Causal Ball Screening: Outcome Model-Free Causal Inference with Ultra-High-Dimensional Covariates

• Activity Number: 244 - Recent Advances in Causal Inference with Applications for the Public Good
• Type: Invited
• Date/Time: Tuesday, August 4, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Dingke Tang and Dehan Kong and Wenliang Pan and Linbo Wang*
• Companies: University of Science and Technology China and University of Toronto and Sun Yat-Sen University and University of Toronto
• Keywords: Average treatment effect; Ball correlation; Confounder selection

Abstract

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal models, including the propensity score models, it is imperative to first extract important features from high dimensional data. Unlike the familiar task of variable selection for prediction modeling, our ultimate goal here is to control for confounding while maintaining efficiency in the resulting causal effect estimate. Previous empirical studies have suggested that one should aim to include all predictors of the outcome, rather than the treatment, in the propensity score model. In this paper, we formalize this intuition through rigorous proofs, and propose the causal ball screening for selecting these variables from modern ultra-high dimensional data sets. A distinctive feature of our proposal is that we do not require any modeling on the outcome regression, thus providing robustness against misspecification of the functional form or violation of smooth-ness conditions. Our theoretical analyses show that the proposed procedure enjoys a number of oracle properties including model selection consistency, normality and efficiency.