Robust Estimation of Population Attributable Fractions in the Presence of Multiple Ordered Mediators

Population Attributable Fraction (PAF) is a key epidemiological measure used to quantify the contribution of risk factors to the overall disease burden. However, when an exposure affects an outcome through multiple ordered mediators, traditional PAF estimation methods face challenges in accurately identifying the impact of each mediating pathway. These challenges arise from mediator-outcome relationships, interactions among mediators, and the presence of potential confounders. In this study, we propose new measures, termed mPAFs, to quantify the fraction of disease attributable to a specific mediation pathway. The proposed framework incorporates a multiply robust estimator that yields consistent estimates of mPAFs provided that at least two of the three types of models are correctly specified: the exposure models, mediator models, or outcome model. The asymptotic properties of the estimator are formally established, and a comprehensive simulation study is conducted to demonstrate its robustness against model misspecification. In a real-data application using TCGA lung cancer cohorts, we analyzed the effect of smoking on mortality mediated through TTK and MAD2L1. In lung adenocarcinoma, the total PAF was estimated at 4.45%, with a direct effect of 1.82% and pathway-specific contributions of -1.95% (TTK) and 0.68% (MAD2L1). In contrast, lung squamous cell carcinoma showed a higher total PAF of 10.43%, with most of the effect attributable to the direct pathway (10.22%), suggesting minimal mediation via the selected genes.