Covariate Selection with Group Lasso and Doubly Robust Estimation of Causal Effects

Abstract

Summary The efficiency of doubly robust estimators of the average causal effect (ACE) of a treatment can be improved by including in the treatment and outcome models only those covariates which are related to both treatment and outcome (i.e., confounders) or related only to the outcome. However, it is often challenging to identify such covariates among the large number that may be measured in a given study. In this paper, we propose GLiDeR (Group Lasso and Doubly Robust Estimation), a novel 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. The selected variables and corresponding coefficient estimates are used in a standard doubly robust ACE estimator. We provide asymptotic results showing that, for a broad class of data generating mechanisms, GLiDeR yields a consistent estimator of the ACE when either the outcome or treatment model is correctly specified. A comprehensive simulation study shows that GLiDeR is more efficient than doubly robust methods using standard variable selection techniques and has substantial computational advantages over a recently proposed doubly robust Bayesian model averaging method. We illustrate our method by estimating the causal treatment effect of bilateral versus single-lung transplant on forced expiratory volume in one year after transplant using an observational registry.

Anemia and perioperative mortality in non-cardiac surgery patients: a secondary analysis based on a single-center retrospective study

“…For a given covariate, standardized differences of less than 10.0%indicate a relatively small imbalance. The doubly robust estimation method, the combination of multivariate regression model and a propensity score model, was also applied to infer the independent associations between anemia status and patients' primary and secondary outcomes [20,21]. Using the estimated propensity scores as weights, an inverse probabilities weighting (IPW) model was used to generate a weighted cohort [22] .…”

Machine Learning-Augmented Propensity Score-Adjusted Multilevel Mixed Effects Panel Analysis of Hands-On Cooking and Nutrition Education versus Traditional Curriculum for Medical Students as Preventive Cardiology: Multisite Cohort Study of 3,248 Trainees over 5 Years

“…Doubly robust estimation features a dual strategy of outcome regression that also accounts for the likelihood of receiving an exposure or treatment, such as with a PS [ 39 , 44 – 46 ]. Simply using multivariable regression or PS analysis can lead to biased treatment estimates if either model is incorrectly specified.…”

Efficiency and robustness of causal effect estimators when noncompliance is measured with error

“…Finally, while our simulation study only considers a two‐dimension covariate vector, X , to focus our investigation on the robustness versus efficiency trade‐off associated with the various proposed estimators, practical application of our methods would likely involve higher dimensional covariates with uncertainty regarding the covariates the must be included to satisfy the “no unmeasured confounders” assumption. Variable selection in the context of causal inference has been the focus of recent methodological development, which could form the basis of an extension of our method to the higher dimensional setting but would likely come at the cost of efficiency. This is a likely subject of future work.…”