Intrinsic Regression Models for Medial Representation of Subcortical Structures

The aim of this article is to develop a semiparametric model to describe the variability of the medial representation of subcortical structures, which belongs to a Riemannian manifold, and establish its association with covariates of interest, such as diagnostic status, age, and gender. We develop a two-stage estimation procedure to calculate the parameter estimates. The first stage is to calculate an intrinsic least squares estimator of the parameter vector using the annealing evolutionary stochastic approximation Monte Carlo algorithm, and then the second stage is to construct a set of estimating equations to obtain a more efficient estimate with the intrinsic least squares estimate as the starting point. We use Wald statistics to test linear hypotheses of unknown parameters and establish their limiting distributions. Simulation studies are used to evaluate the accuracy of our parameter estimates and the finite sample performance of the Wald statistics. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using a medial shape description. This article has online supplementary material.