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Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies

View ORCID ProfileGang Chen, Tiffany A. Nash, Katherine M. Reding, Philip D. Kohn, Shau-Ming Wei, Michael D. Gregory, Daniel P. Eisenberg, Robert W. Cox, Karen F. Berman, J. Shane Kippenhan
doi: https://doi.org/10.1101/2020.11.01.363838
Gang Chen
aScientific and Statistical Computing Core, National Institute of Mental Health, USA
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  • For correspondence: gangchen@mail.nih.gov
Tiffany A. Nash
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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Katherine M. Reding
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
cSection on Behavioral Endocrinology, National Institute of Mental Health, USA
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Philip D. Kohn
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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Shau-Ming Wei
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
cSection on Behavioral Endocrinology, National Institute of Mental Health, USA
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Michael D. Gregory
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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Daniel P. Eisenberg
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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Robert W. Cox
aScientific and Statistical Computing Core, National Institute of Mental Health, USA
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Karen F. Berman
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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J. Shane Kippenhan
bSection on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA
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Abstract

The ubiquitous adoption of linearity for quantitative explanatory variables in statistical modeling is likely attributable to its advantages of straightforward interpretation and computational feasibility. The linearity assumption may be a reasonable approximation especially when the variable is confined within a narrow range, but it can be problematic when the variable’s effect is non-monotonic or complex. Furthermore, visualization and model assessment of a linear fit are usually omitted because of challenges at the whole brain level in neuroimaging. By adopting a principle of learning from the data in the presence of uncertainty to resolve the problematic aspects of conventional polynomial fitting, we introduce a flexible and adaptive approach of multilevel smoothing splines (MSS) to capture any nonlinearity of a quantitative explanatory variable for population-level neuroimaging data analysis. With no prior knowledge regarding the underlying relationship other than a parsimonious assumption about the extent of smoothness (e.g., no sharp corners), we express the unknown relationship with a sufficient number of smoothing splines and use the data to adaptively determine the specifics of the nonlinearity. In addition to introducing the theoretical framework of MSS as an efficient approach with a counterbalance between flexibility and stability, we strive to (a) lay out the specific schemes for population-level nonlinear analyses that may involve task (e.g., contrasting conditions) and subject-grouping (e.g., patients vs controls) factors; (b) provide modeling accommodations to adaptively reveal, estimate and compare any nonlinear effects of an explanatory variable across the brain, or to more accurately account for the effects (including nonlinear effects) of a quantitative confound; (c) offer the associated program 3dMSS to the neuroimaging community for whole-brain voxel-wise analysis as part of the AFNI suite; and (d) demonstrate the modeling approach and visualization processes with a longitudinal dataset of structural MRI scans.

Competing Interest Statement

The authors have declared no competing interest.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted January 15, 2021.
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Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies
Gang Chen, Tiffany A. Nash, Katherine M. Reding, Philip D. Kohn, Shau-Ming Wei, Michael D. Gregory, Daniel P. Eisenberg, Robert W. Cox, Karen F. Berman, J. Shane Kippenhan
bioRxiv 2020.11.01.363838; doi: https://doi.org/10.1101/2020.11.01.363838
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Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies
Gang Chen, Tiffany A. Nash, Katherine M. Reding, Philip D. Kohn, Shau-Ming Wei, Michael D. Gregory, Daniel P. Eisenberg, Robert W. Cox, Karen F. Berman, J. Shane Kippenhan
bioRxiv 2020.11.01.363838; doi: https://doi.org/10.1101/2020.11.01.363838

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