Spatial regression analysis of serial DTI for subject-specific longitudinal changes of neurodegenerative disease

Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging

Geostatistical modeling for continuous point-referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive-definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix-variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost-surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix-variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed-form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods.

Spatial regression analysis of MR diffusion reveals subject-specific white matter changes associated with repetitive head impacts in contact sports

Repetitive head impacts (RHI) are a growing concern due to their possible neurocognitive effects, with research showing a season of RHI produce white matter (WM) changes seen on neuroimaging. We conducted a secondary analysis of diffusion tensor imaging (DTI) data for 28 contact athletes to compare WM changes. We collected pre-season and post-season DTI scans for each subject, approximately 3 months apart. We collected helmet data for the athletes, which we correlated with DTI data. We adapted the SPatial REgression Analysis of DTI (SPREAD) algorithm to conduct subject-specific longitudinal DTI analysis, and developed global inferential tools using functional norms and a novel robust p value combination test. At the individual level, most detected injured regions (93.3%) were associated with decreased FA values. Using meta-analysis techniques to combine injured regions across subjects, we found the combined injured region at the group level occupied the entire WM skeleton, suggesting the WM damage location is subject-specific. Several subject-specific functional summaries of SPREAD-detected WM change, e.g., the [Formula: see text] norm, significantly correlated with helmet impact measures, e.g. cumulative unweighted rotational acceleration (adjusted p = 0.0049), time between hits rotational acceleration (adjusted p value 0.0101), and time until DTI rotational acceleration (adjusted p = 0.0084), suggesting RHIs lead to WM changes.

Highly efficient hypothesis testing methods for regression-type tests with correlated observations and heterogeneous variance structure

BACKGROUND

For many practical hypothesis testing (H-T) applications, the data are correlated and/or with heterogeneous variance structure. The regression t-test for weighted linear mixed-effects regression (LMER) is a legitimate choice because it accounts for complex covariance structure; however, high computational costs and occasional convergence issues make it impractical for analyzing high-throughput data. In this paper, we propose computationally efficient parametric and semiparametric tests based on a set of specialized matrix techniques dubbed as the PB-transformation. The PB-transformation has two advantages: 1. The PB-transformed data will have a scalar variance-covariance matrix. 2. The original H-T problem will be reduced to an equivalent one-sample H-T problem. The transformed problem can then be approached by either the one-sample Student's t-test or Wilcoxon signed rank test.

RESULTS

In simulation studies, the proposed methods outperform commonly used alternative methods under both normal and double exponential distributions. In particular, the PB-transformed t-test produces notably better results than the weighted LMER test, especially in the high correlation case, using only a small fraction of computational cost (3 versus 933 s). We apply these two methods to a set of RNA-seq gene expression data collected in a breast cancer study. Pathway analyses show that the PB-transformed t-test reveals more biologically relevant findings in relation to breast cancer than the weighted LMER test.

CONCLUSIONS

As fast and numerically stable replacements for the weighted LMER test, the PB-transformed tests are especially suitable for "messy" high-throughput data that include both independent and matched/repeated samples. By using our method, the practitioners no longer have to choose between using partial data (applying paired tests to only the matched samples) or ignoring the correlation in the data (applying two sample tests to data with some correlated samples). Our method is implemented as an R package 'PBtest' and is available at https://github.com/yunzhang813/PBtest-R-Package .