Efficient Treatment Effect Estimation with Dimension Reduction
Author | : Ying Zhang |
Publisher | : |
Total Pages | : 94 |
Release | : 2018 |
ISBN-10 | : OCLC:1035948231 |
ISBN-13 | : |
Rating | : 4/5 (31 Downloads) |
Book excerpt: Estimation of average and quantile treatment effects is crucial in causal inference for evaluation of treatments or interventions in biomedical, economic, and social studies. Under the assumption of treatment and potential outcomes are independent conditional on all covariates, valid treatment effect estimators can be obtained using nonparametric inverse propensity weighting and/or regression, which are popular because no model on propensity or regression is imposed. To obtain valid and efficient treatment effect estimators, typically the set of all covariates can be replaced by lower dimensional sets containing linear combinations of covariates. We propose to construct a lower dimensional set separately for each treatment and show that the resulting asymptotic variance of treatment effect estimator reaches a lower bound that is smaller than those based on other sets. Since the lower dimensional sets have to be constructed, for example, using nonparametric sufficient dimension reduction, we derive theoretical results on when the efficiency of treatment effect estimation is affected by sufficient dimension reduction. We find that, except for some special cases, the efficiency of treatment effect estimation is affected even though the sufficient dimension reduction is consistent in the rate of the square root of the sample size. As causal setting is similar with that of missing data, we apply the same technics to handle missing covariate value problems in estimating equations. Our theory is complemented by some simulation results. We use the data from the University of Wisconsin Health Accountable Care Organization as an example for average/quantile treatment effects estimations, and the automobile data from University of California-Irvine as an example for estimating regression parameters in estimating equations with missing covariate value.