# The Effect of Threshold Values and Weighting Factors on the Association between Entropy Measures and Mortality after Myocardial Infarction in the Cardiac Arrhythmia Suppression Trial (CAST)

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Biomedical Systems, Health & Environment Department, AIT Austrian Institute of Technology, Donau-City-Str. 1, 1220 Vienna, Austria

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Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna, Austria

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Research Unit, HCI-KDD, Institute for Medical Informatics, Statistics and Documentation, Medical University Graz, Auenbruggerplatz 2, 8036 Graz, Austria

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Cardiovascular Division, Washington University School of Medicine, 660 S. Euclid Ave., St. Louis, MO 63110, USA

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Author to whom correspondence should be addressed.

Academic Editors: Kevin H. Knuth and Antonio Scarfone

Received: 28 January 2016 / Revised: 23 March 2016 / Accepted: 31 March 2016 / Published: 8 April 2016

(This article belongs to the Special Issue Machine Learning and Entropy: Discover Unknown Unknowns in Complex Data Sets)

Heart rate variability (HRV) is a non-invasive measurement based on the intervals between normal heart beats that characterize cardiac autonomic function. Decreased HRV is associated with increased risk of cardiovascular events. Characterizing HRV using only moment statistics fails to capture abnormalities in regulatory function that are important aspects of disease risk. Thus, entropy measures are a promising approach to quantify HRV for risk stratification. The purpose of this study was to investigate this potential for approximate, corrected approximate, sample, fuzzy, and fuzzy measure entropy and its dependency on the parameter selection. Recently, published parameter sets and further parameter combinations were investigated. Heart rate data were obtained from the "Cardiac Arrhythmia Suppression Trial (CAST) RR Interval Sub-Study Database" (Physionet). Corresponding outcomes and clinical data were provided by one of the investigators. The use of previously-reported parameter sets on the pre-treatment data did not significantly add to the identification of patients at risk for cardiovascular death on follow-up. After arrhythmia suppression treatment, several parameter sets predicted outcomes for all patients and patients without coronary artery bypass grafting (CABG). The strongest results were seen using the threshold parameter as a multiple of the data’s standard deviation ( $r=0.2\xb7\sigma $ ). Approximate and sample entropy provided significant hazard ratios for patients without CABG and without diabetes for an entropy maximizing threshold approximation. Additional parameter combinations did not improve the results for pre-treatment data. The results of this study illustrate the influence of parameter selection on entropy measures’ potential for cardiovascular risk stratification and support the potential use of entropy measures in future studies.