PROFIT: Projection-based Test in Longitudinal Functional Data

TL;DR

This paper introduces PROFIT, a new projection-based statistical test for assessing whether the mean function in longitudinal functional data changes over time, combining dimension reduction with likelihood testing.

Contribution

It presents a novel, efficient methodology for testing mean function variation in longitudinal functional data using data-driven projections and likelihood-based hypothesis testing.

Findings

Maintains correct type I error rate in simulations.

Exhibits high power to detect mean function changes.

Successfully applied to MS brain imaging data.

Abstract

In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function varies over time. Our approach relies on reducing the dimension of the response using data-driven orthogonal projections and it employs a likelihood-based hypothesis testing. We investigate the methodology theoretically and discuss a computationally efficient implementation. The proposed test maintains the type I error rate, and shows excellent power to detect departures from the null hypothesis in finite sample simulation studies. We apply our method to the longitudinal diffusion tensor imaging study of multiple sclerosis (MS) patients to formally assess whether the brain's health tissue, as summarized by fractional anisotropy (FA) profile, degrades over time during the study period.