Primary Submission Category: Causal Inference and Common Support Violations
Contingency in Causal Inference
Authors: AmirEmad Ghassami, Ilya Shpitser,
Presenting Author: AmirEmad Ghassami*
Many causal inference problems involve contingent potential outcomes that are only defined if a specific state of affairs occurs. For instance, a variable such as “quality of life” is only well-defined if the individual is alive. In such settings, the contingency requirement can be represented by conditioning on a set of values of a contingency variable. In this case, seemingly natural contrasts conditioned on the contingency event may not necessarily correspond to causal effects anymore. This specifically happens when contingency variables are post-treatment. Despite prevalence of such situations, unfortunately, no general treatment of contingency in causal inference problems exists in the literature. In this work, we use the formalism of graphical causal models to propose a general methodology for characterizing which contingent contrasts correspond to causally interpretable effects and what causal effect they represent. For the case that our characterization indicates that a contingent contrast cannot be interpreted as a causal effect, we propose the use of an alternative estimand, called component-wise effect. Specifically, given the assumption that the treatment variable and certain other variables in the system have more than one component, we describe a contingent contrast, defined using interventions on treatment components, and provide graphical sufficient conditions under which our introduced contingent contrast corresponds to a causally interpretable effect.