Beckmann Christian F, Jenkinson Mark, Smith Stephen M
Oxford Centre for Functional Magnetic Resonance Imaging of the Brain, Department of Clinical Neurology, University of Oxford, Oxford, OX3 9DU, UK.
Neuroimage. 2003 Oct;20(2):1052-63. doi: 10.1016/S1053-8119(03)00435-X.
This article discusses general modeling of multisubject and/or multisession FMRI data. In particular, we show that a two-level mixed-effects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the single-session level) can be made equivalent to a single complete mixed-effects model (where parameters of interest at the group level are estimated directly from all of the original single sessions' time series data) if the (co-)variance at the second level is set equal to the sum of the (co-)variances in the single-level form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis requires only values of the parameter estimates and their (co-)variance from the first level, generalizing the well-established "summary statistics" approach in FMRI. The simple and generalized framework allows different prewhitening and different first-level regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired t tests and F tests at the group level; explicit examples of such models are given in the article. Using numerical simulations based on typical first-level covariance structures from real FMRI data we demonstrate that by taking into account lower-level covariances and heterogeneity a substantial increase in higher-level Z score is possible.
本文讨论多主体和/或多会话功能磁共振成像（fMRI）数据的一般建模。具体而言，我们表明，如果使用具有已知协方差的最佳线性无偏估计（BLUE），将二级混合效应模型（其中组水平上的感兴趣参数是根据单会话水平的参数和方差估计来估计的）中的二级（协）方差设置为单水平形式的（协）方差之和，则该模型可以等效于单完整混合效应模型（其中组水平上的感兴趣参数是直接从所有原始单会话的时间序列数据中估计的）。这一结果对fMRI的组研究具有重要意义，因为它表明组分析仅需要一级的参数估计值及其（协）方差，推广了fMRI中成熟的“汇总统计”方法。这个简单且通用的框架允许对每个主体使用不同的预白化和不同的一级回归变量。该框架包含多个层次和情况，例如组水平上的重复测量、配对或非配对t检验以及F检验；本文给出了此类模型的具体示例。基于真实fMRI数据的典型一级协方差结构进行数值模拟，我们证明，通过考虑较低层次的协方差和异质性，有可能大幅提高较高层次的Z分数。
