Abstract
There is growing scientific interest in identifying the multitude of chemical exposures related to human diseases through mixture analysis. In this paper, we address the issue of below detection limit (BDL) missing data in mixture analysis using Bayesian group index regression by treating both regression effects and missing BDL observations as parameters in a model estimated through a Markov chain Monte Carlo algorithm that we refer to as pseudo-Gibbs imputation. We compare this with other Bayesian imputation methods found in the literature (Multiple Imputation by Chained Equations and Sequential Full Bayes imputation) as well as with a non-Bayesian single-imputation method. To evaluate our proposed method, we conduct simulation studies with varying percentages of BDL missingness and strengths of association. We apply our method to the California Childhood Leukemia Study (CCLS) to estimate concentrations of chemicals in house dust in a mixture analysis of potential environmental risk factors for childhood leukemia. Our results indicate that pseudo-Gibbs imputation has superior power for exposure effects and sensitivity for identifying individual chemicals at high percentages of BDL missing data. In the CCLS, we found a significant positive association between concentrations of polycyclic aromatic hydrocarbons (PAHs) in homes and childhood leukemia as well as significant positive associations for polychlorinated biphenyls (PCBs) and herbicides among children from the highest quartile of household income. In conclusion, pseudo-Gibbs imputation addresses a commonly encountered problem in environmental epidemiology, providing practitioners the ability to jointly estimate the effects of multiple chemical exposures with high levels of BDL missingness.
Highlights
There are more than 350,000 chemicals and chemical mixtures registered for production and use globally [1]
Several statistical methods have been developed for analyzing chemical mixtures that handle the highly correlated data commonly found in chemical mixtures [16], including weighted quantile sum (WQS) regression [17], quantile g-computation [18], and Bayesian kernel machine regression (BKMR) [19]
We examined the proportion of 95% credible intervals (CIs) of the odds ratios of chemical group associations that did not contain 1.00
Summary
There are more than 350,000 chemicals and chemical mixtures registered for production and use globally [1]. Chemicals used for commercial purposes have been found in human tissues and in household air and dust samples in varying concentrations [2–4], motivating questions as to their impact on human health. Epidemiologic studies have identified environmental chemical exposure as a risk factor in a number of human diseases, including cancer, type 2 diabetes, cardiovascular disease, thyroid disease, and developmental disorders [5–10]. Investigations into the health impact of chemical exposures highlight the fact that they exist as mixtures of many simultaneous exposures [11,12]. Epidemiologists have sought to assess the joint impact of chemical mixtures on health outcomes as opposed to estimating chemicals as independent risk factors [13–15]. Several statistical methods have been developed for analyzing chemical mixtures that handle the highly correlated data commonly found in chemical mixtures [16], including weighted quantile sum (WQS) regression [17], quantile g-computation [18], and Bayesian kernel machine regression (BKMR) [19].
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