Dimension Reduction in Causal Inference: Theory and Data-Driven Algorithms

• Activity Number: 330
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Xavier de Luna* and Ingeborg Waernbaum and Jenny Häggström and Emma Persson
• Companies: Umeå University and Umeå University and Umeå University and Umeå University
• Keywords: average treatment effect ; covariate selection ; dimension reduction

Abstract

In observational studies, the causal effect of a treatment is typically confounded with variables that are related to both the treatment assignment and the outcome of interest. In order to identify a causal effect, such studies often rely on that all confounding variables are observed and controlled for. In applications with a rich reservoir of observed covariates, and where subject matter knowledge provides only partial guidance on the choice of covariates to control for, data-driven covariate selection methods are needed. Indeed, including redundant covariates is suboptimal when the effect is estimated nonparametrically: for instance, efficiency may be improved by not controlling for covariates related only either to treatment assignment or to outcome. Under certain conditions, minimal sufficient subsets of covariates can be defined. Several data-driven algorithms for the selection of such minimal subsets are presented and their properties studied. In particular, we apply the framework of sufficient dimension reduction as well as kernel smoothing. One key issue that our results highlight is that different covariate selection strategies may be optimal depending on the estimand (