Adjusting for Confounders in Cross-correlation Analysis: an Application to Resting State Networks

Resting State Network (RSN) analysis investigates spontaneous brain activity when the brain is not subjected to any external stimuli. The interest in RSN analysis lies primarily in understanding the interaction between different brain regions that occur while the brain is “at rest”, i.e., not prompted by external tasks. The network of brain regions involved and their activity during the resting state has been found to be consistent across broad population and thus could be helpful in identifying aberrations in individual brains or effects of particular adverse events. Testing for functional consistency in RSN requires analysis of time series patterns for multiple time series signal emanating from the different brain regions. An approach for studying reproducibility is testing for stability in the cross-correlations function of the multiple time series signal. However, often the testing procedures do not adequately account for the temporal dependence in the signal and may lead to erroneous conclusion, particularly in the presence of confounder such as scan-to-scan and visit-to-visit variation. In this article, we develop a general paradigm for testing for such confounder in the cross-correlation analysis. Merit of the proposal is demonstrated via simulation and the proposed test is shown to have reasonable type I error and power under a variety of dependence structures for the multivariate signals. The methodology is then applied to the motivating data set involving a motor network and it is shown that unless properly controlled, confounders can significantly affect the test of reproducibility of the network. Once the analysis is adjusted for confounders, the findings reaffirm the conventional wisdom about reproducibility of RSN.