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Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

Author

Listed:
  • Pablo Bonilla-Escribano

    (Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés, Spain and Gregorio Marañón Health Research Institute, 28911 Madrid, Spain)

  • David Ramírez

    (Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés, Spain and Gregorio Marañón Health Research Institute, 28911 Madrid, Spain)

  • Alejandro Porras-Segovia

    (Department of Psychiatry, IIS Fundación Jiménez Díaz, 28040 Madrid, Spain)

  • Antonio Artés-Rodríguez

    (Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés, Spain and Gregorio Marañón Health Research Institute, 28911 Madrid, Spain)

Abstract

Variability is defined as the propensity at which a given signal is likely to change. There are many choices for measuring variability, and it is not generally known which ones offer better properties. This paper compares different variability metrics applied to irregularly (nonuniformly) sampled time series, which have important clinical applications, particularly in mental healthcare. Using both synthetic and real patient data, we identify the most robust and interpretable variability measures out of a set 21 candidates. Some of these candidates are also proposed in this work based on the absolute slopes of the time series. An additional synthetic data experiment shows that when the complete time series is unknown, as it happens with real data, a non-negligible bias that favors normalized and/or metrics based on the raw observations of the series appears. Therefore, only the results of the synthetic experiments, which have access to the full series, should be used to draw conclusions. Accordingly, the median absolute deviation of the absolute value of the successive slopes of the data is the best way of measuring variability for this kind of time series.

Suggested Citation

  • Pablo Bonilla-Escribano & David Ramírez & Alejandro Porras-Segovia & Antonio Artés-Rodríguez, 2020. "Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
  • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:71-:d:472780
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    References listed on IDEAS

    as
    1. Aled Morris & Luca Börger & Elaine Crooks, 2019. "Individual Variability in Dispersal and Invasion Speed," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    2. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    3. Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    4. Jinhyuk Kim & Toru Nakamura & Hiroe Kikuchi & Tsukasa Sasaki & Yoshiharu Yamamoto, 2013. "Co-Variation of Depressive Mood and Locomotor Dynamics Evaluated by Ecological Momentary Assessment in Healthy Humans," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-1, September.
    Full references (including those not matched with items on IDEAS)

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