Average treatment effect on the treated, under lack of positivity

Understand

The use of propensity score (PS) methods has become ubiquitous in causal inference.

• At the heart of these methods is the positivity assumption.
• Violation of the positivity assumption leads to the presence of extreme PS weights when estimating average causal effects of interest, such as the average treatment effect (ATE) or the average treatment effect on the treated (ATT), which renders invalid related statistical inference.
• To circumvent this issue, trimming or truncating the extreme estimated PSs have been widely used.