Analysis of Cough Time Stamps from COPD Patients Using Markov Chain Analysis
American Journal of Theoretical and Applied Statistics
Volume 8, Issue 3, May 2019, Pages: 108-124
Received: May 22, 2019; Accepted: Jul. 9, 2019; Published: Aug. 5, 2019
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Tsega Kahsay Gebretekle, Department of Mathematics, Kotebe Metropolitan University, Addis Ababa, Ethiopia
Stef van Eijndhoven, Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
Bert den Brinker, Philips Electronics Nederland BV, Philips Research, Eindhoven, The Netherlands
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The objective of this study was to identify patterns of cough events for COPD patients. Simultaneously, the study was used to develop a Matlab based graphical user interface (GUI) that enables the user to analyze time-stamps of cough data. The time stamp data was received from Philips Research. They cover 17 data sets of 16 COPD patients and were determined using a semi-automated cough detection algorithm. Cough detection ran for multiple days in the living and bed rooms of the patients. The time stamp marks the event that a cough is assumed to occur. A descriptive statistics and a Markov Chain Model was used for analysis. A pattern of cough events was described by the probability that a COPD patient is in one of three possible states at a specific hour and in another state at the next hour. To define the states, the following three characteristics were used: 1) relative frequency, 2) average value-three times standard deviation band, 3) average value-three times inter-quartile range band. Relaxation time was determined to describe the dynamics of the cough event patterns. To be precise, pattern changes were characterized by considering the time it takes for the probabilities to reach stationarity. To reduce noise, the daily dynamics of the cough events over five day periods with a four day overlap were considered. From the results, we concluded that the distribution of cough events for all data sets was skewed to the right. The developed Matlab based graphical user interface allows the user to analyze the cough events of COPD patients together with their medical history. We conclude that the relaxation time and the stationary distribution of the Markov chain representation were typical characteristics of the patterns of cough events and the cough behavior of COPD patients was patient specific and varies over time.
COPD, Cough, Markov Chain Analysis, Relaxation Time
To cite this article
Tsega Kahsay Gebretekle, Stef van Eijndhoven, Bert den Brinker, Analysis of Cough Time Stamps from COPD Patients Using Markov Chain Analysis, American Journal of Theoretical and Applied Statistics. Vol. 8, No. 3, 2019, pp. 108-124. doi: 10.11648/j.ajtas.20190803.13
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