Identifying effects of multiple treatments in the presence of unmeasured confounding

Abstract

Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be flawed or have relied on fully parametric assumptions. In this paper, we propose two strategies for identifying and estimating causal effects of multiple treatments in the presence of unmeasured confounding. The auxiliary variables approach leverages auxiliary variables that are not causally associated with the outcome; in the case of a univariate confounder, our method only requires one auxiliary variable, unlike existing instrumental variable methods that would require as many instruments as there are treatments. An alternative null treatments approach relies on the assumption that at least half of the confounded treatments have no causal effect on the outcome, but does not require a priori knowledge of which treatments are null. Our identification strategies do not impose parametric assumptions on the outcome model and do not rest on estimation of the confounder.

The Promises of Parallel Outcomes

“…In particular, under linear Gaussian structural equation models for at least three exposures, D'Amour (2019) and Ogburn et al (2019) showed that except in trivial cases, identification of the ACE is not possible without a parametric model for the outcome, while Kong et al (2019) further showed that the ACE is identifiable if one also assumes a parametric binary choice outcome model with a non-probit link. Alternatively, several authors have shown that identification is possible by collecting auxiliary variables such as instrumental variables or negative control outcomes (D'Amour, 2019; Imai and Jiang, 2019;Miao et al, 2020). In contrast to the multi-cause framework, under a conditional independence structure among multiple outcomes, we achieve nonparametric identification with at least three parallel outcomes.…”