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.