An equivalency iterative algorithm for cancer risk assessment of chemical mixtures with additive effects.

To better estimate cumulative cancer risks and avoid the overestimated risk from the linear extrapolation, an equivalency iterative algorithm associated with a carcinogenesis hypothesis was introduced for a mixture of chemicals with the same mode of action (MOA). A lognormal dose-response function was applied for carcinogenic chemicals. Under some circumstances, the repetitive random iterative algorithm could be transformed into the nonrepetitive one. It was also demonstrated that the equivalent value for a lognormal-based equivalency iterative algorithm with the same shape parameter was independent of the operation order. Based on the theorems of the algorithm and Plackett and Hewlett's minimum effective dose assumption, the sum of toxicity-weighted dose for a mixture of chemicals was mathematically derived. Compared to the estimation of risk by the linear extrapolation method (e.g., cancer slope factors), the equivalency iterative algorithm for lognormal functions can avoid overestimated risk significantly, which can help better estimate the cumulative cancer risk for a mixture of chemicals with the same MOA.