Causal Effect Identification via Equivalence Classes of Acyclic Graphs and Data-Driven Adjustment

In our first project, we consider the problem of identifying a conditional causal effect through covariate adjustment. We focus on the setting where the causal graph is known up to one of two types of graphs: a maximally oriented partially directed acyclic graph (MPDAG) or a partial ancestral graph (PAG). Both MPDAGs and PAGs represent equivalence classes of possible underlying causal models. After defining adjustment sets in this setting, we provide a necessary and sufficient graphical criterion – the conditional adjustment criterion – for finding these sets under conditioning on variables unaffected by treatment. We further provide explicit sets from the graph that satisfy the conditional adjustment criterion, and therefore, can be used as adjustment sets for conditional causal effect identification.

In our second project, we again consider covariate adjustment. But we turn our focus to the total effect setting where there is no prior knowledge of the underlying causal graph beyond an assumption that the treatment and outcome are not causal ancestors of the remaining observed variables. In this setting, we present two routes for finding adjustment sets that instead rely on dependencies and independencies in the data directly. Our first route applies a concept known as c-equivalence to extend the work of Entner et al. (2013) in finding adjustment sets for a single treatment. Our second route provides sufficient criteria for finding adjustment sets for multiple treatments.

In our third project, we return to the problem of identifying a conditional causal effect in the setting where the causal graph is known up to an MPDAG and conditioning variables are unaffected by treatment. However, rather than focusing on identification by adjustment, we consider identification more generally. We develop a conditional identification formula, based on graphical criteria, that extends beyond settings where conditional adjustment sets exist, and we pair this with a necessary and sufficient criterion for when this identification is possible. Further, we extend the well-known do calculus to the MPDAG setting and build a conditional identification algorithm based on this calculus that is complete for identifying these conditional effects.