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.

Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression

“…Single-chemical logistic regression analyses have also found significant positive associations between leukemia and PCB138 as well as between leukemia and summed total PCB concentrations [56]. Similarly, the significant positive association found for herbicides (and the dominance of dacthal within the index) closely mirrors prior analyses of these data done using Bayesian group index regression analysis with a different imputation approach [23] and GWQS regression [24]. Besides these mixture analyses, univariable logistic regression analyses have found similar associations between dacthal and childhood acute lymphocytic leukemia (ALL) risk [57].…”

“…We first fit the 7-group exposure model and then evaluated high family income as a potential effect modifier because it was a consistently significant covariate in previous analyses [23,24].To investigate potential effect moderation, we extended the 7-group model to include seven interaction terms between each index and the highest income level. We then conducted a stratified analysis and dichotomized into the highest income bracket ($75,000+) as one level and the lower five brackets ($0-$74,999) as the second.…”

“…More recently, group index models were developed to allow for multiple chemical groups, where each of the groups can have different magnitudes and direction of association with the outcome [20,21]. There are both frequentist and Bayesian versions of group index models, with Bayesian models being able to estimate all model parameters simultaneously in one step [21][22][23][24].…”

The Intersection of Neighborhood Environment and Adverse Childhood Experiences: Methods for Creation of a Neighborhood ACEs Index

“…In addition to PCA, a recently developed method that can be used to develop a neighborhood index is Bayesian index regression [59][60][61][62][63][64]. Bayesian index regression is an index development method grounded in weighted quantile sum regression and Bayesian methods.…”

“…Third, Bayesian index regression results in easily interpretable weights, with weights for exposure variables that prove irrelevant being near 0; this is a contrast from PCA which may retain variables that are unrelated to the outcome of interest. Recent evidence suggests that Bayesian index regression performs better than traditional index development approaches such as PCA [59,[64][65][66][67][68][69].…”