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Tuesday, April 13, 2021 [Link to join] (ID: 995 8569 5110, Password: 007080)
(New non-US times due to daylight-savings time: 8:30 am PT / 11:30 am ET / 3:30 pm London / 4:30 pm Berlin / 11:30 pm Beijing)
- Speaker: Andrea Rotnitzky (Di Tella University, Buenos Aires)
- Title: Optimal adjustment sets in non-parametric graphical models
- Discussant: Ema Perkovic (University of Washington)
- Abstract: We consider the selection of potential confounding variables at the stage of the design of a planned observational study. Given a tentative non-parametric graphical causal model, possibly including unobservable variables, the aim is to select the set of observable covariates that both suffices to control for confounding under the model and yields a non-parametric estimator of the causal contrast of interest with smallest variance. 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. 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. For studies aimed at assessing the effects of interventions at multiple time points, static or dynamic, we derive graphical rules for comparing certain pairs of time dependent adjustment sets but we show that no global graphical rule is possible for determining optimal time dependent adjustment sets, even in graphs without unobservables. Finally, for graphs without unobservables and point interventions, we provide a sound and complete graphical criterion for determining when a non-parametric optimally adjusted estimator of the population average causal effect contrast is semiparametric efficient under the non-parametric causal graphical model. Joint work with Ezequiel Smucler and Facundo Sapienza.