Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression

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.

Neighborhood Deprivation, Indoor Chemical Concentrations, and Spatial Risk for Childhood Leukemia

“…Additionally, there were missing data in the PBDE chemicals due to insufficient levels of house dust for analysis. Both types of missing observations were imputed with log-normal distributions, as previously described [ 15 ].…”

“…In contrast, the California Childhood Leukemia Study (CCLS) evaluated residential exposure to specific persistent chemicals measured in house dust and found significant positive associations between the concentration of individual and/or total polychlorinated biphenyls (PCBs) [ 11 ], polybrominated biphenyl ether (PBDEs) flame retardants [ 12 ], specific herbicides [ 13 ], and polycyclic aromatic hydrocarbons (PAHs) [ 14 ], and childhood leukemia risk. In our previous CCLS analyses, we also assessed simultaneous exposures to six or seven groups of chemicals measured in house dust using Bayesian group index models [ 15 , 16 ] and found a significant positive association for PAHs and childhood leukemia overall [ 15 ], as well as for herbicides among children who were born and raised in the home where the dust samples were taken [ 16 ]. Many of the chemicals in the CCLS data, especially congeners within chemical groups, are strongly correlated (r > 0.6), and thus, they cannot be analyzed together with traditional regression methods.…”

Research on data missing filling of smart watt-hour meter based on variational self-encoder

“…The lack of operation data of smart watt-hour meter will lead to the rapid reduction of sample data in the power system, and the lack of equipment parameters will cause deviation. The missing equipment data cannot present the actual operation state of the equipment, which can effectively improve the safe operation of the power system by filling the missing data during the operation of smart watt-hour meter [10].…”