Improved entropy rate estimation in physiological data

Calculating entropy rate in physiologic signals has proven very useful in many settings. Common entropy estimates for this purpose are sample entropy (SampEn) and its less robust elder cousin, approximate entropy (ApEn). Both approaches count matches within a tolerance r for templates of length m consecutive observations. When physiologic data records are long and well-behaved, both approaches work very well for a wide range of m and r. However, more attention to the details of the estimation algorithm is needed for short records and signals with anomalies. In addition, interpretation of the magnitude of these estimates is highly dependent on how r is chosen and precludes comparison across studies with even slightly different methodologies. In this paper, we summarize recent novel approaches to improve the accuracy of entropy estimation. An important (but not necessarily new) alternative to current approaches is to develop estimates that convert probabilities to densities by normalizing by the matching region volume. This approach leads to a novel concept introduced here of reporting entropy rate in equivalent Gaussian white noise units. Another approach is to allow r to vary so that a pre-specified number of matches are found, called the minimum numerator count, to ensure confident probability estimation. The approaches are illustrated using a simple example of detecting abnormal cardiac rhythms in heart rate records.