Address for correspondence: Steven M. Pincus, 990 Moose Hill Road, Guilford, CT 06437, USA. Voice: 203-458-3455; fax: 203-453-8969.
stevepincus{at}alum.mit.edu
Approximate entropy (ApEn) is a recently formulated family of
parameters and statistics quantifying regularity (orderliness)
in serial data, with developments within theoretical mathematics
as well as numerous applications to multiple biological contexts.
We discuss the motivation for ApEn development, from the study
of inappropriate application of dynamical systems (
complexity)
algorithms to general time-series settings. ApEn is scale invariant
and model independent, evaluates both dominant and subordinant
patterns in data, and discriminates series for which clear feature
recognition is difficult. ApEn is applicable to systems with
at least 50 data points and to broad classes of models: it can
be applied to discriminate both general classes of correlated
stochastic processes, as well as noisy deterministic systems.
Moreover, ApEn is complementary to spectral and autocorrelation
analyses, providing effective discriminatory capability in instances
in which the aforementioned measures exhibit minimal distinctions.
Representative ApEn applications to human aging studies, based
on both heart rate and endocrinologic (hormonal secretory) time
series, are featured. Heart rate (HR) studies include gender-
and age-related changes in HR dynamics in older subjects, and
analyses of "near-SIDS" infants. Endocrinologic applications
establish clear quantitative changes in joint LH-testosterone
secretory dynamics in older versus younger men (a "partial male
menopause"), via cross-ApEn, a related two-variable asynchrony
formulation; a disruption in LH-FSH-NPT (penile tumescence)
synchrony in older subjects; and changes in LH-FSH secretory
dynamics across menopause. The capability of ApEn to assess
relatively subtle disruptions, typically found earlier in the
history of a subject than mean and variance changes, holds the
potential for enhanced preventative and earlier interventionist
strategies.
