The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, UCL, London, UK.
Neuroimage. 2011 Jun 1;56(3):1072-81. doi: 10.1016/j.neuroimage.2011.02.072. Epub 2011 Mar 17.
We address the problem of controlling false positive rates in mass-multivariate tests for electromagnetic responses in compact regions of source space. We show that mass-univariate thresholds based on sensor level multivariate thresholds (approximated using Roy's union-intersection principle) are unduly conservative. We then consider a Bonferroni correction for source level tests based on the number of unique lead-field extrema. For a given source space, the sensor indices corresponding to the maxima and minima (for each dipolar lead field) are listed, and the number of unique extrema is given by the number of unique pairs in this list. Using a multivariate beamformer formulation, we validate this heuristic against empirical permutation thresholds for mass-univariate and mass-multivariate tests (of induced and evoked responses) for a variety of source spaces, using simulated and real data. We also show that the same approximations hold when dealing with a cortical manifold (rather than a volume) and for mass-multivariate minimum norm solutions. We demonstrate that the mass-multivariate framework is not restricted to tests on a single contrast of effects (cf, Roy's maximum root) but also accommodates multivariate effects (cf, Wilk's lambda).
我们解决了在源空间紧凑区域中控制电磁响应的大规模多元测试中假阳性率的问题。我们表明，基于传感器水平多元阈值的大规模单变量阈值（使用 Roy 的并交原理近似）过于保守。然后，我们考虑了基于独特导联场极值数量的源水平测试的 Bonferroni 校正。对于给定的源空间，列出了与最大值和最小值（对于每个偶极导联场）相对应的传感器指数，并且唯一极值的数量由该列表中唯一对的数量给出。使用多元波束形成公式，我们针对各种源空间的感应和诱发响应的大规模单变量和大规模多元测试（使用模拟和真实数据），根据经验置换阈值验证了这种启发式方法。我们还表明，当处理皮质流形（而不是体积）和大规模多元最小范数解时，相同的近似也成立。我们证明了大规模多元框架不仅限于单个效果对比的测试（参照 Roy 的最大根），还可以容纳多元效果（参照 Wilk 的 lambda）。
