Donders Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Kapittelweg 29, Nijmegen 6525 EN, the Netherlands; Department of Cognitive Neuroscience, Radboud University Medical Centre, Nijmegen, the Netherlands.
Donders Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Kapittelweg 29, Nijmegen 6525 EN, the Netherlands.
Neuroimage. 2021 Dec 15;245:118715. doi: 10.1016/j.neuroimage.2021.118715. Epub 2021 Nov 17.
Normative modelling is becoming more popular in neuroimaging due to its ability to make predictions of deviation from a normal trajectory at the level of individual participants. It allows the user to model the distribution of several neuroimaging modalities, giving an estimation for the mean and centiles of variation. With the increase in the availability of big data in neuroimaging, there is a need to scale normative modelling to big data sets. However, the scaling of normative models has come with several challenges. So far, most normative modelling approaches used Gaussian process regression, and although suitable for smaller datasets (up to a few thousand participants) it does not scale well to the large cohorts currently available and being acquired. Furthermore, most neuroimaging modelling methods that are available assume the predictive distribution to be Gaussian in shape. However, deviations from Gaussianity can be frequently found, which may lead to incorrect inferences, particularly in the outer centiles of the distribution. In normative modelling, we use the centiles to give an estimation of the deviation of a particular participant from the 'normal' trend. Therefore, especially in normative modelling, the correct estimation of the outer centiles is of utmost importance, which is also where data are sparsest. Here, we present a novel framework based on Bayesian linear regression with likelihood warping that allows us to address these problems, that is, to correctly model non-Gaussian predictive distributions and scale normative modelling elegantly to big data cohorts. In addition, this method provides likelihood-based statistics, which are useful for model selection. To evaluate this framework, we use a range of neuroimaging-derived measures from the UK Biobank study, including image-derived phenotypes (IDPs) and whole-brain voxel-wise measures derived from diffusion tensor imaging. We show good computational scaling and improved accuracy of the warped BLR for certain IDPs and voxels if there was a deviation from normality of these parameters in their residuals. The present results indicate the advantage of a warped BLR in terms of; computational scalability and the flexibility to incorporate non-linearity and non-Gaussianity of the data, giving a wider range of neuroimaging datasets that can be correctly modelled.
规范建模由于能够对个体参与者水平上偏离正常轨迹的情况进行预测，因此在神经影像学中越来越受欢迎。它允许用户对几种神经影像学模式进行建模，从而对变异性的均值和百分位数进行估计。随着神经影像学中大批量数据的可用性的增加，需要将规范建模扩展到大数据集。但是，规范模型的扩展带来了一些挑战。到目前为止，大多数规范建模方法都使用高斯过程回归，虽然适用于较小的数据集（最多几千个参与者），但不适用于当前可用和正在获取的大型队列。此外，大多数可用的神经影像学建模方法都假设预测分布呈高斯形状。然而，经常会发现偏离高斯性的情况，这可能导致不正确的推断，尤其是在分布的外百分位数。在规范建模中，我们使用百分位数来估计特定参与者与“正常”趋势的偏差。因此，特别是在规范建模中，正确估计外百分位数至关重要，而外百分位数的数据也最稀疏。在这里，我们提出了一个基于贝叶斯线性回归和似然扭曲的新框架，该框架允许我们解决这些问题，即正确地对非高斯预测分布进行建模，并优雅地将规范建模扩展到大批量数据队列。此外，该方法提供基于似然的统计信息，这些信息对于模型选择很有用。为了评估这个框架，我们使用了来自 UK Biobank 研究的一系列神经影像学衍生测量值，包括图像衍生表型（IDP）和来自扩散张量成像的全脑体素测量值。我们发现，如果这些参数的残差偏离正态分布，则扭曲的 BLR 在某些 IDP 和体素上具有良好的计算可扩展性和准确性。目前的结果表明，扭曲的 BLR 在计算可扩展性方面具有优势，并且具有灵活性，可以纳入数据的非线性和非高斯性，从而可以正确建模更广泛的神经影像学数据集。
