Epidemiology of exposure to mixtures: we cant be casual about causality when using or testing methods

Background: There is increasing interest in approaches for analyzing the effect of exposure mixtures on health. A key issue is how to simultaneously analyze often highly collinear components of the mixture, which can create problems such as confounding by co-exposure and co-exposure amplification bias (CAB). Evaluation of novel mixtures methods, typically using synthetic data, is critical to their ultimate utility. Objectives: This paper aims to answer two questions. How do causal models inform the interpretation of statistical models and the creation of synthetic data used to test them? Are novel mixtures methods susceptible to CAB? Methods: We use directed acyclic graphs (DAGs) and linear models to derive closed form solutions for model parameters to examine how underlying causal assumptions affect the interpretation of model results. Results: The same beta coefficients estimated by a statistical model can have different interpretations depending on the assumed causal structure. Similarly, the method used to simulate data can have implications for the underlying DAG (and vice versa), and therefore the identification of the parameter being estimated with an analytic approach. We demonstrate that methods that can reproduce results of linear regression, such as Bayesian kernel machine regression and the new quantile g-computation approach, will be subject to CAB. However, under some conditions, estimates of an overall effect of the mixture is not subject to CAB and even has reduced uncontrolled bias. Discussion: Just as DAGs encode a priori subject matter knowledge allowing identification of variable control needed to block analytic bias, we recommend explicitly identifying DAGs underlying synthetic data created to test statistical mixtures approaches. Estimates of the total effect of a mixture is an important but relatively underexplored topic that warrants further investigation.