State Change Probability: A Measure of the Complexity of Cardiac RR Interval Time Series Using Physiological State Change with Statistical Hypothesis Testing

Abstract

The complexity of biological signals has been proposed to reflect the adaptability of a given biological system to different environments. Two measures of complexity--multiscale entropy (MSE) and entropy of entropy (EoE)--have been proposed, to evaluate the complexity of heart rate signals from different perspectives. The MSE evaluates the information content of a long time series across multiple temporal scales, while the EoE characterizes variation in amount of information, which is interpreted as the \"state changing,\" of segments in a time series. However, both are problematic when analyzing white noise and are sensitive to data size. Therefore, based on the concept of \"state changing,\" we propose state change probability (SCP) as a measure of complexity. SCP utilizes a statistical hypothesis test to determine the physiological state changes between two consecutive segments in heart rate signals. The SCP value is defined as the ratio of the number of state changes to total number of consecutive segment pairs. Two common statistical tests, the t-test and Wilcoxon rank-sum test, were separately used in the SCP algorithm for comparison, yielding similar results. The SCP method is capable of reasonably evaluating the complexity of white noise and other signals, including 1/f noise, periodic signals, and heart rate signals, from healthy subjects, as well as subjects with congestive heart failure or atrial fibrillation. The SCP method is also insensitive to data size. A universal SCP threshold value can be applied, to differentiate between healthy and pathological subjects for data sizes ranging from 100 to 10,000 points. The SCP algorithm is slightly better than the EoE method when differentiating between subjects, and is superior to the MSE method.