Multiply Robust Estimation for Causal Treatment Effect and Average Treatment Effect Among Treated When Treatment Heterogeneity Exists

• Activity Number: 57 - Some Recent Developments and Applications of the Empirical Likelihood Method
• Type: Topic Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Lu Wang* and Peisong Han and Daniel Almirall
• Companies: University of Michigan and University of Waterloo and University of Michigan
• Keywords: Robust Estimation ; Causal Inference ; Average Treatment Effect Among the Treated ; Empirical Likelihood ; Covariate Balancing ; Multiple Robustness

Abstract

We propose robust estimation approaches based on empirical likelihood of (1). Average Treatment Effect (ATE): The ATE of treatment a relative to treatment b is the comparison of mean outcomes had the entire population been observed under one treatment a, versus had the entire population been observed under another treatment b; and (2). Average Treatment Effect Among the Treated (ATT): The ATT of b among those treated with a is the comparison, among study participants who were treated with a, of their mean outcome when treated with a, as they were, with the mean outcome they would have had if they had instead been treated with b. The ATEs and ATTs can differ when there exists treatment effect heterogeneity. The proposed estimating approach postulate multiple models for both the propensity score and the conditional mean of the counterfactual outcome given covariates, and carefully construct the extra balance constraints through an empirical likelihood objective function. Our proposed method preserves the same desired balance of covariate distributions and in addition, it provide consistent estimators if any working model is correctly specified, and thus is multiply robust.