method, based on the basic reproduction number, for calculating the PAF, which bridges the gap between existing methods and addresses shortcomings. We illustrate the methods with two examples of the contribution of badgers to bovine tuberculosis in cattle and the role of commercial sex in an HIV epidemic.
Results: We demonstrate that current methods result in irreconcilable PAF estimates, depending on how chains of transmission are categorized. Using two novel simple formulae for emerging and endemic diseases, we demonstrate that the largest differences occur when transmission in the general population is not self-sustaining. Crucially, some existing methods are not able to discriminate between multiple risk groups. We show that compared with traditional estimates, assortative mixing leads to a decreased PAF, whereas disassortative mixing increases PAF. Conclusions: Recent methods for calculating the population attributable fraction (PAF) are not consistent with traditional approaches. Policy makers and users of PAF statistics should be aware of these differences. Our approach offers a straightforward and parsimonious method for calculating the PAF for infectious diseases.