Wellcome Trust Centre for Neuroimaging, London, UK.
Neuroimage. 2010 Feb 15;49(4):3057-64. doi: 10.1016/j.neuroimage.2009.10.090. Epub 2009 Nov 24.
In this technical note, we describe and validate a topological false discovery rate (FDR) procedure for statistical parametric mapping. This procedure is designed to deal with signal that is continuous and has, in principle, unbounded spatial support. We therefore infer on topological features of the signal, such as the existence of local maxima or peaks above some threshold. Using results from random field theory, we assign a p-value to each maximum in an SPM and identify an adaptive threshold that controls false discovery rate, using the Benjamini and Hochberg (BH) procedure (1995). This provides a natural complement to conventional family wise error (FWE) control on local maxima. We use simulations to contrast these procedures; both in terms of their relative number of discoveries and their spatial accuracy (via the distribution of the Euclidian distance between true and discovered activations). We also assessed two other procedures: cluster-wise and voxel-wise FDR procedures. Our results suggest that (a) FDR control of maxima or peaks is more sensitive than FWE control of peaks with minimal cost in terms of false-positives, (b) voxel-wise FDR is substantially less accurate than topological FWE or FDR control. Finally, we present an illustrative application using an fMRI study of visual attention.
在本技术说明中，我们描述并验证了统计参数映射的拓扑假发现率 (FDR) 方法。该方法旨在处理具有连续信号和理论上无界空间支持的信号。因此，我们推断信号的拓扑特征，例如存在超过某个阈值的局部最大值或峰。使用随机场理论的结果，我们为 SPM 中的每个最大值分配一个 p 值，并使用 Benjamini 和 Hochberg (BH) 方法（1995 年）确定控制 FDR 的自适应阈值。这为传统的基于簇的错误率 (FWE) 控制局部最大值提供了自然的补充。我们使用模拟来对比这些方法；包括它们的发现数量和空间准确性（通过真激活和发现激活之间的欧几里得距离分布）。我们还评估了另外两种方法：基于簇和体素的 FDR 方法。我们的结果表明：(a) 与基于峰的 FWE 控制相比，基于最大值或峰的 FDR 控制在假阳性方面具有更高的敏感性和更低的代价，(b) 体素级 FDR 的准确性远低于拓扑 FWE 或 FDR 控制。最后，我们使用视觉注意力的 fMRI 研究提供了一个说明性的应用。
