Detecting change in biological rhythms: A multivariate permutation test approach to Fourier-transformed data

Treatment-related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier-transformed data, we performed Monte Carlo simulations and compared statistical power and family-wise error for MPT to Bonferroni-corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni-corrected tests, while appropriately controlling family-wise error. We applied this method to human, pre- and post-treatment, serially-sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data.