Statistics and Its Interface

Volume 15 (2022)

Number 2

Average Treatment Effect Estimation in Observational Studies with Functional Covariates

Pages: 237 – 246



Rui Miao (George Washington University)

Wu Xue (George Washington University)

Xiaoke Zhang (George Washington University)


Functional data analysis is an important area in modern statistics and has been successfully applied in many fields. Although many scientific studies aim to find causations, a predominant majority of functional data analysis approaches can only reveal correlations. In this paper, average treatment effect estimation is studied for observational data with functional covariates. This paper generalizes various state-of-art propensity score estimation methods for multivariate data to functional data. The resulting average treatment effect estimators via propensity score weighting are numerically evaluated by a simulation study and applied to a real-world dataset to study the causal effect of duloxitine on the pain relief of chronic knee osteoarthritis patients.


functional principal component analysis, functional regression, direct modeling, covariate balancing, magnetic resonance imaging

2010 Mathematics Subject Classification

Primary 62G05. Secondary 62P10.

Received 27 February 2020

Accepted 15 August 2020

Published 11 January 2022