Physiological time-series analysis: what does regularity quantify?

TLDR

Approximate entropy (ApEn) quantifies regularity and complexity in physiological time‑series and relates to variability measures, Fourier spectra, and chaotic‑dynamics algorithms. The paper aims to clarify ApEn’s use by explaining its algorithm, implementation, and how it can test a general hypothesis about disease dynamics. The authors present a formal definition of ApEn, a multistep algorithm applied to two heart‑rate datasets, and discuss parameter choices, statistical considerations, and modeling caveats. They conclude that careful selection of input parameters, awareness of statistical issues, and modeling considerations are essential for correct ApEn utilization.

Abstract

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.