Partial identification and unmeasured confounding with multiple treatments and multiple outcomes

Estimating the health effects of multiple air pollutants is a crucial problem in public health, but one that is difficult due to unmeasured confounding bias. Motivated by this issue, we develop a framework for partial identification of causal effects in the presence of unmeasured confounding in settings with multiple treatments and multiple outcomes. Under a factor confounding assumption, we show that joint partial identification regions for multiple estimands can be more informative than considering partial identification for individual estimands one at a time. We show how assumptions related to the strength of confounding or magnitude of plausible effect sizes for one estimand can reduce the partial identification regions for other estimands. As a special case of this result, we explore how negative control assumptions reduce partial identification regions and discuss conditions under which point identification can be obtained. We develop novel computational approaches to finding partial identification regions under a variety of these assumptions. We then estimate the causal effect of PM2.5 components on a variety of public health outcomes in the United States Medicare cohort, where we find that, in particular, the detrimental effect of black carbon is robust to the potential presence of unmeasured confounding bias.