Data-Driven Adjustment for Multiple Treatments

Covariate adjustment is one method of causal effect identification in non-experimental settings. Prior research provides routes for finding appropriate adjustments sets, but much of this research assumes knowledge of the underlying causal graph. In this paper, we present two routes for finding adjustment sets that do not require knowledge of a graph -- and instead rely on dependencies and independencies in the data directly. We consider a setting where the adjustment set is unaffected by treatment or outcome. The first route shows how to extend prior research in this area using a concept known as c-equivalence. Our second route provides sufficient criteria for finding adjustment sets in the setting of multiple treatments.