Abstract
Causal inference for air pollution mixtures is an increasingly important issue with appreciable challenges. When the exposure is a multivariate mixture, there are many exposure contrasts that may be of nominal interest for causal effect estimation, but the complex joint mixture distribution often renders observed data extremely limited in their ability to inform estimates of many commonly defined causal effects. We use potential outcomes to (1) define causal effects of air pollution mixtures, (2) formalize the key assumption of mixture positivity required for estimation, and (3) offer diagnostic metrics for positivity violations in the mixture setting that allow researchers to assess the extent to which data can actually support estimation of mixture effects of interest. For settings where there is limited empirical support, we redefine causal estimands that apportion causal effects according to whether they can be directly informed by observed data versus rely entirely on model extrapolation, isolating key sources of information on the causal effect of an air pollution mixture. The ideas are deployed to assess the ability of a national US data set on the chemical components of ambient particulate matter air pollution to support estimation of a variety of causal mixture effects. This article is part of a Special Collection on Environmental Epidemiology.