A regularity statistic for medical data analysis

J Clin Monit. 1991 Oct;7(4):335-45. doi: 10.1007/BF01619355.


A new statistic has been developed to quantify the amount of regularity in data. This statistic, ApEn (approximate entropy), appears to have potential application throughout medicine, notably in electrocardiogram and related heart rate data analyses and in the analysis of endocrine hormone release pulsatility. The focus of this article is ApEn. We commence with a simple example of what we are trying to discern. We then discuss exact regularity statistics and practical difficulties of using them in data analysis. The mathematic formula development for ApEn concludes the Solution section. We next discuss the two key input requirements, followed by an account of a pilot study successfully applying ApEn to neonatal heart rate analysis. We conclude with the important topic of ApEn as a relative (not absolute) measure, potential applications, and some caveats about appropriate usage of ApEn. Appendix A provides example ApEn and entropy computations to develop intuition about these measures. Appendix B contains a Fortran program for computing ApEn. This article can be read from at least three viewpoints. The practitioner who wishes to use a "black box" to measure regularity should concentrate on the exact formula, choices for the two input variables, potential applications, and caveats about appropriate usage. The physician who wishes to apply ApEn to heart rate analysis should particularly note the pilot study discussion. The more mathematically inclined reader will benefit from discussions of the relative (comparative) property of ApEn and from Appendix A.

MeSH terms

  • Algorithms*
  • Artifacts
  • Electrocardiography
  • Heart Rate / physiology*
  • Humans
  • Infant, Newborn
  • Infant, Newborn, Diseases / physiopathology
  • Mathematical Computing
  • Models, Statistical
  • Pilot Projects
  • Probability
  • Time Factors