Optimal adjustment sets in non-parametric causal graphical models
12/11, 12h
Seminario online
El Departamento de Matemáticas y Estadística junto con el Departamento de Economía de la Universidad Torcuato Di Tella, invitan al seminario sobre Optimal adjustment sets in non-parametric causal graphical models, a cargo de Andrea Rotnitzky (PhD. in Statistics, U.C. Berkeley).
Abstract
Causal graphical models are statistical models represented by a directed acyclic graph in which each vertex stands for a random variable and a structural equation that generates it which is a function of its parents in the graph and an independent error.
I will start with a brief introduction of causal graphical models and of their use in the determination of identifiability and optimal estimation of the so-called average treatment effect (ATE) of static and personalized treatments in the presence of confounding variables.
I will then consider the problem of determining the best set of potential confounding variables at the stage of the design of a planned observational study aimed at assessing the population average causal effect of a point exposure personalized, i.e. dynamic, or static treatment. Given a tentative non-parametric graphical causal model, possibly including unobservable variables, the goal is to select the "best" set of observable covariates in the sense that it suffices to control for confounding under the model and it yields a non-parametric estimator of ATE 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. 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.
This is joint work with Ezequiel Smucler and Facundo Sapienza.
I will start with a brief introduction of causal graphical models and of their use in the determination of identifiability and optimal estimation of the so-called average treatment effect (ATE) of static and personalized treatments in the presence of confounding variables.
I will then consider the problem of determining the best set of potential confounding variables at the stage of the design of a planned observational study aimed at assessing the population average causal effect of a point exposure personalized, i.e. dynamic, or static treatment. Given a tentative non-parametric graphical causal model, possibly including unobservable variables, the goal is to select the "best" set of observable covariates in the sense that it suffices to control for confounding under the model and it yields a non-parametric estimator of ATE 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. 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.
This is joint work with Ezequiel Smucler and Facundo Sapienza.
Andrea Rotnitzky es profesora plenaria del Departamento de Economía de la Universidad Torcuato Di Tella, profesora adjunta de Harvard T. H. Chan School of Public Health e investigadora principal del CONICET. Tiene artículos científicos publicados en Biometrika, Journal of the American Statistical Association, Biometrics y Journal of the Royal Statistical Science, entre otros. Fue editora asociada de Biometrics, Annals of Statistics, Statistical Science. Actualmente es editora asociada de Journal of the American Statistical Association y del Journal of Causal Inference.