Modeling time-varying covariance with FEMA for large-scale longitudinal imaging and omics data
Poster No:
689
Submission Type:
Abstract Submission
Authors:
Pravesh Parekh1, Nadine Parker1, Evgeniia Frei1, Diana Smith2, Diliana Pecheva2, Carolina Makowski3, Piotr Jahołkowski1, Viktoria Birkenæs1, Nora Bakken1, Dennis Van der Meer1, Alexey Shadrin1, Thomas Nichols4, Oleksandr Frei1, Ole Andreassen1, Anders Dale3
Institutions:
1University of Oslo, Oslo, Oslo, 2University of California, San Diego, San Diego, CA, 3University of California San Diego, San Diego, CA, 4University of Oxford, Oxford, Oxfordshire
First Author:
Co-Author(s):
Introduction:
The linear mixed effects (LME) model is a versatile analytical approach for non-independent data (e.g., repeated measurements, related individuals). Fitting LMEs using standard tools is computationally prohibitive for voxel- or vertex-wise data. Recently, we presented a novel solution, the Fast and Efficient Mixed Effects Algorithm (FEMA; Parekh et al (2024)), which enables users to fit voxel- or vertex-wise LMEs in a matter of seconds to minutes. We have recently extended FEMA to support non-linear spline interactions and for performing imaging-genetics association analyses which can help capture time-dependent effects which are critical during phases like neurodevelopment and aging.
Conventionally, LMEs are only fit with random intercepts or at most random slopes for time. We have found that such restrictive assumptions lead to inflated false positives when fit to complex, multi-time point data such as the Adolescent Brain Cognitive Development (ABCD) Study. Here, we extend the FEMA framework to include time-varying random effects (or unstructured covariance), which not only improves estimation accuracy but also opens the door for novel discoveries, especially when performing imaging-genetics analyses.
Conventionally, LMEs are only fit with random intercepts or at most random slopes for time. We have found that such restrictive assumptions lead to inflated false positives when fit to complex, multi-time point data such as the Adolescent Brain Cognitive Development (ABCD) Study. Here, we extend the FEMA framework to include time-varying random effects (or unstructured covariance), which not only improves estimation accuracy but also opens the door for novel discoveries, especially when performing imaging-genetics analyses.
Methods:
Given an outcome measure (e.g., cortical thickness at a vertex), the LME specifies the variance in the outcome to be a combination of fixed effects (covariates), random effects (known grouping variables such as repeated measurement), and the error term. In FEMA, we compute the ordinary least squares residuals of the outcome measure and use it to estimate the variance components of the random effects using a regression estimator. Then, we re-estimate the fixed effects using generalized least squares (GLS) with the estimated variance parameters.
For imaging-genetics analyses, we use a two-stage modeling setup: first, fit a reduced model without the genetic variants; second, GLS residualize the variants and the outcome; and finally, fit a second model using these residuals. This leads to computationally fast estimates for imaging-genetics analyses. In addition, to perform non-linear interactions (say genetic variants interacting with age), we use natural cubic spline bases.
To model time-varying random effects and covariances between v repeated measurements ("visits"), for each pair of visits we perform the regression estimation of the random effects: if the visit IDs are the same, the estimates are the variances in the outcome (for that visit) explained by the known grouping; if the visit IDs are different, then the estimates are the covariances between two time points. Hence instead of a scalar variance for each random effect, we estimate v×(v-1) covariance values for each random effect (Figure 1, right), which we use for GLS estimation of the fixed effects. Importantly, this framework does not assume a balanced experimental design; different subjects may have differing number of repeated measurements.
For imaging-genetics analyses, we use a two-stage modeling setup: first, fit a reduced model without the genetic variants; second, GLS residualize the variants and the outcome; and finally, fit a second model using these residuals. This leads to computationally fast estimates for imaging-genetics analyses. In addition, to perform non-linear interactions (say genetic variants interacting with age), we use natural cubic spline bases.
To model time-varying random effects and covariances between v repeated measurements ("visits"), for each pair of visits we perform the regression estimation of the random effects: if the visit IDs are the same, the estimates are the variances in the outcome (for that visit) explained by the known grouping; if the visit IDs are different, then the estimates are the covariances between two time points. Hence instead of a scalar variance for each random effect, we estimate v×(v-1) covariance values for each random effect (Figure 1, right), which we use for GLS estimation of the fixed effects. Importantly, this framework does not assume a balanced experimental design; different subjects may have differing number of repeated measurements.
Results:
We have extended the methodology in FEMA to incorporate spline interactions as well as modeling time-varying covariances between random effects in an LME context. Using simulations, we show the importance of modeling these interaction terms and time varying random effects coefficients which lead to i) well-controlled type I error (Figure 2); ii) improved statistical power in imaging-genetics framework, and iii) more accurate parameter estimates. Additionally, we show results using cortical thickness data from the ABCD Study (release 6.0, up to four imaging visits).
Conclusions:
We have developed a software that enables users to perform accurate modeling of large-scale longitudinal neuroimaging data as well as perform imaging-genetics analyses. Our approach provides an expanded framework for accurately analyzing longitudinal data and can boost discovery of genetic variants associated with neuroimaging measures by allowing for non-linear interactions. FEMA is available at: https://github.com/cmig-research-group/cmig_tools.
Genetics:
Genetic Association Studies
Genetic Modeling and Analysis Methods 1
Modeling and Analysis Methods:
Methods Development
Univariate Modeling 2
Keywords:
Data analysis
Modeling
Statistical Methods
Univariate
Other - Longitudinal modeling; imaging-genetics; GWAS
1|2Indicates the priority used for review