Scientific and Statistical Computing Core, National Institute of Mental Health, USA.
Section on Integrative Neuroimaging, Clinical and Translational Neuroscience Branch, National Institute of Mental Health, USA.
Neuroimage. 2021 Jun;233:117891. doi: 10.1016/j.neuroimage.2021.117891. Epub 2021 Mar 3.
The ubiquitous adoption of linearity for quantitative predictors 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 predictor 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 a predictor 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.
在统计建模中，对定量预测因子采用线性方法可能是由于其具有易于解释和计算可行性的优点。在线性假设下，当变量在较窄的范围内时，这种假设可能是合理的近似，但当变量的效应是非单调或复杂时，就会出现问题。此外，由于神经影像学中存在全脑水平的挑战，线性拟合的可视化和模型评估通常被省略。通过采用在存在不确定性的情况下从数据中学习的原则来解决传统多项式拟合的问题方面，我们引入了一种灵活的、自适应的多层次平滑样条（MSS）方法，以捕捉群体水平神经影像学数据分析中定量预测因子的任何非线性。除了在尽可能少地假设平滑程度（例如，没有尖锐的拐角）之外，我们对潜在关系没有任何先验知识，而是用足够数量的平滑样条来表示未知的关系，并使用数据自适应地确定非线性的具体细节。除了介绍 MSS 作为一种在灵活性和稳定性之间取得平衡的有效方法的理论框架外，我们还努力：（a）制定可能涉及任务（例如，对比条件）和被试分组（例如，患者与对照）因素的群体水平非线性分析的具体方案；（b）提供建模适应，以自适应地揭示、估计和比较预测因子在大脑中的任何非线性效应，或者更准确地解释（包括非线性效应）定量混杂因素的效应；（c）为神经影像学社区提供相关程序 3dMSS，作为 AFNI 套件的一部分，用于全脑体素分析；（d）用结构 MRI 扫描的纵向数据集演示建模方法和可视化过程。
