Multivariate left-censored Bayesian modeling for predicting exposure using multiple chemical predictors

Environmental health exposures to airborne chemicals often originate from chemical mixtures. Environmental health professionals may be interested in assessing exposure to one or more of the chemicals in these mixtures, but often, exposure measurement data are not available, either because measurements were not collected/assessed for all exposure scenarios of interest or because some of the measurements were below the analytical methods' limits of detection (i.e., censored). In some cases, based on chemical laws, two or more components may have linear relationships with one another, whether in single or multiple mixtures. Although bivariate analyses can be used if the correlation is high, correlations are often low. To serve this need, this paper develops a multivariate framework for assessing exposure using relationships of the chemicals present in these mixtures. This framework accounts for censored measurements in all chemicals, allowing us to develop unbiased exposure estimates. We assessed our model's performance against simpler models at a variety of censoring levels and assessed our model's 95% coverage. We applied our model to assess vapor exposure from measurements of three chemicals in crude oil taken on the Ocean Intervention III during the Deepwater Horizon oil spill response and cleanup.