## Abstract

Background: In 1995, Eide and Gefeller introduced the concepts of sequential and average attributable fractions as methods to partition the risk of disease among differing exposures. In particular, sequential attributable fractions are interpreted in terms of an incremental reduction in disease prevalence associated with removing a particular risk factor from the population, having removed other risk factors. Clearly, both concepts are causal entities, but are not usually estimated within a causal inference framework.

Methods: We propose causal definitions of sequential and average attributable fractions using the potential outcomes framework. To estimate these quantities in practice, we model exposure-exposure and exposure-disease interrelationships using a causal Bayesian network, assuming no unmeasured latent confounders. This allows us to model not only the direct impact of removing a risk factor on disease, but also the indirect impact through the effect on the prevalence of causally downstream risk factors that are typically ignored when calculating sequential and average attributable fractions. The procedure for calculating sequential attributable fractions involves repeated applications of Pearl’s do-operator over a fitted Bayesian network, and simulation from the resulting joint probability distributions.

Results: The methods are applied to the INTERSTROKE study, which was designed to quantify disease burden attributable to the major risk factors for stroke. The resulting sequential and average attributable fractions are compared with results from a prior estimation approach which uses a single logistic model and which does not properly account for differing causal pathways.

Conclusions: In contrast to estimation using a single regression model, the proposed approaches allow consistent estimation of sequential, joint and average attributable fractions under general causal structures.

Methods: We propose causal definitions of sequential and average attributable fractions using the potential outcomes framework. To estimate these quantities in practice, we model exposure-exposure and exposure-disease interrelationships using a causal Bayesian network, assuming no unmeasured latent confounders. This allows us to model not only the direct impact of removing a risk factor on disease, but also the indirect impact through the effect on the prevalence of causally downstream risk factors that are typically ignored when calculating sequential and average attributable fractions. The procedure for calculating sequential attributable fractions involves repeated applications of Pearl’s do-operator over a fitted Bayesian network, and simulation from the resulting joint probability distributions.

Results: The methods are applied to the INTERSTROKE study, which was designed to quantify disease burden attributable to the major risk factors for stroke. The resulting sequential and average attributable fractions are compared with results from a prior estimation approach which uses a single logistic model and which does not properly account for differing causal pathways.

Conclusions: In contrast to estimation using a single regression model, the proposed approaches allow consistent estimation of sequential, joint and average attributable fractions under general causal structures.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Archives of Public Health |

Volume | 78 |

Issue number | 67 |

DOIs | |

Publication status | Published - 21 Jul 2020 |

## Keywords

- attributable fraction
- casual DAG
- do-operator
- Bayesian network
- casual inference