Time series analysis is critical for understanding brain signals and their relationship to behavior and cognition. Cluster-based permutation tests (CBPT) are commonly used to analyze a variety of electrophysiological signals including EEG, MEG, ECoG, and sEEG data without assumptions about specific temporal effects. However, two major limitations of CBPT include the inability to directly analyze experiments with multiple fixed effects and the inability to account for random effects (e.g. variability across subjects). Here, we propose a flexible multi-step hypothesis testing strategy using CBPT with Linear Mixed Effects Models (LMEs) and Generalized Linear Mixed Effects Models (GLMEs) that can be applied to a wide range of experimental designs and data types. We first evaluate the statistical robustness of LMEs and GLMEs using simulated data distributions. Second, we apply a multi-step hypothesis testing strategy to analyze ERPs and broadband power signals extracted from human ECoG recordings collected during a simple image viewing experiment with image category and novelty as fixed effects. Third, we assess the statistical power differences between analyzing signals with CBPT using LMEs compared to CBPT using separate t-tests run on each fixed effect through simulations that emulate broadband power signals. Finally, we apply CBPT using GLMEs to high-gamma burst data to demonstrate the extension of the proposed method to the analysis of nonlinear data. First, we found that LMEs and GLMEs are robust statistical models. In simple simulations LMEs produced highly congruent results with other appropriately applied linear statistical models, but LMEs outperformed many linear statistical models in the analysis of “suboptimal” data and maintained power better than analyzing individual fixed effects with separate t-tests. GLMEs also performed similarly to other nonlinear statistical models. Second, in real world human ECoG data, LMEs performed at least as well as separate t-tests when applied to predefined time windows or when used in conjunction with CBPT. Additionally, fixed effects time courses extracted with CBPT using LMEs from group-level models of pseudo-populations replicated latency effects found in individual category-selective channels. Third, analysis of simulated broadband power signals demonstrated that CBPT using LMEs was superior to CBPT using separate t-tests in identifying time windows with significant fixed effects especially for small effect sizes. Lastly, the analysis of high-gamma burst data using CBPT with GLMEs produced results consistent with CBPT using LMEs applied to broadband power data. We propose a general approach for statistical analysis of electrophysiological data using CBPT in conjunction with LMEs and GLMEs. We demonstrate that this method is robust for experiments with multiple fixed effects and applicable to the analysis of linear nonlinear data. Our methodology maximizes the statistical power available in a dataset across multiple experimental variables while accounting for hierarchical random effects and controlling FWER across fixed effects. This approach substantially improves power leading to better reproducibility. Additionally, CBPT using LMEs and GLMEs can be used to analyze individual channels or pseudo-population data for the comparison of functional or anatomical groups of data.

中文翻译：

---

使用基于集群的 GLME 排列测试对人类 ECoG 数据进行灵活的多步骤假设检验

时间序列分析对于理解大脑信号及其与行为和认知的关系至关重要。基于聚类的排列测试 (CBPT) 通常用于分析各种电生理信号，包括 EEG、MEG、ECoG 和 sEEG 数据，无需假设特定的时间效应。然而，CBPT 的两个主要局限性包括无法直接分析具有多个固定效应的实验以及无法解释随机效应（例如受试者之间的变异性）。在这里，我们提出了一种灵活的多步骤假设检验策略，使用 CBPT 与线性混合效应模型 (LME) 和广义线性混合效应模型 (GLME)，可应用于广泛的实验设计和数据类型。我们首先使用模拟数据分布评估 LME 和 GLME 的统计稳健性。其次，我们应用多步骤假设检验策略来分析从人类 ECoG 记录中提取的 ERP 和宽带功率信号，这些记录是在简单的图像观看实验中收集的，其中图像类别和新颖性作为固定效应。第三，我们评估了使用 LME 的 CBPT 分析信号与通过模拟宽带功率信号的模拟对每个固定效应运行单独 t 检验的 CBPT 分析信号之间的统计功效差异。最后，我们将使用 GLME 的 CBPT 应用于高伽玛突发数据，以证明所提出的方法可扩展到非线性数据分析。首先，我们发现 LME 和 GLME 是稳健的统计模型。在简单的模拟中，LME 与其他适当应用的线性统计模型产生了高度一致的结果，但 LME 在分析“次优”数据方面优于许多线性统计模型，并且比使用单独的 t 检验分析个体固定效应更好地保持功效。 GLME 的表现也与其他非线性统计模型类似。其次，在现实世界的人类 ECoG 数据中，当应用于预定义的时间窗口或与 CBPT 结合使用时，LME 的表现至少与单独的 t 检验一样好。此外，使用 CBPT 使用 LME 从伪群体的群体级模型中提取的固定效应时间过程复制了单个类别选择通道中发现的延迟效应。第三，对模拟宽带功率信号的分析表明，在识别具有显着固定效应的时间窗口（特别是对于小效应大小）时，使用 LME 的 CBPT 优于使用单独 t 检验的 CBPT。最后，使用 CBPT 和 GLME 对高伽玛突发数据进行的分析产生的结果与使用 LME 应用于宽带功率数据的 CBPT 一致。我们提出了一种使用 CBPT 结合 LME 和 GLME 进行电生理数据统计分析的通用方法。我们证明该方法对于具有多个固定效应的实验具有鲁棒性，并且适用于线性非线性数据的分析。我们的方法最大化了多个实验变量数据集中可用的统计功效，同时考虑了分层随机效应并控制固定效应的 FWER。这种方法大大提高了功效，从而实现了更好的再现性。此外，使用 LME 和 GLME 的 CBPT 可用于分析单个通道或伪群体数据，以比较功能或解剖数据组。