Sensitivity analysis with multiple treatments and multiple outcomes with applications to air pollution mixtures

Understanding the health impacts of air pollution is vital in public health research. Numerous studies have estimated negative health effects of a variety of pollutants, but accurately gauging these impacts remains challenging due to the potential for unmeasured confounding bias that is ubiquitous in observational studies. In this study, we develop a framework for sensitivity analysis in settings with both multiple treatments and multiple outcomes simultaneously. This setting is of particular interest because one can identify the strength of association between the unmeasured confounders and both the treatment and outcome, under a factor confounding assumption. This provides informative bounds on the causal effect leading to partial identification regions for the effects of multivariate treatments that account for the maximum possible bias from unmeasured confounding. We also show that when negative controls are available, we are able to refine the partial identification regions substantially, and in certain cases, even identify the causal effect in the presence of unmeasured confounding. We derive partial identification regions for general estimands in this setting, and develop a novel computational approach to finding these regions.