On the Relations Between Excess Fraction, Attributable Fraction, and Etiologic Fraction

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Abstract
It has been noted that there is ambiguity in the expression “attributable fraction,” and epidemiologic literature has drawn a distinction between “excess fraction” and “etiologic fraction.” These quantities do not necessarily approximate one another, and the etiologic fraction is not generally estimable without strong biologic assumptions. In previous studies, researchers have explained the relations between excess and etiologic fractions in the potential-outcome framework, and few authors have explained the relations between these concepts by showing the correspondence between the potential-outcome model and the sufficient-cause model. In this article, the authors thoroughly clarify the conceptual relations between excess, attributable, and etiologic fractions by explicating the correspondence between these 2 models. In so doing, the authors take into account the potential completion time of each sufficient cause, which contributes to further insight to clarify the 2 types of etiologic fraction, i.e., accelerating etiologic proportion and total etiologic proportion. These 2 measures cannot be distinguished in epidemiologic data, and the differences might be subtle. However, they are closely related to a very fundamental issue of causal inference, that is, how researchers define etiology. Further, the authors clarify the relation between 3 distinct assumptions—positive monotonicity, no preventive action (or sufficient-cause positive monotonicity), and no preventive sequence.