Standard multiscale entropy reflects spectral power at mismatched temporal scales: What’s signal irregularity got to do with it?

Multiscale Entropy (MSE) is used to characterize the temporal irregularity of neural time series patterns. Due to its’ presumed sensitivity to non-linear signal characteristics, MSE is typically considered a complementary measure of brain dynamics to signal variance and spectral power. However, the divergence between these measures is often unclear in application. Furthermore, it is commonly assumed (yet sparingly verified) that entropy estimated at specific time scales reflects signal irregularity at those precise time scales of brain function. We argue that such assumptions are not tenable. Using simulated and empirical electroencephalogram (EEG) data from 47 younger and 52 older adults, we indicate strong and previously underappreciated associations between MSE and spectral power, and highlight how these links preclude traditional interpretations of MSE time scales. Specifically, we show that the typical definition of temporal patterns via “similarity bounds” biases coarse MSE scales – that are thought to reflect slow dynamics – by high-frequency dynamics. Moreover, we demonstrate that entropy at fine time scales – presumed to indicate fast dynamics – is highly sensitive to broadband spectral power, a measure dominated by low-frequency contributions. Jointly, these issues produce counterintuitive reflections of frequency-specific content on MSE time scales. We emphasize the resulting inferential problems in a conceptual replication of cross-sectional age differences at rest, in which scale-specific entropy age effects could be explained by spectral power differences at mismatched temporal scales. Furthermore, we demonstrate how such problems may be alleviated, resulting in the indication of scale-specific age differences in rhythmic irregularity. By controlling for narrowband contributions, we indicate that spontaneous alpha rhythms during eyes open rest transiently reduce broadband signal irregularity. Finally, we recommend best practices that may better permit a valid estimation and interpretation of neural signal irregularity at time scales of interest. Author Summary Brain signals exhibit a wealth of dynamic patterns that that are thought to reflect ongoing neural computations. Multiscale sample entropy (MSE) intends to describe the temporal irregularity of such patterns at multiple time scales of brain function. However, the notion of time scales may often be unintuitive. In particular, traditional implementations of MSE are sensitive to slow fluctuations at fine time scales, and fast dynamics at coarse time scales. This conceptual divergence is often overlooked and may lead to difficulties in establishing the unique contribution of MSE to effects of interest over more established spectral power. Using simulations and empirical data, we highlight these issues and provide evidence for their relevance for valid practical inferences. We further highlight that standard MSE and traditional spectral power are highly collinear in our example. Finally, our analyses indicate that spectral filtering can be used to estimate temporal signal irregularity at matching and intuitive time scales. To guide future studies, we make multiple recommendations based on our observations. We believe that following these suggestions may advance our understanding of the unique contributions of neural signal irregularity to neural and cognitive function across the lifespan.