The population-attributable fraction for time-to-event data

Abstract

Background Even though the population-attributable fraction (PAF) is a well-established metric, it is often incorrectly estimated or interpreted not only in clinical application, but also in statistical research articles. The risk of bias is especially high in more complex time-to-event data settings. Methods We explain how the PAF can be defined, identified and estimated in time-to-event settings with competing risks and time-dependent exposures. By using multi-state methodology and inverse probability weighting, we demonstrate how to reduce or completely avoid severe types of biases including competing risks bias, immortal time bias and confounding due to both baseline and time-varying patient characteristics. Results The method is exemplarily applied to a real data set. Moreover, we estimate the number of deaths that were attributable to ventilator-associated pneumonia in France in the year 2016. The example demonstrates how, under certain simplifying assumptions, PAF estimates can be extrapolated to a target population of interest. Conclusions Defining and estimating the PAF in advanced time-to-event settings within a framework that unifies causal and multi-state modelling enables to tackle common sources of bias and allows straightforward implementation with standard software packages.

Dealing with time‐dependent exposures and confounding when defining and estimating attributable fractions—Revisiting estimands and estimators

“…Third, following recent work by Young et al, 13 we point out that alternative, algebraically equivalent representations of the identifying g-functional for the counterfactual risk may not only help to sharpen interpretational intuition, but also give rise to various estimators, including both previously proposed 6,23 and novel estimators. In addition, these alternative representations provide a theoretical basis for understanding why multistate modeling methodology requires reweighting the analytical sample to account for time-dependent confounding, in line with an estimation approach recently proposed by von Cube et al 24…”

“…The identifying g-functional for the counterfactual risk 𝜑 K gives rise to a class of IPCW estimators, 13 including certain estimators proposed in the literature. 6,23,24 Importantly, while prevailing multistate modeling estimation approaches 1,47,30 target estimand (1), multistate modeling methodology can also be applied to target estimand (2). However, to reduce bias due to time-dependent confounding, multistate modeling approaches require appropriately reweighting the time-dependent risk sets.…”

“…Even under correct specification of $$$ p\left(k,{\overline{L}}_{k-1};\theta \right) $$$, due to sampling variability, $$$ {\hat{\varphi}}_K $$$ is not upper bounded by 1. To accommodate for this, sample bounded IPC weighted estimators 42 can be used, such as the one proposed by Bekaert, Mertens and Vansteelandt 6 (see Appendix I.2 in Data S2) or the following IPC weighted Aalen‐Johansen estimator 13 recently proposed by von Cube et al 24 in the context of PAF estimation …”

“…Moreover, because this estimator relies on a representation of the identifying g‐functional in terms of event‐specific hazards, ie. the building blocks of competing risks and multistate models, one can resort to multistate modeling methodology for estimation, upon appropriately weighting the time‐dependent risk sets 24 …”

The potential impact fraction of population weight reduction scenarios on non-communicable diseases in Belgium: Application of the g-computation approach

“…A DAG is a graphical representation that illustrates the hypothesized causal structure of the processes under study (23,26). Compared to standard analytic techniques, the g-computation approach offers many additional bene ts such as the ability to handle time-varying confounders (27) or the impact assessment of joint interventions, when interventions involve multiple factors. The method also enables modelling the impact of dynamic interventions, where different subjects can receive different levels of the exposure under study (28).…”