Simultaneous Confidence Corridors for Mean Functions in Functional Data Analysis of Imaging Data

TL;DR

This paper introduces a new method for constructing simultaneous confidence corridors for mean functions in biomedical imaging data, using flexible bivariate splines on irregular domains, with proven consistency and asymptotic properties.

Contribution

It develops a novel spline-based approach for confidence corridors in imaging data analysis, accommodating irregular domains and extending to two-sample comparisons.

Findings

Method shows good finite-sample performance in simulations.

Applied successfully to brain PET imaging data.

Provides consistent and asymptotically normal estimators.

Abstract

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies we examine the finite-sample performance of the proposed method. Finally, the proposed method is applied to analyze brain Positron Emission Tomography (PET) data in two different studies. One dataset used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.