  Causal inference has been increasingly reliant on observational studies with
rich covariate information. To build tractable causal procedures, such as the
doubly robust estimators, it is imperative to first extract important features
from high or even ultra-high dimensional data. In this paper, we propose causal
ball screening for confounder selection from modern ultra-high dimensional data
sets. Unlike the familiar task of variable selection for prediction modeling,
our confounder selection procedure aims to control for confounding while
improving efficiency in the resulting causal effect estimate. Previous
empirical and theoretical studies suggest excluding causes of the treatment
that are not confounders. Motivated by these results, our goal is to keep all
the predictors of the outcome in both the propensity score and outcome
regression models. A distinctive feature of our proposal is that we use an
outcome model-free procedure for propensity score model selection, thereby
maintaining double robustness in the resulting causal effect estimator. Our
theoretical analyses show that the proposed procedure enjoys a number of
properties, including model selection consistency and point-wise normality.
Synthetic and real data analysis show that our proposal performs favorably with
existing methods in a range of realistic settings. Data used in preparation of
this article were obtained from the Alzheimer's Disease Neuroimaging Initiative
(ADNI) database.
