I thank Dr. Walter for his letter (1) and his observations on an invited commentary (2) that I coauthored with the late Sholom Wacholder (3). Dr. Wacholder and I wrote, “Walter showed that for a rare outcome, the sum of the PAFs from removing each exposure separately equals the PAF from removing both exposures under the additive model…” (2, p. 1154). Walter correctly points out that, contrary to what can be inferred from this sentence in our commentary, the rare disease assumption is not necessary for the population attributable fraction (PAF)—also referred to as population attributable risk—for the combined effects of 2 risk factors to be equal to the sum of the PAFs of each risk factor separately (1). The assumptions under which the PAF for the joint effects of 2 exposures is equal to the sum of the PAFs of each exposure separately are explained in detail in Walter's seminal paper in the Journal (4).
Walter mentions that disease rarity may be invoked in practical situations in which additivity is “empirically untenable” (as he also nicely describes in his letter) if it predicts PAFs greater than 100% in persons exposed to both risk factors (1). In our commentary (2), we demonstrate this by giving the example of phenylketonuria, a disease which is clinical manifested only in those individuals who have mutations in the phenylalanine hydroxylase gene (PAH) and are exposed to phenylalanine in the diet—that is, both conditions have to be met in order for the phenotype to be expressed. Each risk factor alone does not increase risk: Persons with the mutations do not manifest the disease if no phenylalanine is present in their diet, while persons whose diets include phenylalanine do not express the phenotype if their PAH gene is not mutated. The PAF for each disease determinant alone is 100%, but elimination of both determinants in the doubly exposed will not reduce disease risk by more than 100%.
I thank Walter once again for pointing out to us the confusing statement in our commentary and for the opportunity to clarify this.
Acknowledgments
Conflict of interest: none declared.
References
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