  Prior work applying semiparametric theory to causal inference has primarily
focused on deriving estimators that exhibit statistical robustness under a
prespecified causal model that permits identification of a desired causal
parameter. However, a fundamental challenge is correct specification of such a
model, which usually involves making untestable assumptions. Evidence factors
is an approach to combining hypothesis tests of a common causal null hypothesis
under two or more candidate causal models. Under certain conditions, this
yields a test that is valid if at least one of the underlying models is
correct, which is a form of causal robustness. We propose a method of combining
semiparametric theory with evidence factors. We develop a causal null
hypothesis test based on joint asymptotic normality of K asymptotically linear
semiparametric estimators, where each estimator is based on a distinct
identifying functional derived from each of K candidate causal models. We show
that this test provides both statistical and causal robustness in the sense
that it is valid if at least one of the K proposed causal models is correct,
while also allowing for slower than parametric rates of convergence in
estimating nuisance functions. We demonstrate the effectiveness of our method
via simulations and applications to the Framingham Heart Study and Wisconsin
Longitudinal Study.
