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The Appropriate Use of Approximate Entropy and Sample Entropy with Short Data Sets

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Abstract

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.

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Abbreviations

ApEn:

Approximate entropy

SampEn:

Sample entropy

SE diff :

Standard error of the difference

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Acknowledgments

Funding was provided by the NASA Nebraska Space Grant & EPSCoR, Patterson Fellowship through the University of Nebraska Medical Center and NIH/NIA (R01AG034995).

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Authors and Affiliations

  1. Nebraska Biomechanics Core Facility, Department of Health, Physical Education, and Recreation, University of Nebraska at Omaha, 6001 Dodge Street, HPER 207, Omaha, NE, 68182, USA

    Jennifer M. Yentes, Nathaniel Hunt, Jeffrey P. Kaipust, Denise McGrath & Nicholas Stergiou

  2. Department of Biostatistics, College of Public Health, University of Nebraska Medical Center, 984355 Nebraska Medical Center, Omaha, NE, 68198, USA

    Kendra K. Schmid

  3. Department of Environmental, Agricultural & Occupational Health, College of Public Health, University of Nebraska Medical Center, 984355 Nebraska Medical Center, Omaha, NE, 68198, USA

    Nicholas Stergiou

Authors
  1. Jennifer M. Yentes
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Correspondence to Nicholas Stergiou.

Additional information

Associate Editor Thurmon E. Lockhart oversaw the review of this article.

Appendix

Appendix

In order to understand the stabilization of entropy values as N increased in theoretical data, the chaotic logistic map was subjected to entropy analysis up to an N of 10,000 data points. For this particular analysis, an m of 2 and r of 0.2 times the standard deviation of the time series were chosen, as they are the most popular choice in past and current literature. Using the same procedures as outlined in the methods above, SampEn and ApEn were quantified on generated data from 100 to 10,000 data points, in increments of 100. As can be seen in Fig. 10, the entropy values for both SampEn and ApEn stabilize around an N of 2000.

Figure 10
figure 10

The ApEn and SampEn values are plotted for the chaotic logistic map using an m of 2 and r of 0.2. The entropy values were calculated for data of lengths 100–10,000 increasing in increments of 100. Based on this figure, it appears that the entropy values stabilize around an N of 2000

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Yentes, J.M., Hunt, N., Schmid, K.K. et al. The Appropriate Use of Approximate Entropy and Sample Entropy with Short Data Sets. Ann Biomed Eng 41, 349–365 (2013). https://doi.org/10.1007/s10439-012-0668-3

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