Primary Submission Category: Heterogeneous Treatment Effects
Tilted Intervention Effect and its Limiting Causal Estimand for Continuous Treatments
Authors: Yikun Zhang, Yen-Chi Chen, Andrea Rotnitzky,
Presenting Author: Yikun Zhang*
There is growing interest in the causal inference literature in defining causal estimands through stochastic, rather than static, interventions, motivated by both improved identifiability without strong positivity assumptions and greater flexibility in treatment assignment. In this paper, we study a causal estimand for continuous treatments induced by a class of stochastic interventions known as the tilted intervention, in which the estimand is identifiable without positivity. Specifically, our general tilted intervention framework unifies several constructions, including exponential, kernel-smoothed, Beta, Gamma, and weighted nearest neighbors tilting. The proposed estimand depends on a sensitivity parameter $hin [0,infty)$, allowing it to interpolate between the causal estimand under a static intervention and the mean outcome under no interventions. We further characterize the limiting behavior of the estimand under static interventions when positivity fails, yielding a generalized version of the G-computation formula with both causal and geometric interpretations. Finally, we develop estimation procedures for the tilted estimand and its limiting form, and establish their asymptotic properties.