  The estimation of the potential impact fraction (including the population
attributable fraction) with continuous exposure data frequently relies on
strong distributional assumptions. However, these assumptions are often
violated if the underlying exposure distribution is unknown or if the same
distribution is assumed across time or space. Nonparametric methods to estimate
the potential impact fraction are available for cohort data, but no
alternatives exist for cross-sectional data. In this article, we discuss the
impact of distributional assumptions in the estimation of the population impact
fraction, showing that under an infinite set of possibilities, distributional
violations lead to biased estimates. We propose nonparametric methods to
estimate the potential impact fraction for aggregated (mean and standard
deviation) or individual data (e.g. observations from a cross-sectional
population survey), and develop simulation scenarios to compare their
performance against standard parametric procedures. We illustrate our
methodology on an application of sugar-sweetened beverage consumption on
incidence of type 2 diabetes. We also present an R package pifpaf to implement
these methods.
