Not All Entropy Is Equal: Parameter Sensitivity and Cross-Dataset Fragility of Band-Filtered Entropy in Dementia EEG

Abstract Permutation entropy (PE) is increasingly studied as an EEG biomarker for Alzheimer’s disease and related dementias, but it requires an embedding order and delay whose interaction with the sampling rate sets the physical timescale of the measurement, and these choices are rarely justified. On 1,177 clinical EEGs from the CAUEEG dataset (457 Normal, 414 MCI, 306 Dementia) we computed alpha-band (8-12 Hz) PE under four parameterizations on eyes-closed, artifact-excluded, per-segment data. Effect sizes for dementia vs. normal ranged from d = −0.700 to d = +0.709–a reversal in direction–with two parameterizations null; the timescale-appropriate parameterization (order = 5, delay = 5; one full alpha cycle) was a null ( d = −0.025). We prove that sub-cycle PE reduces to the entropy of the instanta-neous phase and confirm this on the real EEG: the ordinal pattern is fixed by the Hilbert phase on 90% of samples, and pe_o3d1 equals the phase-predicted entropy ( r = 0.95). Applying the same scrutiny symmetrically, sample entropy (SE) is not exempt: the alpha-band SE effect nearly doubles between the two conventional embedding dimensions m = 2 ( d = +0.52) and m = 3 ( d = +0.86), and is null at the degenerate m = 1; within m ≥ 2 it is tolerance-robust and independent of spectral power ( r = −0.04). We then harmonized the pipeline and matched the physical timescale across datasets by downsampling an independent cohort (ds004504, 500 → 200 Hz). The PE parameter-sensitivity profile reproduced across datasets (Pearson r = 0.997), but absolute effects were cohort-dependent in measure-specific ways: the PE profile reproduced but shifted upward by a near-constant offset large enough to carry the one negative CAUEEG parameterization (pe_o3d1) across zero, whereas SE moved in the opposite direction (higher in disease on CAUEEG, lower on ds004504). The relative alpha/theta power ratio was the strongest single classifier (AUC = 0.739, d = −0.727) and replicated its direction across cohorts, whereas neither PE nor SE did. The alpha/theta Lempel-Ziv Complexity ratio ( d = 0.471) shared 52% of its variance with the power ratio, indicating it largely indexes spectral content; the LZC ratio’s elevation in dementia was pre-specified from a discovery dataset ( N = 88). On band-filtered EEG, entropy measures are parameter- and cohort-dependent, and a simple spectral power ratio is the robust baseline they do not surpass. We recommend reporting the physical timescale, testing multiple parameterizations, and benchmarking any entropy biomarker against the spectral baseline before claiming complexity-specific information.