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

Abstract:

The (ir)regularity of neural time series patterns as assessed via Multiscale Sample Entropy (MSE; e.g., Costa et al., 2002) has been proposed as a complementary measure to signal variance, but the con- and divergence between these measures often remains unclear in applications. Importantly, the estimation of sample entropy is referenced to the magnitude of fluctuations, leading to a trade-off between variance and entropy that questions unique entropy modulations. This problem deepens in multi-scale implementations that aim to characterize signal irregularity at distinct timescales. Here, the normalization parameter is traditionally estimated in a scale-invariant manner that is dominated by slow fluctuations. These issues question the validity of the assumption that entropy estimated at finer/coarser time scales reflects signal irregularity at those same scales. While accurate scale-wise mapping is critical for valid inference regarding signal entropy, systematic analyses have been largely absent to date. Here, we first simulate the relations between spectral power (i.e., frequency-specific signal variance) and MSE, highlighting a diffuse reflection of rhythms in entropy time scales. Second, we replicate known cross-sectional age differences in EEG data, while highlighting how timescale-specific results depend on the spectral content of the analyzed signal. In particular, we note that the presence of both low- and high-frequency dynamics leads to the reflection of power spectral density slopes in finer time scales. This association co-occurs with previously reported age differences in both measures, suggesting a common, power-based origin. Furthermore, we highlight that age differences in high frequency power can account for observed entropy differences at coarser scales via the traditional normalization procedure. By systematically assessing the impact of spectral signal content and normalization choice, our findings highlight fundamental biases in traditional MSE implementations. We make multiple recommendations for future work to validly interpret estimates of signal irregularity at time scales of interest.