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

Abstract

Identifying a causal effect involves finding a function of observational densities that serves as an equivalent form of the interventional density of interest -- denoted by $f(y | do(x))$ in the unconditional setting and $f(y | do(x), z)$ in the conditional setting. This equivalency allows researchers to rely on observational data alone to estimate a causal effect. We consider the problem of identifying causal effects across three chapters. In our first chapter, we focus on identifying conditional effects through covariate adjustment in a 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). We provide a necessary and sufficient graphical criterion for finding these sets when conditioning on variables unaffected by treatment, and we provide explicit sets from the graph that satisfy this criterion. In our second chapter, we continue exploring covariate adjustment but turn to focus on the unconditional setting where there is no prior knowledge of the underlying causal graph. We present two routes for finding adjustment sets that instead rely on in/dependencies in the data directly. One route applies a concept known as c-equivalence to extend the work of Entner et al. (2013) under a single treatment, and another provides sufficient criteria for finding adjustment sets under multiple treatments. In our third chapter, we return to conditional identification where the causal graph is known up to an MPDAG. But rather than focusing on covariate 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.