A Unified Framework for Causal Estimand Selection

Music City Center 

Estimating the causal effect of a treatment with observational data can be challenging due to an imbalance of and a lack of overlap between treated and control covariate distributions. In the presence of limited overlap, researchers choose between 1) methods that imply traditional estimands (e.g., ATE) but whose estimators are at risk of considerable bias and variance; and 2) methods (e.g., overlap weighting) which imply a different estimand, thereby modifying the target population to reduce variance. We propose a framework for navigating the tradeoffs between variance and bias due to imbalance and lack of overlap and the targeting of the estimand of scientific interest. We introduce a bias decomposition that encapsulates bias due to 1) the statistical bias of the estimator; and 2) estimand mismatch, i.e., deviation from the population of interest. We propose two design-based metrics and an estimand selection procedure that illustrate the tradeoffs between these sources of bias and variance of the resulting estimators. We demonstrate how to select an estimand based on preferences between these characteristics with an application to right heart catheterization data.

average treatment effect

causal inference

inverse probability weighting

propensity score

target population 

Section on Statistics in Epidemiology