As has been noted elsewhere, confusion abounds regarding the definition and interpretation of population attributable fractions (PAF) in epidemiology [1]. For instance, in their seminal paper where Eide and Gefeller introduce average and sequential attributable fractions [2], they define the population attributable fraction as ‘the proportion by which a disease prevalence (or incidence) is reduced if the whole population is hypothesized to attain the same risk of disease as the individuals within the lowest exposure category.’ The problem with such a definition is it is non-causal. That is, if individuals in the lowest exposure category do have a lower disease risk, it might not be because of any health benefit attributable to the exposure, but because of spurious correlations or even reverse causation. Taking this kind of logic to the extreme, one could make quite non-sensible conclusions regarding say the cot-death risk attributable to Swiss cheese consumption, or the risk of heart disease attributable to doctor visits. Of course, Eide and Gefeller clearly understand this, and later in the paper mention that ‘if there exists a direct cause-effect relationship between the exposure and the disease, the attributable fraction may be interpreted as the proportion of the diseased that would have been prevented if the exposure was totally eliminated from it’ (note that the use of the word eliminate is convenient but slightly misleading as it refers to a hypothetical population where the risk factor of interest was always absent rather than eliminated at a point in time). They then define this second quantity as the ‘etiologic fraction’, introduced by Miettinen [3]. Incidentally, Robins and Greenland [4] discuss a subtly different metric, more directly interpretable as the proportion of disease caused by a risk factor which they also call an etiologic fraction. More recently, the epidemiological community seems to have settled on Miettinen’s definition ([5, 6]). This seems sensible to us as it does have a direct causal implication (that is, it will only be non-zero if the exposure has some causal effect on disease), and can be estimated in real data, provided we can adequately adjust for confounding [7].
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