Untangling the Relatedness among Correlations, Part III: Inter-Subject Correlation Analysis through Bayesian Multilevel Modeling for Naturalistic Scanning
Authors: Chen Gang , Taylor Paul A. , Qu Xianggui , Molfese Peter J. , Bandettini Peter A. , Cox Robert W. , Finn Emily S. 
Published: May 2019

While inter-subject correlation (ISC) analysis is a powerful tool for naturalistic scanning data, drawing appropriate statistical inferences is difficult due to the daunting task of accounting for the intricate relatedness in data structure as well as the intricacy of handling the multiple testing issue. In our previous work we proposed nonparametric approaches to performing group ISC analysis through bootstrapping for one group of subjects and permutation testing for two groups (Chen et al., 2016). A more flexible methodology is to parametrically build a linear mixed-effects (LME) model that captures the relatedness embedded in the data (Chen et al., 2017); in addition, the LME approach also has the capability of incorporating explanatory variables such as subject-grouping factors and quantitative covariates. However, the whole-brain LME modeling methodology still faces some challenges. When an LME model becomes sophisticated, it becomes difficult or even impossible to assign accurate degrees of freedom for each testing statistic. In addition, the typical correction methods for multiple testing through spatial extent tend to be over-penalizing, and dichotomous decisions through thresholding under null hypothesis significance testing (NHST) are controversial in general and equally problematic in neuroimaging as well. For instance, the popular practice of only reporting “statistically significant” results in neuroimaging not only wastes data information, but also distorts the full results as well as perpetuates the reproducibility crisis because of the fact that the difference between a “significant” result and a “non-significant” one is not necessarily significant.

Here we propose a Bayesian multilevel (BML) framework for ISC data analysis that integrates all the spatial elements (i.e., regions of interest) into one model. By loosely constraining the regions through a weakly informative prior, BML conservatively pools the effect of each region toward the center, and improves collective fitting and overall model performance. The BML paradigm leverages the commonality or similarity among brain regions and the information across multiple levels embedded in the hierarchical data structure instead of leveraging the spatial extent adopted in the conventional correction method for multiple testing. In addition to potentially achieving a higher inference efficiency than the conventional LME approach, BML improves spatial specificity and easily allows the investigator to adopt a philosophy of full results reporting (instead of dichotomizing into “significant” and “non-significant” results), thus minimizing loss of information while enhancing reproducibility. A dataset of naturalistic scanning is utilized to illustrate the modeling approach with 268 parcels and to showcase the modeling capability, flexibility and advantages in reports reporting. The associated program will be available as part of the AFNI suite for general use.