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Abstract:
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The efficiency of doubly robust (DR) 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. Here, we propose GLiDeR, 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 unlike traditional variable selection methods which consider each model separately. The selected variables and corresponding coefficient estimates are used in a standard DR ACE estimator. We derive an oracle result and conduct a simulation study which shows that GLiDeR is more efficient than DR methods which use standard variable selection techniques and has substantial computational benefits over a new DR Bayesian model averaging method. We illustrate our method to estimate the causal treatment effect of bilateral versus single-lung transplant on forced expiratory volume one year after transplant using an observational registry.
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