Kim Junghi, Wozniak Jeffrey R, Mueller Bryon A, Pan Wei
1 Division of Biostatistics, School of Public Health, University of Minnesota , Minneapolis, Minnesota.
Brain Connect. 2015 May;5(4):214-31. doi: 10.1089/brain.2014.0319. Epub 2015 Feb 25.
Resting-state functional magnetic resonance imaging allows one to study brain functional connectivity, partly motivated by evidence that patients with complex disorders, such as Alzheimer's disease, may have altered functional brain connectivity patterns as compared with healthy subjects. A functional connectivity network describes statistical associations of the neural activities among distinct and distant brain regions. Recently, there is a major interest in group-level functional network analysis; however, there is a relative lack of studies on statistical inference, such as significance testing for group comparisons. In particular, it is still debatable which statistic should be used to measure pairwise associations as the connectivity weights. Many functional connectivity studies have used either (full or marginal) correlations or partial correlations for pairwise associations. This article investigates the performance of using either correlations or partial correlations for testing group differences in brain connectivity, and how sparsity levels and topological structures of the connectivity would influence statistical power to detect group differences. Our results suggest that, in general, testing group differences in networks deviates from estimating networks. For example, high regularization in both covariance matrices and precision matrices may lead to higher statistical power; in particular, optimally selected regularization (e.g., by cross-validation or even at the true sparsity level) on the precision matrices with small estimation errors may have low power. Most importantly, and perhaps surprisingly, using either correlations or partial correlations may give very different testing results, depending on which of the covariance matrices and the precision matrices are sparse. Specifically, if the precision matrices are sparse, presumably and arguably a reasonable assumption, then using correlations often yields much higher powered and more stable testing results than using partial correlations; the conclusion is reversed if the covariance matrices, not the precision matrices, are sparse. These results may have useful implications to future studies on testing functional connectivity differences.
静息态功能磁共振成像使人们能够研究大脑功能连接，部分原因是有证据表明，患有诸如阿尔茨海默病等复杂疾病的患者与健康受试者相比，其大脑功能连接模式可能发生了改变。功能连接网络描述了不同且遥远的脑区之间神经活动的统计关联。最近，人们对组水平的功能网络分析产生了浓厚兴趣；然而，关于统计推断的研究相对较少，例如用于组间比较的显著性检验。特别是，对于应使用哪种统计量来测量作为连接权重的成对关联仍存在争议。许多功能连接研究在成对关联中使用了（完全或边际）相关性或偏相关性。本文研究了使用相关性或偏相关性来检验大脑连接性组间差异的性能，以及连接性的稀疏水平和拓扑结构如何影响检测组间差异的统计功效。我们的结果表明，一般来说，检验网络中的组间差异与估计网络有所不同。例如，协方差矩阵和精度矩阵中的高正则化可能会导致更高的统计功效；特别是，在估计误差较小的精度矩阵上进行最优选择的正则化（例如通过交叉验证甚至在真实稀疏水平上）可能功效较低。最重要的是，也许令人惊讶的是，使用相关性或偏相关性可能会给出非常不同的检验结果，这取决于协方差矩阵和精度矩阵哪一个是稀疏的。具体而言，如果精度矩阵是稀疏的，大概且可以说是一个合理的假设，那么使用相关性通常会比使用偏相关性产生更高功效且更稳定的检验结果；如果是协方差矩阵而不是精度矩阵是稀疏的，结论则相反。这些结果可能对未来关于检验功能连接差异的研究具有有益的启示。
