Bayesian Group Index Regression for Modeling Chemical Mixtures and Cancer Risk

Abstract

There has been a growing interest in the literature on multiple environmental risk factors for diseases and an increasing emphasis on assessing multiple environmental exposures simultaneously in epidemiologic studies of cancer. One method used to analyze exposure to multiple chemical exposures is weighted quantile sum (WQS) regression. While WQS regression has been demonstrated to have good sensitivity and specificity when identifying important exposures, it has limitations including a two-step model fitting process that decreases power and model stability and a requirement that all exposures in the weighted index have associations in the same direction with the outcome, which is not realistic when chemicals in different classes have different directions and magnitude of association with a health outcome. Grouped WQS (GWQS) was proposed to allow for multiple groups of chemicals in the model where different magnitude and direction of associations are possible for each group. However, GWQS shares the limitation of WQS of a two-step estimation process and splitting of data into training and validation sets. In this paper, we propose a Bayesian group index model to avoid the estimation limitation of GWQS while having multiple exposure indices in the model. To evaluate the performance of the Bayesian group index model, we conducted a simulation study with several different exposure scenarios. We also applied the Bayesian group index method to analyze childhood leukemia risk in the California Childhood Leukemia Study (CCLS). The results showed that the Bayesian group index model had slightly better power for exposure effects and specificity and sensitivity in identifying important chemical exposure components compared with the existing frequentist method, particularly for small sample sizes. In the application to the CCLS, we found a significant negative association for insecticides, with the most important chemical being carbaryl. In addition, for children who were born and raised in the home where dust samples were taken, there was a significant positive association for herbicides with dacthal being the most important exposure. In conclusion, our approach of the Bayesian group index model appears able to make a substantial contribution to the field of environmental epidemiology.

Keywords: cancer; chemical mixtures; environment; mixture analysis.

Figure 1

Forest plot of odds ratios and 95% credible intervals for chemical groups for childhood leukemia from the Bayesian group index model with a line at the null value of 1.0.

Figure 2

Weights for chemicals in each of the chemical groups from the Bayesian group index model for childhood leukemia in the CCLS.

Figure 3

Forest plot of odds ratios and 95% credible intervals for chemical groups for childhood leukemia in children who lived at the same residence since birth with a line at the null value of 1.0.

Figure 4

Estimated chemical weights for chemical groups from the Bayesian group index model for childhood leukemia in the CCLS in children with same residence since birth.