A Comparison of Statistical Methods for Studying Interactions of Chemical Mixtures

Properly assessing the effects of environmental chemical exposures on disease risk remains a challenging problem in environmental epidemiology. Various analytic approaches have been proposed, but there are few papers that have compared the performance of different statistical methods on a single dataset. In this paper, we compare different regression-based approaches for estimating interactions between chemical mixture components using data from a case-control study on non-Hodgkin's lymphoma. An analytic challenge is the high percentage of exposures that are below the limit of detection (LOD). Using imputation for LOD, we compare different Bayesian shrinkage prior approaches including an approach that incorporates the hierarchical principle where interactions are only included when main effects exist. Further, we develop an approach where main and interactive effects are represented by a series of distinct latent functions. We also fit the Bayesian kernel machine regression to these data. All of these approaches show little evidence of an interaction among the chemical mixtures when measurements below the LOD were imputed. The imputation approach makes very strong assumptions about the relationship between exposure and disease risk for measurements below the LOD. As an alternative, we show the results of an analysis where we model the exposure relationship with two parameters per mixture component; one characterizing the effect of being below the LOD and the other being a linear effect above the LOD. In this later analysis, we identify numerous strong interactions that were not identified in the analyses with imputation. This case study demonstrated the importance of developing new approaches for mixtures when the proportions of exposure measurements below the LOD are high.