Statistical Methods for Variable Selection in Causal Inference

Abstract

Estimating the causal effect of a binary intervention or action (referred to as a "treatment") on a continuous outcome is often an investigator's primary goal. Randomized trials are ideal for estimating causal effects because randomization eliminates selection bias in treatment assignment. However, randomized trials are not always ethically or practically possible, and observational data must be used to estimate the causal effect of treatment. Unbiased estimation of causal effects with observational data requires adjustment for confounding variables that are related to both the outcome and treatment assignment. Adjusting for all measured covariates in a study protects against bias, but including covariates unrelated to outcome may increase the variability of the estimated causal effect. Standard variable selection techniques aim to maximize predictive ability of a model for the outcome and are used to decrease variability of the estimated causal effect, but they ignore covariate associations with treatment and may not adjust for important confounders weakly associated to outcome. We propose two approaches for estimating causal effects that simultaneously consider models for both outcome and treatment assignment. The first approach is a variable selection technique for identifying confounders and predictors of outcome using an adaptive group lasso approach that simultaneously performs coefficient selection, regularization, and estimation across the treatment and outcome models. In the second approach, two methods are proposed that simultaneously model outcome and treatment assignment using a Bayesian formulation with spike and slab priors on each covariate coefficient; the Spike and Slab Causal Estimator (SSCE) aims to achieve minimum bias of the causal effect estimator while Bilevel SSCE (BSSCE) aims to minimize its mean squared error. We also propose TEHTrees, a new method that combines matching and conditional inference trees to characterize treatment effect heterogeneity. One of its main virtues is that, by employing formal hypothesis testing procedures in constructing the tree, TEHTrees preserves the Type I error rate.