Clusterwise Shape Regression Analysis for Monitoring Heterogeneous Normal Aging in Brain Subcortex

Music City Center 

Structural brain changes (such as alterations in volume and area) are typically associated with normal brain aging. Therefore, to monitor brain health, it is crucial to monitor the geometric variations of subcortical brain structures as early as possible. However, current statistical approaches in modeling such variations face several challenges, including (i) the non-Euclidean representation of 3D shapes; (ii) the complex spatial correlation structure in local geometry; (iii) subject-level imaging heterogeneity due to misalignment of shapes in imaging preprocessing steps; (iv) group-level imaging heterogeneity due to distinct brain aging patterns within normal controls; and (v) geometric variations associated with covariates of interest (e.g., gender and education length), which may be high-dimensional.
To address these challenges, we propose a Clusterwise Shape-on-scalar FActor Regression Model (CS-FARM). In each cluster, a geodesic regression structure including covariates of interest and alignment step is established along with the Riemannian Gaussian distribution in the pre-shape space, and a latent factor model is built in the tangent space. A penalized likelihood approach is used to implement the variable selection in CS-FARM. In addition, a Monte Carlo EM algorithm is provided for the parameter estimation procedure. Finally, both simulation studies and real data analysis based on 3D brain subcortical structures from two brain aging imaging studies are conducted to evaluate the finite sample performance of CS-FARM.