GCS-fMRI Group, Koelliker Hospital and Department of Psychology, University of Turin, Turin, Italy.
FOCUS Laboratory, Department of Psychology, University of Turin, Via Verdi 10, 10124, Turin, Italy.
Neuroinformatics. 2023 Apr;21(2):365-374. doi: 10.1007/s12021-023-09626-6. Epub 2023 Mar 28.
Activation likelihood estimation (ALE) is among the most used algorithms to perform neuroimaging meta-analysis. Since its first implementation, several thresholding procedures had been proposed, all referred to the frequentist framework, returning a rejection criterion for the null hypothesis according to the critical p-value selected. However, this is not informative in terms of probabilities of the validity of the hypotheses. Here, we describe an innovative thresholding procedure based on the concept of minimum Bayes factor (mBF). The use of the Bayesian framework allows to consider different levels of probability, each of these being equally significant. In order to simplify the translation between the common ALE practice and the proposed approach, we analised six task-fMRI/VBM datasets and determined the mBF values equivalent to the currently recommended frequentist thresholds based on Family Wise Error (FWE). Sensitivity and robustness toward spurious findings were also analyzed. Results showed that the cutoff log(mBF) = 5 is equivalent to the FWE threshold, often referred as voxel-level threshold, while the cutoff log(mBF) = 2 is equivalent to the cluster-level FWE (c-FWE) threshold. However, only in the latter case voxels spatially far from the blobs of effect in the c-FWE ALE map survived. Therefore, when using the Bayesian thresholding the cutoff log(mBF) = 5 should be preferred. However, being in the Bayesian framework, lower values are all equally significant, while suggesting weaker level of force for that hypothesis. Hence, results obtained through less conservative thresholds can be legitimately discussed without losing statistical rigor. The proposed technique adds therefore a powerful tool to the human-brain-mapping field.
激活似然估计 (ALE) 是进行神经影像学荟萃分析最常用的算法之一。自首次实施以来，已经提出了几种阈值处理程序，所有这些程序都参考了频率主义框架，根据所选的临界 p 值返回对零假设的拒绝标准。然而，这在假设有效性的概率方面并没有提供信息。在这里，我们描述了一种基于最小贝叶斯因子 (mBF) 概念的创新阈值处理程序。贝叶斯框架的使用允许考虑不同概率水平，这些水平同样重要。为了简化常见 ALE 实践和所提出方法之间的翻译，我们分析了六个任务 fMRI/VBM 数据集，并根据总体错误 (FWE) 确定了与当前推荐的频率主义阈值等效的 mBF 值。还分析了对虚假发现的敏感性和稳健性。结果表明，log(mBF) = 5 的截止值与 FWE 阈值等效，通常称为体素水平阈值，而 log(mBF) = 2 的截止值与簇级 FWE (c-FWE) 阈值等效。然而，只有在后一种情况下，c-FWE ALE 映射中远离效应团的体素才得以幸存。因此，当使用贝叶斯阈值时，应首选 log(mBF) = 5 的截止值。然而，在贝叶斯框架中，所有较低的值都同样重要，同时暗示该假设的力度较弱。因此，可以合法地讨论通过不太保守的阈值获得的结果，而不会失去统计严谨性。所提出的技术为人脑映射领域增加了一个强大的工具。
