Primary Submission Category: Matching, Weighting
Estimating Average Treatment Effect via Marginal Outcome Density Ratio
Authors: Linying Yang, Robin Evans,
Presenting Author: Linying Yang*
Doubly robust estimators, such as AIPW, offer the advantage of providing `two chances’ to perform estimation correctly and still obtain a consistent estimator. However, due to inverse probability weighting by the propensity score, these estimators can suffer from practical positivity violation, where some covariates predict the treatment so well that our weights become extremely large; this inflates the efficiency bound and estimation variance. This leads to the concept of the marginal density ratio. Instead of manually evaluating propensity scores or selecting features in the pre-treatment covariate space, we shift our focus to the outcome space, allowing the observed outcomes to determine which information should be included. In this paper, we introduce the Marginal outcome density Ratio estimator (MR) and the Augmented Marginal outcome density Ratio estimator (AMR); we demonstrate the advantages of these estimators in filtering necessary information to obtain treatment effects. We argue in this paper that, using this information filtering, MR and AMR are able to estimate the average treatment effect more effectively in small samples than their direct counterparts, IPW and AIPW. We also give examples on its contribution to sparsity condition of ATE estimation in the high-dimensional context.