Unbiased estimation for additive exposure models

TL;DR

This paper introduces linear unbiased estimators for causal effects in additive exposure models, expanding estimation capabilities beyond traditional assumptions and demonstrating robustness through simulations.

Contribution

It proposes a new class of unbiased estimators for general causal effects under additive assumptions, with optimality conditions and robustness analysis.

Findings

Proposed estimators are unbiased and optimal under additive assumptions.

Estimators show robustness to violations of additivity in simulations.

Leveraging all exposure information improves estimation accuracy.

Abstract

Causal inference methods have been applied in various fields where researchers want to estimate treatment effects. In traditional causal inference settings, one assumes that the outcome of a unit does not depend on treatments of other units. However, as causal inference methods are extended to more applications, there is a greater need for estimators of general causal effects. We use an exposure mapping framework [Aronow and Samii, 2017] to map the relationship between the treatment allocation and the potential outcomes. Under the exposure model, we propose linear unbiased estimators (LUEs) for general causal effects under the assumption that treatment effects are additive. Additivity provides statistical advantages, where contrasts in exposures are now equivalent, and so the set of estimators considered grows. We identify a subset of LUEs that forms an affine basis for LUEs, and we characterize optimal LUEs with minimum integrated variance through defining conditions on the support of the estimator. We show, through simulations that our proposed estimators are fairly robust to violations of the additivity assumption, and in general, there is benefit in leveraging information from all exposures.