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. This work extends and generalizes
existing work on unmeasured confounding with a single treatment, and provides a
nonparametric extension of models commonly used in bioinformatics