Hierarchical Second-Order Monte Carlo Simulation for Uncertainty Quantification in Incremental Lifetime Cancer Risk Assessment from PAH Inhalation Exposure

Polycyclic aromatic hydrocarbons (PAHs) are major carcinogenic pollutants in urban air, and inhalation exposure poses health risks, particularly for primary school children aged 6–14 years in school environments. Traditional deterministic models for incremental lifetime cancer risk (ILCR) assessment often fail to adequately quantify variability and epistemic uncertainty in exposure parameters. This study develops a multi-layered probabilistic framework that progresses from deterministic calculations through one-dimensional Monte Carlo and sensitivity-guided two-dimensional Monte Carlo to a hierarchical (second-order) two-dimensional Monte Carlo simulation. The hierarchical approach samples hyper-parameters of the input distributions (means, standard deviations, and modes) in the outer loop, while exposure variables are sampled in the inner loop using Latin hypercube sampling. Applied to PAH and BaPeq concentrations measured indoors and outdoors during heating and non-heating seasons, the framework yielded mean total ILCR values of 1.42 × 10−6 for children and 1.18 × 10−6 for adults. The hierarchical 2D MC produced 95% confidence intervals on the 95th percentiles of [9.17 × 10−7, 5.67 × 10−6] for children and [6.48 × 10−7, 5.57 × 10−6] for adults, with outdoor heating identified as the dominant exposure pathway. Although the air sampling campaign was conducted in 2011–2012, the data remain representative for evaluating seasonal and microenvironmental variability of PAHs in urban school settings in the region, as PAH levels are predominantly driven by persistent combustion sources. This framework provides more comprehensive uncertainty quantification for complex environmental exposure scenarios.