Doubly Robust Triple Cross-Fit Estimation for Causal Inference with Imaging Data

Abstract This paper develops a novel doubly robust triple cross-fit estimator to estimate the average treatment effect (ATE) using observational and imaging data. The construction of the proposed estimator consists of two stages. The first stage extracts representative image features using the high-dimensional functional principal component analysis model. The second stage incorporates the image features into the propensity score and outcome models and then analyzes these models through machine learning algorithms. A doubly robust estimator for ATE is obtained based on the estimation results. In addition, we extend the double cross-fit to a triple cross-fit algorithm to accommodate the imaging data that typically exhibit more subtle variation and yield less stable estimation compared to conventional scalar variables. The simulation study demonstrates the satisfactory performance of the proposed estimator. An application to the Alzheimer’s Disease Neuroimaging Initiative dataset confirms the utility of our method.