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

1902 

Abstract Submission 

Pravesh Parekh¹, Chun Chieh Fan^2,3, Oleksandr Frei¹, Clare Palmer³, Diana Smith³, Carolina Makowski³, John Iversen³, Diliana Pecheva³, Dominic Holland³, Robert Loughnan³, Pierre Nedelec⁴, Wesley Thompson², Donald Hagler Jr.³, Ole Andreassen¹, Terry Jernigan³, Thomas Nichols⁵, Anders Dale³

¹University of Oslo, Oslo, Norway, ²Laureate Institute for Brain Research, Tulsa, OK, ³University of California San Diego, San Diego, CA, ⁴University of California San Francisco, San Francisco, CA, ⁵University of Oxford, Oxford, United Kingdom

Pravesh Parekh  
University of Oslo
Oslo, Norway

Chun Chieh Fan  
Laureate Institute for Brain Research|University of California San Diego
Tulsa, OK|San Diego, CA

Oleksandr Frei  
University of Oslo
Oslo, Norway

Clare Palmer  
University of California San Diego
San Diego, CA

Diana Smith  
University of California San Diego
San Diego, CA

Carolina Makowski  
University of California San Diego
San Diego, CA

John Iversen  
University of California San Diego
San Diego, CA

Diliana Pecheva  
University of California San Diego
San Diego, CA

Dominic Holland  
University of California San Diego
San Diego, CA

Robert Loughnan  
University of California San Diego
San Diego, CA

Pierre Nedelec  
University of California San Francisco
San Francisco, CA

Wesley Thompson  
Laureate Institute for Brain Research
Tulsa, OK

Donald Hagler Jr.  
University of California San Diego
San Diego, CA

Ole Andreassen  
University of Oslo
Oslo, Norway

Terry Jernigan  
University of California San Diego
San Diego, CA

Thomas Nichols  
University of Oxford
Oxford, United Kingdom

Anders Dale  
University of California San Diego
San Diego, CA

The linear mixed effects (LME) model is a versatile approach for accounting for dependence between observations. In neuroimaging there are sources of such dependence, such as repeated measurements, family structure, or acquisition site. Not accounting for these covariance patterns can bias standard errors and inflate false positives. However, fitting LMEs for large sample data is computationally challenging. Therefore, there is a need within the neuroimaging community for efficient algorithms for fitting LMEs. We have developed Fast and Efficient Mixed-effects Algorithm (FEMA) that can perform whole-brain LME analyses in a matter of seconds to minutes without sacrificing estimation accuracy. Here, we will introduce FEMA, present its implementation details, and demonstrate its efficiency with respect to standard maximum likelihood (ML)-based solutions.

A LME estimates fixed effects regression coefficients and random effect variance parameters that capture the dependence. The FEMA estimation procedure starts with an ordinary least squares (OLS) estimation for the fixed effects, producing residuals. The residuals are expanded, creating cross products among all dependent measurements, and this expanded data is regressed on predictors expanded from the random effects design matrix. We then use a non-negativity constrained OLS to estimate these variance parameters. The variance parameters are quantized into discrete bins before the fixed effects coefficients are re-estimated with generalized least squares (GLS), where GLS uses the variance parameters to produce more efficient estimates and more accurate standard errors.

FEMA achieves computational efficiency due to i) use of a regression estimator, using the residual cross-products, for the estimation of variance parameters; ii) the binning of random effect parameters (which then allows) iii) the use of efficient vectorized operations over voxels/surface elements.

We have tested FEMA across a wide range of simulations and with real data from the Adolescent Brain Cognitive DevelopmentSM Study (ABCD Study®) and compared the estimates with standard ML estimates (fitlmematrix in MATLAB). Our results show that FEMA provides accurate estimates of fixed effects (Figure 1, top panel) in a fraction of computational time, compared to fitlmematrix or even fitlmematrix invoked in parallel.

As a function of number of observations (for 50 outcome variables), FEMA was between 3.8 to 27.1 times faster than MATLAB's fitlmematrix and between 1.3 and 8.7 times faster than the fitlmematrix called in parallel (Figure 2a-c). As a function of number of imaging variables (10,000 observations, up to five family members, and up to five repeated observations), FEMA was between 40.2 and 1020.6 times faster than fitlmematrix and 7.3 and 125 times faster than fitlmematrix called in parallel (Figure 2d). We were able to perform whole-brain vertex-wise cortical thickness analyses for ABCD Study in 11 seconds (6314 subjects, two time points, 18,742 vertices) and connectome-wide analyses in 54 seconds (4994 subjects, two time points, 169,071 pairs of connectivity values).

As an application of FEMA, we examined the effect of age on vertex-wise cortical thickness and resting state-derived connectivity values in the ABCD Study, which revealed interesting patterns of the longitudinal effect of age on cortical thickness and functional connectivity values (Figure 1, bottom panel).

We have developed an efficient solution for performing LME analyses for large sample sizes without compromising estimation accuracy. This opens the possibilities of novel biological applications such as examining neurodevelopmental trajectories, exploration of genetic factors underlying these trajectories, and performing linear and non-linear interaction analyses (of variables of interest like genetic variants) with age/time for longitudinal imaging variables. FEMA is available at: https://github.com/cmig-research-group/cmig_tools/.

Early life, Adolescence, Aging

Methods Development ¹

Univariate Modeling ²

Data analysis

FUNCTIONAL MRI

Modeling

Statistical Methods

STRUCTURAL MRI

Univariate

Other - longitudinal modeling