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Background: The relative contribution of environmental contaminants is an important, and frequently unanswered, question in human or ecological risk assessments. This interpretation of relative importance allows determination of the overall effect of a set of variables relative to other variables on an adverse health outcome. There are no underlying assumptions of independence of variables. The tool developed and used here is specifically designed for studying the effects of mixtures of chemicals on a particular function of the human body. Methods: We apply the approach to estimate the contributions of total exposure to six PFAS (perfluorodecanoic acid, perfluorohexane sulfonic acid, 2-(N-methyl-PFOSA) acetate, perfluorononanoic acid, perfluoroundecanoic acid and perfluoroundecanoic acid) to loss of bone mineral density relative to other factors related to risk of osteoporosis and bone fracture, using data from subjects who participated in the US National Health Examination and Nutrition Surveys (NHANES) of 2013–2014. Results: PFAS exposures contribute to bone mineral density changes relative to the following variables: age, weight, height, vitamin D2 and D3, gender, race, sex hormone binding globulin, testosterone, and estradiol. Conclusion: We note significant alterations to bone mineral density among more highly exposed adults and significant differences in effects between men and women.

PFASs have been detected in nearly every serum sample collected over the last two decades from US adults as part of the National Health and Nutrition Examination Survey (NHANES) and are commonly found in other data sets from around the world. However, less is known about infant PFAS exposures, primarily because the collection of infant serum samples is less common and frequently avoided. Cord blood samples are often preferred for chemical exposure assessments because this is thought to provide a good representation of infant serum concentrations, at least at the time of birth. In this paper, we will provide a statistical and probabilistic analysis of what can be expected for infants living in the US using NHANES from 2007 to 2008, which contains a rare subset of infant data. Regulatory efforts that require estimation of exposures among the very youth can be challenging, both because of a lack of data in general and because variability among this most vulnerable population can be uncertain. We report that US infant exposures are extremely common and that serum concentrations remain fairly constant, despite infant growth rates and relatively high caloric and fluid intake, with the possible exception of PFOS. Infant serum PFOS concentrations between months 1 and 3 are consistently higher than at less than one month, even though healthy infants at 1 and 2 months weigh more than they did at birth. This suggests that the babies are exposed to greater concentrations of PFOS after birth or that excretion kinetics differ for this PFAS.

The potential for numerical instabilities of Dynamic Mode Decomposition (DMD), which assumes the completeness of the eigenspace is discussed for cases where the underlying system is defective or nearly defective. A numerically stable approach based on Schur decomposition is presented. The proposed method complements the DMD for cases where eigendecomposition is ill-conditioned. Both mathematical analysis and the results of numerical experiments are presented.