Measuring body temperature time series regularity using Approximate Entropy and Sample Entropy

Fifty years of Shannon information theory in assessing the accuracy and agreement of diagnostic tests

Since 1948, Shannon theoretic methods for modeling information have found a wide range of applications in several areas where information plays a key role, which goes well beyond the original scopes for which they have been conceived, namely data compression and error correction over a noisy channel. Among other uses, these methods have been applied in the broad field of medical diagnostics since the 1970s, to quantify diagnostic information, to evaluate diagnostic test performance, but also to be used as technical tools in image processing and registration. This review illustrates the main contributions in assessing the accuracy of diagnostic tests and the agreement between raters, focusing on diagnostic test performance measurements and paired agreement evaluation. This work also presents a recent unified, coherent, and hopefully, final information-theoretical approach to deal with the flows of information involved among the patient, the diagnostic test performed to appraise the state of disease, and the raters who are checking the test results. The approach is assessed by considering two case studies: the first one is related to evaluating extra-prostatic cancers; the second concerns the quality of rapid tests for COVID-19 detection.

Entropy Analysis in Gait Research: Methodological Considerations and Recommendations

The usage of entropy analysis in gait research has grown considerably the last two decades. The present paper reviews the application of different entropy analyses in gait research and provides recommendations for future studies. While single-scale entropy analysis such as approximate and sample entropy can be used to quantify regularity/predictability/probability, they do not capture the structural richness and component entanglement characterized by a complex system operating across multiple spatial and temporal scales. Thus, for quantification of complexity, either multiscale entropy or refined composite multiscale entropy is recommended. For both single- and multiscale-scale entropy analyses, care should be made when selecting the input parameters of tolerance window r, vector length m, time series length N and number of scales. This selection should be based on the proposed research question and the type of data collected and not copied from previous studies. Parameter consistency should be investigated and published along with the main results to ensure transparency and enable comparisons between studies. Furthermore, since the interpretation of the absolute size of both single- and multiscale entropy analyses outcomes is not straightforward, comparisons should always be made with a control condition or group.

Entropy Measures as Descriptors to Identify Apneas in Rheoencephalographic Signals

Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea should be reflected in REG signals under the form of increased complexity, several entropy metrics were assessed for REG analysis during apnea and resting periods in 16 healthy subjects: approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), corrected conditional entropy (CCE) and Shannon entropy (SE). To compute these entropy metrics, a set of parameters must be defined a priori, such as, for example, the embedding dimension m, and the tolerance threshold r. A thorough analysis of the effects of parameter selection in the entropy metrics was performed, looking for the values optimizing differences between apnea and baseline signals. All entropy metrics, except SE, provided higher values for apnea periods (p-values < 0.025). FuzzyEn outperformed all other metrics, providing the lowest p-value (p = 0.0001), allowing to conclude that REG signals during apnea have higher complexity than in resting periods. Those findings suggest that REG signals reflect CBF changes provoked by apneas, even though further studies are needed to confirm this hypothesis.

Pattern Analysis of Oxygen Saturation Variability in Healthy Individuals: Entropy of Pulse Oximetry Signals Carries Information about Mean Oxygen Saturation

Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterize the pattern of OSV using several parameters; the regularity (sample entropy analysis), the self-similarity [detrended fluctuation analysis (DFA)] and the complexity [multiscale entropy (MSE) analysis]. Secondly, to determine if there were any changes that occur with age. The study population consisted of 36 individuals. The “young” population consisted of 20 individuals [Mean (±1 SD) age = 21.0 (±1.36 years)] and the “old” population consisted of 16 individuals [Mean (±1 SD) age = 50.0 (±10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was also a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (p < 0.05). These findings suggest partial “uncoupling” of the cardio-respiratory control system that occurs with aging. Overall, this study has characterized OSV using pre-existing tools. We have showed that entropy analysis of pulse oximetry signals carries information about body oxygenation. This may have the potential to be used in clinical practice to detect differences in diseased patient subsets.

The appropriate use of approximate entropy and sample entropy with short data sets

Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms created to measure the repeatability or predictability within a time series. Both algorithms are extremely sensitive to their input parameters: m (length of the data segment being compared), r (similarity criterion), and N (length of data). There is no established consensus on parameter selection in short data sets, especially for biological data. Therefore, the purpose of this research was to examine the robustness of these two entropy algorithms by exploring the effect of changing parameter values on short data sets. Data with known theoretical entropy qualities as well as experimental data from both healthy young and older adults was utilized. Our results demonstrate that both ApEn and SampEn are extremely sensitive to parameter choices, especially for very short data sets, N ≤ 200. We suggest using N larger than 200, an m of 2 and examine several r values before selecting your parameters. Extreme caution should be used when choosing parameters for experimental studies with both algorithms. Based on our current findings, it appears that SampEn is more reliable for short data sets. SampEn was less sensitive to changes in data length and demonstrated fewer problems with relative consistency.