A1120
Title: Causal inference meets functional data: On the estimation of functional average and conditional treatment effects
Authors: Lorenzo Testa - Carnegie Mellon University (United States) [presenting]
Francesca Chiaromonte - The Pennsylvania State University (United States)
Edward Kennedy - Carnegie Mellon University (United States)
Tobia Boschi - The Pennsylvania State University (United States)
Filippo Salmaso - Sant Anna School of Advanced Studies (Italy)
Abstract: Understanding causal relationships is a central goal in science, but traditional methods often fall short when dealing with complex data. This challenge is pronounced in applications where outcomes are not simple scalars but are instead functions observed over a continuous domain. The purpose is to introduce a unified framework for causal inference with functional outcomes. The problem of estimating the Functional Average Treatment Effect (FATE) is addressed to understand the overall impact of an intervention across a population. The aim is to present a novel, doubly robust estimator that guarantees consistent estimation even if one of the underlying models -- either for treatment assignment or outcome -- is misspecified. Its theoretical properties are established, ensuring valid inference through the construction of simultaneous confidence bands. Building on this foundation, the more nuanced challenge of personalization is then tackled by estimating the functional conditional average treatment effect (F-CATE). A novel meta-learning framework is introduced, designed to uncover how functional treatment effects vary across individuals. This approach is also doubly robust, integrating advanced functional regression techniques to provide reliable, individualized causal insights. Across both problems, the robustness of the methods is demonstrated through simulations. Their real-world utility in uncovering meaningful causal effects from complex health data is illustrated.
