Chapter 5 Flexible approaches for complex settings
In the previous sections we have discussed the challenges that arise when evaluating environmental mixtures and the several available techniques based on regression modeling that can be used to to address different research questions in this context. The final section of section 3 discussed the two major limitations shared by all regression techniques, namely the difficulties in estimating overall mixture effects and to include additional model complexities such as non-linearities and (possibly high-order) interactions. In the previous section we have discussed WQS as a useful tool to address the first limitation. Note than, interestingly, this technique can be actually seen as yet another regression extension, as it is based on integrating a summary score into a generalized linear model.
To tackle the second challenge, let’s first note that any regression would allow integrating interactions of any order (this is done by simply including product terms between any pair, or higher combination, of exposures) as well as non-linear associations. Splines modeling is probably the best way of accounting for non-linear effects in regression modeling, or one can also consider using generalized additive models (GAM), which have been successfully applied in the context of environmental mixtures (Zheng et al. (2020)). Nevertheless, both the inclusion of product terms and spline transformations will rapidly increase the number of parameters that have to be estimated, and we might be in need of alternative techniques that can more flexibly tackle these issues. We are going to describe two approaches: first, Bayesian Kernel Machine Regression (BKMR), a method specifically developed for evaluating environmental mixtures that is increasing in popularity because of its several advantages and flexibility (Bobb et al. (2015)),(Bobb et al. (2018)). Second, the use of machine learning techniques, and specifically tree-based modeling such as boosted regression trees (Lampa et al. (2014)),(Bellavia et al. (2021)). Additional techniques that can be considered when the specific focus is on detecting interactions will not be discussed here, and the reader can refer to these publications summarizing and discussing methodologies in this context: Barrera-Gómez et al. (2017), Sun et al. (2013).