  Randomized Controlled Trials (RCT)s are relied upon to assess new treatments,
but suffer from limited power to guide personalized treatment decisions. On the
other hand, observational (i.e., non-experimental) studies have large and
diverse populations, but are prone to various biases (e.g. residual
confounding). To safely leverage the strengths of observational studies, we
focus on the problem of falsification, whereby RCTs are used to validate causal
effect estimates learned from observational data. In particular, we show that,
given data from both an RCT and an observational study, assumptions on internal
and external validity have an observable, testable implication in the form of a
set of Conditional Moment Restrictions (CMRs). Further, we show that expressing
these CMRs with respect to the causal effect, or "causal contrast", as opposed
to individual counterfactual means, provides a more reliable falsification
test. In addition to giving guarantees on the asymptotic properties of our
test, we demonstrate superior power and type I error of our approach on
semi-synthetic and real world datasets. Our approach is interpretable, allowing
a practitioner to visualize which subgroups in the population lead to
falsification of an observational study.
