Dealing with time-dependent exposures and confounding when defining and estimating attributable fractions-Revisiting estimands and estimators.

The population-attributable fraction (PAF) is commonly interpreted as the proportion of events that can be ascribed to a certain exposure in a certain population. Its estimation is sensitive to common forms of time-dependent bias in the face of a time-dependent exposure. Predominant estimation approaches based on multistate modeling fail to fully eliminate such bias and, as a result, do not permit a causal interpretation, even in the absence of confounding. While recently proposed multistate modeling approaches can successfully eliminate residual time-dependent bias, and moreover succeed to adjust for time-dependent confounding by means of inverse probability of censoring weighting, inadequate application, and misinterpretation prevails in the medical literature. In this paper, we therefore revisit recent work on previously proposed PAF estimands and estimators in settings with time-dependent exposures and competing events and extend this work in several ways. First, we critically revisit the interpretation and applied terminology of these estimands. Second, we further formalize the assumptions under which a causally interpretable PAF estimand can be identified and provide analogous weighting-based representations of the identifying functionals of other proposed estimands. This representation aims to enhance the applied statistician's understanding of different sources of bias that may arise when the aim is to obtain a valid estimate of a causally interpretable PAF. To illustrate and compare these representations, we present a real-life application to observational data from the Ghent University Hospital ICUs to estimate the fraction of ICU deaths attributable to hospital-acquired infections.