Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies
Tiffany A Nash,
Katherine M Reding,
Philip D Kohn,
Michael D Gregory,
Daniel P Eisenberg,
Robert W. Cox,
Karen F Berman,
J. Shane Kippenhan
Posted 02 Nov 2020
bioRxiv DOI: 10.1101/2020.11.01.363838
Posted 02 Nov 2020
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.
- Downloaded 443 times
- Download rankings, all-time:
- Site-wide: 104,418
- In neuroscience: 14,684
- Year to date:
- Site-wide: 112,124
- Since beginning of last month:
- Site-wide: 67,605
Downloads over time
Distribution of downloads per paper, site-wide
- 27 Nov 2020: The website and API now include results pulled from medRxiv as well as bioRxiv.
- 18 Dec 2019: We're pleased to announce PanLingua, a new tool that enables you to search for machine-translated bioRxiv preprints using more than 100 different languages.
- 21 May 2019: PLOS Biology has published a community page about Rxivist.org and its design.
- 10 May 2019: The paper analyzing the Rxivist dataset has been published at eLife.
- 1 Mar 2019: We now have summary statistics about bioRxiv downloads and submissions.
- 8 Feb 2019: Data from Altmetric is now available on the Rxivist details page for every preprint. Look for the "donut" under the download metrics.
- 30 Jan 2019: preLights has featured the Rxivist preprint and written about our findings.
- 22 Jan 2019: Nature just published an article about Rxivist and our data.
- 13 Jan 2019: The Rxivist preprint is live!