Title: Modeling Interference Via Symmetric Treatment Decomposition,
Abstract: Classical causal inference assumes a treatment meant for a given unit does
not have an effect on other units. When this "no interference" assumption is
violated, new types of spillover causal effects arise, and causal inference
becomes much more difficult. In addition, interference introduces a unique
complication where outcomes may transmit treatment influences to each other,
which is a relationship that has some features of a causal one, but is
symmetric. In settings where detailed temporal information on outcomes is not
available, addressing this complication using statistical inference methods
based on Directed Acyclic Graphs (DAGs) (Ogburn & VanderWeele, 2014) leads to
conceptual difficulties.
In this paper, we develop a new approach to decomposing the spillover effect
into direct (also known as the contagion effect) and indirect (also known as
the infectiousness effect) components that extends the DAG based treatment
decomposition approach to mediation found in (Robins & Richardson, 2010) to
causal chain graph models (Lauritzen & Richardson, 2002). We show that when
these components of the spillover effect are identified in these models, they
have an identifying functional, which we call the symmetric mediation formula,
that generalizes the mediation formula in DAGs (Pearl, 2011). We further show
that, unlike assumptions in classical mediation analysis, an assumption
permitting identification in our setting leads to restrictions on the observed
data law, making the assumption empirically falsifiable. Finally, we discuss
statistical inference for the components of the spillover effect in the special
case of two interacting outcomes, and discuss a maximum likelihood estimator,
and a doubly robust estimator.