Diffusion tensor image (DTI) is a powerful tool for quantitatively assessing the integrity of anatomical connectivity
in white matter in clinical populations. The prevalent methods for group-level analysis of DTI are statistical
analyses of invariant measures (e.g., fractional anisotropy) and principal directions across groups. The invariant
measures and principal directions, however, do not capture all information in full diffusion tensor, which can
decrease the statistical power of DTI in detecting subtle changes of white matters. Thus, it is very desirable to
develop new statistical methods for analyzing full diffusion tensors.
In this paper, we develop a set of toolbox, called RADTI, for the analysis of the full diffusion tensors as
responses and establish their association with a set of covariates. The key idea is to use the recent development
of log-Euclidean metric and then transform diffusion tensors in a nonlinear space into their matrix logarithms
in a Euclidean space. Our regression model is a semiparametric model, which avoids any specific parametric
assumptions. We develop an estimation procedure and a test procedure based on score statistics and a resampling
method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest.
Monte Carlo simulations are used to examine the finite sample performance of the test procedure for controlling
the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic and
age effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus.
A novel hierarchical unbiased group-wise registration is developed to robustly transform each individual image towards
a common space for atlas based analysis. This hierarchical group-wise registration approach consists of two main
components, (1) data clustering to group similar images together and (2) unbiased group-wise registration to generate a
mean image for each cluster. The mean images generated in the lower hierarchical level are regarded as the input
images for the higher hierarchy. In the higher hierarchical level, these input images will be further clustered and then
registered by using the same two components mentioned. This hierarchical bottom-up clustering and within-cluster
group-wise registration is repeated until a final mean image for the whole population is formed. This final mean image
represents the common space for all the subjects to be warped to in order for the atlas based analysis. Each individual
image at the bottom of the constructed hierarchy is transformed towards the root node through concatenating all the
intermediate displacement fields. In order to evaluate the performance of the proposed hierarchical registration in atlas
based statistical analysis, comparisons were made with the conventional group-wise registration in detecting simulated
brain atrophy as well as fractional anisotropy differences between neonates and 1-year-olds. In both cases, the proposed
approach demonstrated improved sensitivity (higher t-scores) than the conventional unbiased registration approach.
Longitudinal imaging studies are essential to understanding the neural development of neuropsychiatric disorders,
substance use disorders, and normal brain. Using appropriate image processing and statistical tools to analyze
the imaging, behavioral, and clinical data is critical for optimally exploring and interpreting the findings from
those imaging studies. However, the existing imaging processing and statistical methods for analyzing imaging
longitudinal measures are primarily developed for cross-sectional neuroimaging studies. The simple use of these
cross-sectional tools to longitudinal imaging studies will significantly decrease the statistical power of longitudinal
studies in detecting subtle changes of imaging measures and the causal role of time-dependent covariate in disease
process.
The main objective of this paper is to develop longitudinal statistics toolbox, called LSTGEE, for the analysis
of neuroimaging data from longitudinal studies. We develop generalized estimating equations for jointly modeling
imaging measures with behavioral and clinical variables from longitudinal studies. We develop a test procedure
based on a score test statistic and a resampling method to test linear hypotheses of unknown parameters,
such as associations between brain structure and function and covariates of interest, such as IQ, age, gene,
diagnostic groups, and severity of disease. We demonstrate the application of our statistical methods to the
detection of the changes of the fractional anisotropy across time in a longitudinal neonate study. Particularly,
our results demonstrate that the use of longitudinal statistics can dramatically increase the statistical power in
detecting the changes of neuroimaging measures. The proposed approach can be applied to longitudinal data
with multiple outcomes and accommodate incomplete and unbalanced data, i.e., subjects with different number
of measurements.
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