Spring 2022

Causality Program Visitor Speaker Series: Optimal Adjustment Sets in Non-parametric Causal Graphical Models

Tuesday, Mar. 8, 2022 2:00 pm3:00 pm PST

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Parent Program: 

Andrea Rotnitzky (Di Tella University, Buenos Aires, Argentina)


Calvin Lab Room 116

Abstract: Given a non-parametric causal graphical model, possibly including unobservable variables, we consider the problem of determining the set of observable covariates that both suffices to control for confounding under the model and yields a non-parametric estimator of the population average treatment effect (ATE) of a point exposure on an outcome with smallest asymptotic variance. We consider both personalized, i.e. dynamic, and static treatments. For studies without unobservables aimed at assessing the effect of a static point exposure we show that graphical rules recently derived for identifying optimal covariate adjustment sets in linear causal graphical models and treatment effects estimated via ordinary least squares also apply in the non-parametric setting. We further extend these results to personalized treatments. Moreover, we show that, in graphs with unobservable variables, but with at least one adjustment set fully observable, there exist adjustment sets that are optimal minimal (minimum), yielding non-parametric estimators with the smallest variance among those that control for observable adjustment sets that are minimal (of minimum cardinality). In addition, although a globally optimal adjustment set among observable adjustment sets does not always exist, we provide a sufficient condition for its existence. We provide polynomial time algorithms to compute the observable globally optimal (when it exists), optimal minimal, and optimal minimum adjustment sets. If time allows, we will also discuss, for studies aimed at assessing the effects of interventions at multiple time points,  graphical rules for comparing certain pairs of time dependent adjustment sets but we will show that there exist graphs in which no global optimal time dependent adjustment sets exist.