Copulas and other multivariate models of personal exposures to VOC mixtures
While exposures to most pollutants occur in mixtures with other pollutants, joint distributions of pollutants have not been characterized, even for pollutants that frequently occur together. This study investigates exposures to volatile organic compounds (VOCs), and presents and evaluates innovative ways of modeling mixtures. Personal exposures to ten VOCs for 655 individuals were evaluated using a semi parametric framework that estimates probabilities of mixtures containing components greater than specified levels. Common mixtures were identified using positive matrix factorization. Copulas were tested for their ability to model inter-pollutant dependencies, focusing on the most exposed individuals. For highly correlated VOCs, Gumbel and Gaussian copulas best described the joint probability. For VOCs with low correlations, distributions could be described by the product copula, among other approaches. High concentration mixtures usually resulted from strong sources (e.g., residence with attached garage), certain behaviors (e.g., cigarette smoking), and sometimes from multiple but unrelated sources (e.g., mothballs, solvents). This is the first article to characterize exposures to VOC mixtures measured using personal monitoring and a population-based sample, and it appears to be the first to apply the copula technique, which allows accurate modeling of joint distributions with only one additional parameter beyond those needed to represent the marginal distributions. © Taylor & Francis Group, LLC.
Human and Ecological Risk Assessment
Jia, C., Batterman, S., & D'Souza, J. (2010). Copulas and other multivariate models of personal exposures to VOC mixtures. Human and Ecological Risk Assessment, 16 (4), 873-900. https://doi.org/10.1080/15435075.2010.502031