Bootstrapped Permutation Test for Multiresponse Inference on Brain Behavior Associations

Abstract

Despite that diagnosis of neurological disorders commonly involves a collection of behavioral assessments, most neuroimaging studies investigating the associations between brain and behavior largely analyze each behavioral measure in isolation. To jointly model multiple behavioral scores, sparse multiresponse regression (SMR) is often used. However, directly applying SMR without statistically controlling for false positives could result in many spurious findings. For models, such as SMR, where the distribution of the model parameters is unknown, permutation test and stability selection are typically used to control for false positives. In this paper, we present another technique for inferring statistically significant features from models with unknown parameter distribution. We refer to this technique as bootstrapped permutation test (BPT), which uses Studentized statistics to exploit the intuition that the variability in parameter estimates associated with relevant features would likely be higher with responses permuted. On synthetic data, we show that BPT provides higher sensitivity in identifying relevant features from the SMR model than permutation test and stability selection, while retaining strong control on the false positive rate. We further apply BPT to study the associations between brain connectivity estimated from pseudo-rest fMRI data of 1139 fourteen year olds and behavioral measures related to ADHD. Significant connections are found between brain networks known to be implicated in the behavioral tasks involved. Moreover, we validate the identified connections by fitting a regression model on pseudo-rest data with only those connections and applying this model on resting state fMRI data of 337 left out subjects to predict their behavioral scores. The predicted scores significantly correlate with the actual scores, hence verifying the behavioral relevance of the found connections.