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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.

Individuals are exposed to a large number of diverse environmental chemicals simultaneously and the evaluation of multiple chemical exposures is important for identifying cancer risk factors. The measurement of a large number of chemicals (the exposome) in epidemiologic studies is allowing for a more comprehensive assessment of cancer risk factors than was done in earlier studies that focused on only a few chemicals. Empirical evidence from epidemiologic studies shows that chemicals from different chemical classes have different magnitudes and directions of association with cancers. Given increasing data availability, there is a need for the development and assessment of statistical methods to model environmental cancer risk that considers a large number of diverse chemicals with different effects for different chemical classes. The method of grouped weighted quantile sum (GWQS) regression allows for multiple groups of chemicals to be considered in the model such that different magnitudes and directions of associations are possible for each group of chemicals. In this paper, we assessed the ability of GWQS regression to estimate exposure effects for multiple chemical groups and correctly identify important chemicals in each group using a simulation study. We compared the performance of GWQS regression with WQS regression, the least absolute shrinkage and selection operator (lasso), and the group lasso in estimating exposure effects and identifying important chemicals. The simulation study results demonstrate that GWQS is an effective method for modeling exposure to multiple groups of chemicals and compares favorably with other methods used in mixture analysis. As an application, we used GWQS regression in the California Childhood Leukemia Study (CCLS), a population-based case-control study of childhood leukemia in California to estimate exposure effects for many chemical classes while also adjusting for demographic factors. The CCLS analysis found evidence of a positive association between exposure to the herbicide dacthal and an increased risk of childhood leukemia.

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.

Individuals are exposed to a large number of diverse environmental chemicals simultaneously and the evaluation of multiple chemical exposures is important for identifying cancer risk factors. The measurement of a large number of chemicals (the exposome) in epidemiologic studies is allowing for a more comprehensive assessment of cancer risk factors than was done in earlier studies that focused on only a few chemicals. Empirical evidence from epidemiologic studies shows that chemicals from different chemical classes have different magnitudes and directions of association with cancers. Given increasing data availability, there is a need for the development and assessment of statistical methods to model environmental cancer risk that considers a large number of diverse chemicals with different effects for different chemical classes. The method of grouped weighted quantile sum (GWQS) regression allows for multiple groups of chemicals to be considered in the model such that different magnitudes and directions of associations are possible for each group of chemicals. In this paper, we assessed the ability of GWQS regression to estimate exposure effects for multiple chemical groups and correctly identify important chemicals in each group using a simulation study. We compared the performance of GWQS regression with WQS regression, the least absolute shrinkage and selection operator (lasso), and the group lasso in estimating exposure effects and identifying important chemicals. The simulation study results demonstrate that GWQS is an effective method for modeling exposure to multiple groups of chemicals and compares favorably with other methods used in mixture analysis. As an application, we used GWQS regression in the California Childhood Leukemia Study (CCLS), a population-based case-control study of childhood leukemia in California to estimate exposure effects for many chemical classes while also adjusting for demographic factors. The CCLS analysis found evidence of a positive association between exposure to the herbicide dacthal and an increased risk of childhood leukemia.