Bayesian Covariate Selection in Mixed-Effects Models For Longitudinal Shape Analysis.

The goal of longitudinal shape analysis is to understand how anatomical shape changes over time, in response to biological processes, including growth, aging, or disease. In many imaging studies, it is also critical to understand how these shape changes are affected by other factors, such as sex, disease diagnosis, IQ, etc. Current approaches to longitudinal shape analysis have focused on modeling age-related shape changes, but have not included the ability to handle covariates. In this paper, we present a novel Bayesian mixed-effects shape model that incorporates simultaneous relationships between longitudinal shape data and multiple predictors or covariates to the model. Moreover, we place an Automatic Relevance Determination (ARD) prior on the parameters, that lets us automatically select which covariates are most relevant to the model based on observed data. We evaluate our proposed model and inference procedure on a longitudinal study of Huntington's disease from PREDICT-HD. We first show the utility of the ARD prior for model selection in a univariate modeling of striatal volume, and next we apply the full high-dimensional longitudinal shape model to putamen shapes.

Diffeomorphic shape trajectories for improved longitudinal segmentation and statistics.

Longitudinal imaging studies involve tracking changes in individuals by repeated image acquisition over time. The goal of these studies is to quantify biological shape variability within and across individuals, and also to distinguish between normal and disease populations. However, data variability is influenced by outside sources such as image acquisition, image calibration, human expert judgment, and limited robustness of segmentation and registration algorithms. In this paper, we propose a two-stage method for the statistical analysis of longitudinal shape. In the first stage, we estimate diffeomorphic shape trajectories for each individual that minimize inconsistencies in segmented shapes across time. This is followed by a longitudinal mixed-effects statistical model in the second stage for testing differences in shape trajectories between groups. We apply our method to a longitudinal database from PREDICT-HD and demonstrate our approach reduces unwanted variability for both shape and derived measures, such as volume. This leads to greater statistical power to distinguish differences in shape trajectory between healthy subjects and subjects with a genetic biomarker for Huntington's disease (HD).

Mixed-Effects Shape Models for Estimating Longitudinal Changes in Anatomy.

In this paper, we propose a new method for longitudinal shape analysis that fits a linear mixed-effects model, while simultaneously optimizing correspondences on a set of anatomical shapes. Shape changes are modeled in a hierarchical fashion, with the global population trend as a fixed effect and individual trends as random effects. The statistical significance of the estimated trends are evaluated using specifically designed permutation tests. We also develop a permutation test based on the Hotelling T2 statistic to compare the average shapes trends between two populations. We demonstrate the benefits of our method on a synthetic example of longitudinal tori and data from a developmental neuroimaging study.

Sasaki Metrics for Analysis of Longitudinal Data on Manifolds.

Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T 2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.