Probability waves: adaptive cluster-based correction by convolution of p-value series from mass univariate analysis

dataset and Octave/MatLab codes/scripts for data analysis Background: Methods for p-value correction are criticized for either increasing Type II error or improperly reducing Type I error. This problem is worse when dealing with thousands or even hundreds of paired comparisons between waves or images which are performed point-to-point. This text considers patterns in probability vectors resulting from multiple point-to-point comparisons between two event-related potentials (ERP) waves (mass univariate analysis) to correct p-values, where clusters of signiticant p-values may indicate true H0 rejection. New method: We used ERP data from normal subjects and other ones with attention deficit hyperactivity disorder (ADHD) under a cued forced two-choice test to study attention. The decimal logarithm of the p-vector (p') was convolved with a Gaussian window whose length was set as the shortest lag above which autocorrelation of each ERP wave may be assumed to have vanished. To verify the reliability of the present correction method, we realized Monte-Carlo simulations (MC) to (1) evaluate confidence intervals of rejected and non-rejected areas of our data, (2) to evaluate differences between corrected and uncorrected p-vectors or simulated ones in terms of distribution of significant p-values, and (3) to empirically verify rate of type-I error (comparing 10,000 pairs of mixed samples whit control and ADHD subjects). Results: the present method reduced the range of p'-values that did not show covariance with neighbors (type I and also type-II errors). The differences between simulation or raw p-vector and corrected p-vectors were, respectively, minimal and maximal for window length set by autocorrelation in p-vector convolution. Comparison with existing methods: Our method was less conservative while FDR methods rejected basically all significant p-values for Pz and O2 channels. The MC simulations, gold-standard method for error correction, presented 2.78±4.83% of difference (all 20 channels) from p-vector after correction, while difference between raw and corrected p-vector was 5,96±5.00% (p = 0.0003). Conclusion: As a cluster-based correction, the present new method seems to be biological and statistically suitable to correct p-values in mass univariate analysis of ERP waves, which adopts adaptive parameters to set correction.用于数据分析的数据集及Octave/MatLab代码/脚本 背景：现有p值校正方法常因增加II类错误或不当降低I类错误而广受诟病。在针对数千乃至数百个逐点比对的波或图像开展成对比较时，该问题尤为突出。本研究针对两类事件相关电位（Event-related Potentials, ERP）波之间的逐点多重比较所得到的概率向量特征展开分析，以实现p值校正，其中显著p值的簇可用于指示真实的零假设（H0）拒绝。 新方法：我们采用正常受试者与注意缺陷多动障碍（Attention Deficit Hyperactivity Disorder, ADHD）受试者在提示性强制二选测试下的ERP数据开展注意力研究。将p向量的十进制对数值（p'）与高斯窗进行卷积，高斯窗长度设定为可认为各ERP波自相关已消失的最短滞后值。为验证本校正方法的可靠性，我们开展了蒙特卡洛模拟（Monte-Carlo Simulations, MC），具体包括：(1) 评估数据中被拒绝与未被拒绝区域的置信区间；(2) 从显著p值分布的维度，比较校正前后的p向量或模拟p向量之间的差异；(3) 经验证I类错误率（通过比对10000对混合了对照组与ADHD受试者的样本实现）。 结果：本方法缩小了未与邻域存在协方差的p'值范围（即I类与II类错误的发生范围）。当通过p向量卷积的自相关结果设置窗长时，模拟p向量与校正后p向量的差异最小，而原始p向量与校正后p向量的差异最大。 与现有方法的比较：本方法的保守性更低，而错误发现率（False Discovery Rate, FDR）方法几乎会拒绝Pz与O2通道的全部显著p值。作为误差校正的金标准方法，蒙特卡洛模拟结果显示，全部20个通道中，校正后的p向量与模拟结果的差异为2.78±4.83%，而原始p向量与校正后p向量的差异为5.96±5.00%（p=0.0003）。 结论：作为一种基于簇的校正方法，本新型方法在ERP波的批量单变量分析的p值校正中兼具生物学与统计学适用性，且采用自适应参数完成校正设置。