Statistics and Its Interface

Volume 10 (2017)

Number 2

Analysis of cortical morphometric variability using labeled cortical distance maps

Pages: 313 – 341

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n2.a13

Authors

E. Ceyhan (Department of Mathematics, Koç University, Sarıyer, Istanbul, Turkey)

T. Nishino (Department of Psychiatry, Washington University School of Medicine, St. Louis, Missouri, U.S.A.)

K. N. Botteron (Department of Psychiatry and Department of Radiology, Washington University School of Medicine, St. Louis, Missouri, U.S.A.)

M. I. Miller (Center for Imaging Science, Institute for Computational Medicine, and Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland, U.S.A.)

J. T. Ratnanather (Center for Imaging Science, Institute for Computational Medicine, and Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Abstract

Morphometric (i.e., shape and size) differences in the anatomy of cortical structures are associated with neurodevelopmental and neuropsychiatric disorders. Such differences can be quantized and detected by a powerful tool called Labeled Cortical Distance Map (LCDM). The LCDM method provides distances of labeled gray matter (GM) voxels from the GM/white matter (WM) surface for specific cortical structures (or tissues). Here we describe a method to analyze morphometric variability in the particular tissue using LCDM distances. To extract more of the information provided by LCDM distances, we perform pooling and censoring of LCDM distances. In particular, we employ Brown-Forsythe (BF) test of homogeneity of variance (HOV) on the LCDM distances. HOV analysis of pooled distances provides an overall analysis of morphometric variability of the LCDMs due to the disease in question, while the HOV analysis of censored distances suggests the location(s) of significant variation in these differences (i.e., at which distance from the GM/WM surface the morphometric variability starts to be significant). We also check for the influence of assumption violations on the HOV analysis of LCDM distances. In particular, we demonstrate that BF HOV test is robust to assumption violations such as the non-normality and within sample dependence of the residuals from the median for pooled and censored distances and are robust to data aggregation which occurs in analysis of censored distances. We recommend HOV analysis as a complementary tool to the analysis of distribution/location differences. We also apply the methodology on simulated normal and exponential data sets and assess the performance of the methods when more of the underlying assumptions are satisfied. We illustrate the methodology on a real data example, namely, LCDM distances of GM voxels in ventral medial prefrontal cortices (VMPFCs) to see the effects of depression or being of high risk to depression on the morphometry of VMPFCs. The methodology used here is also valid for morphometric analysis of other cortical structures.

Keywords

Brown–Forsythe test, censoring, computational anatomy, homogeneity of variance, pooled distances, simultaneous inference

2010 Mathematics Subject Classification

Primary 62H35. Secondary 62-07, 62F03, 62P10.

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