Model averaging methods for the evaluation of dose-response model uncertainty when assessing the suitability of studies for estimating risk

This paper describes the use of multiple models and model averaging for considering dose–response uncertainties when extrapolating low-dose risk from studies of populations with high levels of exposure. The model averaging approach we applied builds upon innovative methods developed by the U.S. Food and Drug Administration (FDA), principally through the relaxing of model constraints. The relaxing of model constraints allowed us to evaluate model uncertainty using a broader set of model forms and, within the context of model averaging, did not result in the extreme supralinearity that is the primary concern associated with the application of individual unconstrained models. A study of the relationship between inorganic arsenic exposure to a Taiwanese population and potential carcinogenic effects is used to illustrate the approach. We adjusted the reported number of cases from two published prospective cohort studies of bladder and lung cancer in a Taiwanese population to account for potential covariates and less-than-lifetime exposure (for estimating effects on lifetime cancer incidence), used bootstrap methods to estimate the uncertainty surrounding the µg/kg-day inorganic arsenic dose from drinking water and dietary intakes, and fit multiple models weighted by Bayesian Information Criterion to the adjusted incidence and dose data to generate dose-specific mean, 2.5th and 97.5th percentile risk estimates. Widely divergent results from adequate model fits for a broad set of constrained and unconstrained models applied individually and in a model averaging framework suggest that substantial model uncertainty exists in risk extrapolation from estimated doses in the Taiwanese studies to lower doses more relevant to countries like the U.S. that have proportionally lower arsenic intake levels.