Variable Selection and Estimation in Causal Inference Using a Bayesian Group Lasso Approach

• Activity Number: 619 - Causal Inference in Biometric Data
• Type: Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Brandon Koch* and Julian Wolfson and David Vock
• Companies: University of Minnesota, Division of Biostatistics and University of Minnesota, Division of Biostatistics and University of Minnesota
• Keywords: Causal inference ; Bayesian group lasso ; Variable selection ; Average treatment effect

Abstract

Efficient estimation of causal treatment effects can achieved by adjusting only for those covariates which are related to both treatment and outcome (i.e., confounders) or related only to the outcome. A new method is proposed that simultaneously considers models for both outcome and treatment using a Bayesian group lasso formulation with spike and slab priors on each covariate coefficient. A bilevel selection technique is used that first selects covariates related to outcome or treatment (or both) into the model to protect against bias, and a second level of selection allows covariates related only to the treatment to be removed from the model with the aim of reducing variance. The specification of the proposed approach enables the use of an efficient block Gibbs sampler that allows for estimation when the number of covariates exceeds the sample size. We conduct a simulation study that shows the proposed method can greatly reduce bias without increasing mean squared error (MSE) over using a similar approach that does not consider a model for treatment, and can reduce variance without increasing MSE over a recently proposed method that considers models for outcome and treatment.