A local group differences test for subject-level multivariate density neuroimaging outcomes

Abstract

A great deal of neuroimaging research focuses on voxel-wise analysis or segmentation of damaged tissue, yet many diseases are characterized by diffuse or non-regional neuropathology. In simple cases, these processes can be quantified using summary statistics of voxel intensities. However, the manifestation of a disease process in imaging data is often unknown, or appears as a complex and nonlinear relationship between the voxel intensities on various modalities. When the relevant pattern is unknown, summary statistics are often unable to capture differences between disease groups, and their use may encourage post hoc searches for the optimal summary measure. In this study, we introduce the multi-modal density testing (MMDT) framework for the naive discovery of group differences in voxel intensity profiles. MMDT operationalizes multi-modal magnetic resonance imaging (MRI) data as multivariate subject-level densities of voxel intensities and utilizes kernel density estimation to develop a local two-sample test for individual points within the density space. Through simulations, we show that this method controls type I error and recovers relevant differences when applied to a specified point. Additionally, we demonstrate the ability to maintain power while controlling the family-wise error rate and false discovery rate when applying the test over a grid of points within the density space. Finally, we apply this method to a study of subjects with either multiple sclerosis (MS) or conditions that tend to mimic MS on MRI, and find significant differences between the two groups in their voxel intensity profiles within the thalamus.

Trial registration: ClinicalTrials.gov NCT00001246.

Keywords: High-dimensional data; Multivariate densities; Neuroimaging.

© The Author 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Figures

Fig. 1.

Design of the simulation studies. (A) Illustration of the voxel intensity generating distributions across values of . (B) Visualization of the expected group differences in densities across simulation scenarios. The first column shows the scenario in which values are drawn from the same beta distribution for subjects in group A and group B. Second, third, and fourth columns show the scenarios in which values are drawn from increasingly divergent beta distributions for subjects in Group A and Group B.

Fig. 2.

Type I error and power of MMDT applied to a single point. Columns represent the four simulation scenarios, in which values are either drawn from the same beta distribution for subjects from both groups (column 1) or increasingly divergent beta distributions (columns 2–4). Rows show the rate at which the local null hypothesis is rejected at four exemplary points in the density space. Rows 1 and 2 show points at which there is a true group difference in the generating distribution. Rows 3 and 4 show points at which there is no true group difference in the generating distribution. Each plot shows the rejection rate as a factor of the number of voxels per subject and the number of subjects per group.

Fig. 3.

Type I error and power of MMDT applied over a grid. Columns represent the four multiple comparison methods being compared. Row 1 shows the power for two exemplary points at which there is a true group difference in the data generating distribution. Row 2 shows the FWER (columns 1 and 2) and the FDR (columns 3 and 4) in the mixed null case, with the purple box highlighting the region of the density space at which there is no true group difference in the data generating distribution. Row 3 shows the FWER in the global null case, with the green box highlighting the full density space, across which there is no true group difference in the data generating distribution.

Fig. 4.

Application of the MMDT procedure for testing thalamic intensity profiles. (A) Visualization of four example subjects and their T1 and FLAIR volumes, with thalami highlighted in red. (B) Scatterplots and kernel density estimates for the subjects’ bivariate voxel intensity densities. (C) Results of the MMDT for detecting density differences between MS and non-MS (nMS) subjects. Top row shows the test-statistic map across the bivariate density, bottom row shows significant regions following Benjamini–Hochberg correction. (D) Example of MMDT test statistics being mapped back to subjects’ brain spaces for exploratory visualization.