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Title: "A Natural Projection for Functional Sliced Inverse Regression with Applications to the Chronic Renal Insufficiency Cohort Study"

Abstract:
We propose a natural projection for functional data in carrying out functional sliced inverse regression (FSIR). Sliced Inverse Regression is a popular supervised dimension reduction tool with numerous extensions, including to functional data. We prove consistency of our estimator with conventional non-parametric rates. The motivation for our proposal is to leverage the functional nature of routine electrocardiograms (ECGs) collected in patients with chronic kidney disease (CKD), in order to identify features that can characterize increased risks of adverse events, such as atrial fibrillation and heart failure (HF). Our natural projection for FSIR demonstrates potential for identifying single-lead ECG features for HF with preserved ejection fraction (HFpEF) and HF with reduced ejection fraction (HFrEF). In validation, we found the longitudinal changes of these identified features differed between HFpEF, HFrEF and healthy individuals, demonstrating potential as a longitudinal tracker of subtle changes in ECG patterns.