Average Treatment Effect Estimation in Observational Studies with Functional Covariates

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.Comment: Section 3.1.1: added discussions and Remark 1.3; Section 3.1.2: added Eq. (5) and related discussions; Sections 5 and 6: added discussion