Assessment of Weighted Quantile Sum Regression for Modeling Chemical Mixtures and Cancer Risk

Abstract

In evaluation of cancer risk related to environmental chemical exposures, the effect of many chemicals on disease is ultimately of interest. However, because of potentially strong correlations among chemicals that occur together, traditional regression methods suffer from collinearity effects, including regression coefficient sign reversal and variance inflation. In addition, penalized regression methods designed to remediate collinearity may have limitations in selecting the truly bad actors among many correlated components. The recently proposed method of weighted quantile sum (WQS) regression attempts to overcome these problems by estimating a body burden index, which identifies important chemicals in a mixture of correlated environmental chemicals. Our focus was on assessing through simulation studies the accuracy of WQS regression in detecting subsets of chemicals associated with health outcomes (binary and continuous) in site-specific analyses and in non-site-specific analyses. We also evaluated the performance of the penalized regression methods of lasso, adaptive lasso, and elastic net in correctly classifying chemicals as bad actors or unrelated to the outcome. We based the simulation study on data from the National Cancer Institute Surveillance Epidemiology and End Results Program (NCI-SEER) case–control study of non-Hodgkin lymphoma (NHL) to achieve realistic exposure situations. Our results showed that WQS regression had good sensitivity and specificity across a variety of conditions considered in this study. The shrinkage methods had a tendency to incorrectly identify a large number of components, especially in the case of strong association with the outcome.

Extending the Distributed Lag Model framework to handle chemical mixtures

“…whether each exposure is positively or negatively correlated with the outcome. Because of the way the WQS method aggregates exposure variables to form an index [32], individual exposure effects should be homogeneous with respect to directionality of the relationship with the outcome. A degree of signal attenuation is expected at time points wherein some exposure variables are positively associated with the outcome and others are negatively associated.…”

A preliminary study on prenatal polybrominated diphenyl ether serum concentrations and intrinsic functional network organization and executive functioning in childhood

“…In order to examine the associations of intrinsic functional network organization with prenatal PBDE serum concentrations and parent-reported executive functioning in childhood, we performed a series of Weighted Quantile Sum (WQS) regression analyses (Czarnota, Gennings, & Wheeler, 2015), using SAS version 9.4. WQS is a statistical approach developed to examine associations between co-exposure to multiple, highly correlated environmental toxicants with health outcomes.…”

“…WQS is a statistical approach developed to examine associations between co-exposure to multiple, highly correlated environmental toxicants with health outcomes. Using WQS, we estimated a weighted linear PBDE exposure index, in which the weights are empirically estimated using bootstrap sampling (n = 100 bootstrap samples) (Czarnota et al, 2015;Gennings et al, 2013). WQS reduces multicollinearity issues associated with highly correlated congeners, and has increased power compared to performing separate analyses for each congener (Gennings et al, 2013).…”

Environmental Exposure Mixtures: Questions and Methods to Address Them

“…Exposure weights may be based on their expected potency relative to a reference exposure, a concept drawn from toxicology,[6] or based on their percent contribution to the total mixture effect. [7] We use the description of summed over the term cumulative used by previous authors,[3] because the latter suggests an exposure quantity that is calculated based on repeated exposures, over time, to the same chemical. There are many examples of summed approaches, which often employ toxic equivalency factors and related metrics.…”

“…Notably, this procedure requires the assumption that any effects of exposures on the outcome are all in the same direction (positive or negative). [7] BKMR provides a summed mixture effect as well; however, rather than an estimate of the percent contribution to the effect, BKMR provides the probability of inclusion in the summed mixture effect, and allows for examining multiple exposure-response shapes. [11] BKMR is also capable of examining independent effects of mixture components, and considers the impact of individual components holding the others constant at pre-specified percentile values (such as the 50 th percentile of the exposure distribution).…”