Local Interference: Removing Interference Bias in Semi-Parametric Causal Models

Michael O'Riordan, Ciarán Mark Gilligan-Lee

Keywords: interference, SUTVA, graphical model, valid adjustment

Abstract:

Interference bias is a major impediment to identifying causal effects in real-world settings. For
example, vaccination reduces the transmission of a virus in a population such that everyone benefits—
even those who are not treated. This is a source of bias that must be accounted for if one wants to
learn the true effect of a vaccine on an individual’s immune system. Previous approaches addressing
interference bias require strong domain knowledge in the form of a graphical interaction network
fully describing interference between units. Moreover, they place additional constraints on the
form the interference can take, such as restricting to linear outcome models, and assuming that
interference experienced by a unit does not depend on the unit’s covariates. Our work addresses these
shortcomings. We first provide and justify a novel definition of causal models with local interference.
We prove that the True Average Causal Effect, a measure of causality where interference has been
removed, can be identified in certain semi-parametric models satisfying this definition. These
models allow for non-linearity, and also for interference to depend on a unit’s covariates. An analytic
estimand for the True Average Causal Effect is given in such settings. We further prove that the True
Average Causal Effect cannot be identified in arbitrary models with local interference, showing that
identification requires semi-parametric assumptions. Finally, we provide an empirical validation of
our method on both simulated and real-world datasets.

Submission Number: 77