Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

David C. Wheeler

Second Advisor

Caroline K. Carrico

Third Advisor

Resa M. Jones

Fourth Advisor

Nitai D. Mukhopadhyay

Fifth Advisor

Yongyon Shin


Humans are exposed to multiple chemicals every day. Epidemiological studies have shown that chemical mixtures are associated with cancers, allergies, neurodevelopmental disorders, and other adverse health effects. To assess these associations, investigators are increasingly using chemical mixture approaches like weighted quantile sum (WQS) regression. In these studies, the research objectives are to determine whether a mixture of correlated chemicals is associated with an adverse health outcome and to identify the important chemicals. However, as experimental equipment measures each exposure to a chemical-specific detection limit, the exposures are unknown between zero and the detection limit. Indeed, the number of exposures below the detection limit (BDL) is so pervasive that complete-case analyses would remove all or most of the subjects in many studies. As WQS regression requires complete data, current strategies that account for BDL values into WQS include: substitution of the detection limit over the square root of two for all BDL values, placement of BDL values in the first quantile of the weighted index (BDLQ1), and single imputation. These approaches do not fully capture the variability due to the BDL exposures. Although multiple imputation (MI) is used to accommodate the uncertainty due to missing data in other fields, its application to mixture data is limited.

In response, we created a foundation to appropriately handle BDL values: the integration of WQS into the MI framework (MI-WQS). In this work, we introduced the bootstrapped, univariate Bayesian, and multivariate Bayesian regression imputation models in MI-WQS. Through two simulation studies surveying over a wide range of BDL values, the bootstrapped or univariate Bayesian MI approaches generally performed better than the others when most of the chemical values were less than 80% of the BDL values. We provide a vignette to give a stepwise and hands-on approach in using the corresponding package available on CRAN, miWQS. Lastly, we applied the bootstrapped and univariate-Bayesian MI-WQS approaches to determine an association between the chemical mixture and childhood leukemia and to find chemical exposures in a case-control study. The MI-WQS approach can be used to appropriately find chemical exposures that impact adverse human health effects in the presence of missing exposure data.


Library of Congress Indices: RA407-409.5; RA565-600; RA648.5-767; RA1190-1270


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Graphical Abstract

Available for download on Tuesday, August 05, 2025