Modelling beyond additive risks: A framework for estimating the cascading burden of environmental exposure

Standard models for assessing the acute health effects of environmental exposures assume that risks from daily exposures are additive, ignoring “cascading effects” where prior events modify an individual's vulnerability. Here, we introduce and validate the Interactive Distributed Lag Model (iDLM), which quantifies these dynamics by incorporating interaction terms between exposures at different lags. Simulation studies confirm that traditional models are biased when cascading effects are present, whereas the iDLM accurately recovers the true risk structure. We applied this model to a nationwide U.S. dataset to analyze the mortality risks of short-term exposure to PM 2.5 and O 3 . Consistent with the standard models, the iDLM shows that short-term exposure to PM 2.5 or O 3 is significantly associated with increased risk of all-cause mortality. For each 10-μg/m 3 increment in PM 2.5 and 10-ppb increase in O 3 on the day of exposure, the risk of all-cause mortality increased by 0.26% (95% confidence interval [CI]: 0.12, 0.40) or 0.18% (95% CI: 0.11, 0.24), respectively. We find that PM 2.5 exhibits a strong, synergistic amplification effect, while the cascading effects of O 3 are weaker. Critically, we demonstrate that for both pollutants, a substantial component of the mortality burden appears to be driven by cascading interactions, which are largely overlooked by traditional models. These findings fundamentally reframe the understanding of air pollution's public health impact, revealing that the history-dependent dynamics of vulnerability, not just independent daily insults, are a crucial mechanism of harm.