Doubly robust estimation of the generalized impact fraction

The attributable fraction (AF) is commonly used in epidemiology to quantify the impact of an exposure to a disease. Recently, Sjölander and Vansteelandt (2011. Doubly robust estimation of attributable fractions. Biostatistics 12, 112-121) introduced the doubly robust (DR) estimator of the AF, which involves positing models for both the exposure and the outcome and is consistent if at least one of these models is correct. In this article, we derived a DR estimator of the generalized impact fraction (IF) with a polytomous exposure. The IF is a measure that generalizes the AF by allowing the possibility of incomplete removal of the exposure. We demonstrated the performance of the proposed estimator via a simulation study and by application to data from a large prospective cohort study conducted in Japan.