Semiparametric Inference for Causal Effects in Graphical Models with Hidden Variables

• Activity Number: 124 - Innovative Development of Semiparametrics for Heterogeneous Causal Effects in Epidemiology
• Type: Invited
• Date/Time: Monday, August 8, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Ilya Shpitser* and Razieh Nabi and Rohit Bhattacharya
• Companies: Johns Hopkins University and Emory University and Williams College
• Keywords: Causal graphical models; Semi-parametric inference; The ID algorithm

Abstract

Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. In this work, we bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of hidden variable DAGs where the treatment satisfies a simple graphical criterion; this class includes models yielding the adjustment and front-door functionals as special cases. Further, we derive an important class of hidden variable DAGs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed DAGs. In these classes of DAGs, we derive estimators that achieve the semiparametric efficiency bounds for the target of interest.