Functional-mixed effects models for candidate genetic mapping in imaging genetic studies.

The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.