6.1 Causal mixture effects

To improve our understanding of the associations between environmental exposures and health outcomes, and facilitate the development of more stringent public health regulations and interventions, it is important to determine extent to which these associations reflect causal relationships. To establish causal links, researchers are advocating the use of a pluralistic approach in terms of study design, to reduce the potential harm due to typical epidemiological bias such as confounding or selection bias, as well in terms of statistical methodologies for causal inference (Vandenbroucke, Broadbent, and Pearce (2016)), (Dominici and Zigler (2017)). In the specific case of environmental exposures, this switch from association to causation has to account for the co-occurrence of multiple components or constituents, present in the real world as a complex mixture. At this time, regulatory policies are still mostly designed to regulate one pollutant or chemical at the time, thus hampering the implementation of integrated policies and possibly resulting in uncertainties about the exact impact of regulations. For this reasons, several researchers, as well as and both governmental and private institutions, are increasingly advocating for more research that could improve our understanding of the causal effects of environmental mixtures evaluated as a complex exposure situation of high-dimensional data.

The first step to improve findings interpretation towards a causal perspective is to focus on study design and pre-analytic considerations. The paper from Dominici and Zigler (2017) provides an excellent introduction that tackles these issues in the context of air pollution epidemiology, but can easily be extended to any set of environmental exposures. Another important contribution in terms of pre-analytic aspects was provided by Weisskopf and Webster (Weisskopf, Seals, and Webster (2018)),(Webster and Weisskopf (2020)) who have discussed the issue of bias amplification when evaluating environmental mixtures. Their work directly addresses issues of co-confounding related bias, presenting direct acyclic graphs (DAGs) in different contexts of interest.

After these pre-analytic aspects have been taken into consideration, the focus can be transferred to the statistical approaches that can be used to improve the causal understanding of mixture-outcome associations. Here several points should be mentioned:

  • As the exposures mixture gets more and more complex, the time spent on the pre-processing phase (unsupervised analysis) will be more and more important.

  • After this pre-processing phase, the assessment of the mixture-outcome effect should be conducted in two stages. First, by using some of the techniques described here (WQS, BKMR, tree-based methods …) one can identify a set of exposures (and interactions) that can be included in a causal model that will later be investigated in a secondary step.

  • This 2-stages approach is highly recommended because most of the available methodologies for causal inference are based on extensions of regression techniques (e.g. propensity score, difference in differences, marginal structural models, inverse probability weighting). If the setting is not too complex (i.e. those settings where multiple regression is a potentially good choice), one can directly build the regression-based causal inference technique. A good introduction of causal inference techniques based on regression that can be useful in environmental epidemiology was provided by Bind (2019).

  • Out of the possible methods for causal inference, a versatile option in the context of environmental mixtures is the multivariate version of the generalized propensity score (mvGPS), which we have applied and described in the context of air pollution epidemiology in a recent publication (Traini et al. under review).

  • Finally, it is useful to remember that one of the recent extensions of WQS (quantile G-comp) was developed with the aim of improving the causal interpretation of the estimated weights and overall effect and could be used to provide a validation of the cumulative mixture effect from a causal perspective.


Bind, Marie-Abèle. 2019. “Causal Modeling in Environmental Health.” Annual Review of Public Health 40: 23–43.
Dominici, Francesca, and Corwin Zigler. 2017. “Best Practices for Gauging Evidence of Causality in Air Pollution Epidemiology.” American Journal of Epidemiology 186 (12): 1303–9.
Vandenbroucke, Jan P, Alex Broadbent, and Neil Pearce. 2016. “Causality and Causal Inference in Epidemiology: The Need for a Pluralistic Approach.” International Journal of Epidemiology 45 (6): 1776–86.
Webster, Thomas F, and Marc G Weisskopf. 2020. “Epidemiology of Exposure to Mixtures: We Cant Be Casual about Causality When Using or Testing Methods.” arXiv Preprint arXiv:2007.01370.
Weisskopf, Marc G, Ryan M Seals, and Thomas F Webster. 2018. “Bias Amplification in Epidemiologic Analysis of Exposure to Mixtures.” Environmental Health Perspectives 126 (4): 047003.