  Selection of covariates is crucial in the estimation of average treatment
effects given observational data with high or even ultra-high dimensional
pretreatment variables. Existing methods for this problem typically assume
sparse linear models for both outcome and univariate treatment, and cannot
handle situations with ultra-high dimensional covariates. In this paper, we
propose a new covariate selection strategy called double screening prior
adaptive lasso (DSPAL) to select confounders and predictors of the outcome for
multivariate treatments, which combines the adaptive lasso method with the
marginal conditional (in)dependence prior information to select target
covariates, in order to eliminate confounding bias and improve statistical
efficiency. The distinctive features of our proposal are that it can be applied
to high-dimensional or even ultra-high dimensional covariates for multivariate
treatments, and can deal with the cases of both parametric and nonparametric
outcome models, which makes it more robust compared to other methods. Our
theoretical analyses show that the proposed procedure enjoys the sure screening
property, the ranking consistency property and the variable selection
consistency. Through a simulation study, we demonstrate that the proposed
approach selects all confounders and predictors consistently and estimates the
multivariate treatment effects with smaller bias and mean squared error
compared to several alternatives under various scenarios. In real data
analysis, the method is applied to estimate the causal effect of a
three-dimensional continuous environmental treatment on cholesterol level and
enlightening results are obtained.

Methodology