Spatial Nonparametric Mixed-Effects Model with Spatial-Varying Coefficients for Analysis of Populations

Abstract

Voxel-wise comparisons have been largely used in the analysis of populations to identify biomarkers for pathologies, disease progression, or to predict a treatment outcome. On the basis of a good interindividual spatial alignment, 3D maps are produced, allowing to localise regions where significant differences between groups exist. However, these techniques have received some criticism as they rely on conditions wich are not always met. Firstly, the results may be affected by misregistrations; secondly, the statistics behind the models assumes normally distributed data; finally, because of the size of the images, some strategies must be used to control for the rate of false detection. In this paper, we propose a spatial (3D) nonparametric mixed-effects model for population analysis. It overcomes some of the issues of classical voxel-based approaches, namely robustness to false positive rates, misregistrations and large variances between groups. Examples on numerical phantoms and real clinical data illustrate the feasiblity of the approach. An example of application within the development of voxel-wise predictive models of rectal toxicity in prostate cancer radiotherapy is presented. Results demonstrate an improved sensitivity and reliability for group analysis compared with standard voxel-wise methods and open the way for potential applications in computational anatomy.