Approximate entropy for short-term heart rate variability analysis: Is the threshold value computed by chon's formula appropriate?

Approximate entropy (ApEn) is a measure of signals' complexity and is widely used in physiological time series analyses, and in particular for the Heart Rate Variability (HRV) analysis. However the choice of the threshold value r, requested for its computation, is controversial. A recent study provided the valuable insight that the most appropriate threshold value is the one that provides the maximum ApEn value. Nonetheless, this method is computationally expensive and not feasible for real time processing in m-health applications. In order to reduce the computational cost, a formula for estimating the threshold value has been proposed by other researchers (Chon et al.). The aim of this study was to compare the two methods to estimate the ApEn proposed by other researchers for selecting threshold values in normal subject and in patients suffering from congestive heart failure. Thus, 19459 stationary HRV time series, extracted from electrocardiographic public databases, were analyzed. We computed the values of r threshold and the corresponding ApEn estimates using both the methods and the differences between the two estimated were assessed by a non-parametric test. Our analysis showed that the two methods provided significantly different (p<0.001) values. For that reason, we recommend that ApEn, in particular the estimation obtained with the formula given by Chon et al., should be used with caution since different threshold values r could affect the analysis and provide incorrect conclusions. Future works may propose more reliable methods to estimate ApEn with lower computational cost, that could be feasible also for real time processing in telemedicine services.