Accounting for the uncertainty due to chemicals below the detection limit in mixture analysis

Simultaneous exposure to a mixture of chemicals over a lifetime may increase an individual's risk of disease to a greater extent than individual exposures. Researchers have used weighted quantile sum (WQS) regression to estimate the effect of multiple exposures in a manner that identifies the important (etiologically relevant) components in the mixture. However, complications arise when an experimental apparatus detects concentrations for each chemical with a different detection limit. Current strategies to account for values below the detection limit (BDL) in WQS include single imputation or placing the BDL values into the first quantile of the weighted index (BDLQ1), which do not fully capture the uncertainty in the data when estimating mixture effects. In response, we integrated WQS regression into the multiple imputation framework (MI-WQS). In a simulation study, we compared the BDLQ1 approach to MI-WQS when using either a Bayesian imputation or bootstrapping imputation approach over a range of BDL values. We examined the ability of each method to estimate the mixture's overall effect and to identify important chemicals. The results showed that as the number of BDL values increased, the accuracy, precision, model fit, and power declined for all imputation approaches. When chemical values were missing at 10%, 33%, or 50%, the MI approaches generally performed better than single imputation and BDLQ1. In the extreme case of 80% of all the chemical values were missing, the BDLQ1 approach was superior in some examined metrics.