FEMA: Fast and efficient mixed-effects algorithm for large sample whole-brain imaging data

The linear mixed-effects model (LME) is a versatile approach to account for dependence among observations. Many large-scale neuroimaging datasets with complex designs have increased the need for LME; however LME has seldom been used in whole-brain imaging analyses due to its heavy computational requirements. In this paper, we introduce a fast and efficient mixed-effects algorithm (FEMA) that makes whole-brain vertex-wise, voxel-wise, and connectome-wide LME analyses in large samples possible. We validate FEMA with extensive simulations, showing that the estimates of the fixed effects are equivalent to standard maximum likelihood estimates but obtained with orders of magnitude improvement in computational speed. We demonstrate the applicability of FEMA by studying the cross-sectional and longitudinal effects of age on region-of-interest level and vertex-wise cortical thickness, as well as connectome-wide functional connectivity values derived from resting state functional MRI, using longitudinal imaging data from the Adolescent Brain Cognitive Development^SM Study release 4.0. Our analyses reveal distinct spatial patterns for the annualized changes in vertex-wise cortical thickness and connectome-wide connectivity values in early adolescence, highlighting a critical time of brain maturation. The simulations and application to real data show that FEMA enables advanced investigation of the relationships between large numbers of neuroimaging metrics and variables of interest while considering complex study designs, including repeated measures and family structures, in a fast and efficient manner. The source code for FEMA is available via: https://github.com/cmig-research-group/cmig_tools/.