  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 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. This paper extends and generalizes existing work
on unmeasured confounding with a single treatment and models commonly used in
bioinformatics.
