# Improving Accuracy of Heart Failure Detection Using Data Refinement

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Physical Threshold-based SampEn

^{−1}times the number of ${X}_{j}^{m}$ (1 ≤ j ≤ N − m) that meets ${d}_{i,j}^{m}$ ≤ r. Similarly, set ${A}_{i}^{m}$(r) as (N−m)

^{−1}times the number of ${X}_{j}^{m+1}$ that meets ${d}_{i,j}^{m+1}$ ≤ r for all 1 ≤ j ≤ N − m. Typically, recommended r for clinical use is between 0.10 and 0.25 times the standard deviation (SD) of the data [31]. Nevertheless, under certain circumstances, NSR group presented higher SampEn results than those in CHF group when r was set to 0.10, while the outcomes reversed as r increased to 0.25 [32]. The inverted entropy results make it hard to establish a unified standard to detect CHF subjects with a constant r value. To avoid such inconsistency, we proposed a physical threshold as multiple of sampling period, and proved that it is more adaptive to CHF detection than the traditional threshold [29]. Since the signals were sampled at 128 Hz, we regarded sampling period as 8 ms, and set threshold r as 1.5 times the sampling period, which equals to 12 ms.

^{m}to 10

^{m}

^{+1}.

#### 2.2. Why SampEn Results of Heart Failure Individuals Resemble Normal Ones

#### 2.3. Discrimination of fast HR Sequences

#### 2.4. Dynamic Time Warping

- ⬤
- It starts and finishes in diagonally opposite corner sides of the matrix.
- ⬤
- The cells in the warping path have to be adjacent (including diagonally).
- ⬤
- The points in W have to be placed monotonically in space.

## 3. Data and Experiment

#### 3.1. Data

#### 3.2. Experiment Scheme

#### 3.3. Statistical Analysis

- Sensitivity: $\mathrm{Se}=\mathrm{TP}/\left(\mathrm{TP}+\mathrm{FN}\right)$
- Specificity: $\mathrm{Sp}=\mathrm{TN}/\left(\mathrm{TN}+\mathrm{FP}\right)$
- Accuracy: $\mathrm{Acc}=\left(\mathrm{TP}+\mathrm{TN}\right)/\left(\mathrm{TP}+\mathrm{FP}+\mathrm{FN}+\mathrm{TN}\right)$

- $\mathrm{J}=\underset{c}{\mathrm{max}}\left\{Se\left(c\right)+Sp\left(c\right)-1\right\}$

## 4. Results

#### 4.1. Results of Fast HR Sequences Selection and DTW Processing

#### 4.2. Results of Subject Filtering

## 5. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The average SampEn values when using m = 1, r = 12 ms and N = 300 for (

**A**) NSR subjects and (

**B**) CHF subjects.

**Figure 2.**The SampEn distribution of all RR segments when m = 1, r = 12 ms and N = 300 for (

**A**) NSR group and (

**B**) CHF group.

**Figure 3.**The distribution ranges of SD values using N = 300 for (

**A1**) NSR001, (

**A2**) NSR002, (

**B1**) CHF205 and (

**B2**) CHF202.

**Figure 4.**Selection of fast HR sequence with length N = 1000 and 300 respectively for (

**A**) NSR001 and (

**B**) CHF205.

**Figure 6.**Block diagram of the proposed procedure. NSR: normal sinus rhythm, CHF: congestive heart failure, SD: standard deviation, DTW: dynamic time warping. Herein, segments imply RR segments of length 300.

**Figure 7.**The SampEn distribution of RR segments involved in calculation when m = 1, r = 12 ms and N = 300 for (

**A**) Datast0 and (

**B**) Dataset1.

**Figure 8.**Distribution ranges of SampEn between NSR and CHF groups when m = 1, r = 12 ms and N = 300 for Datast0 and Dataset1. *’means there is a significant difference between NSR and CHF groups.

**Figure 9.**ROC curve plots with AUC values in the RR Interval Databases for classifying NSR and CHF subjects. SampEn results using Dataset0, Dataset1 and Dataset2 are presented respectively. Parameter combination of m = 1, r = 12 ms and N = 300 was used.

**Figure 10.**The SampEn distribution of RR segments involved in calculation before and after DTW processing when m = 1, r = 12 ms and N = 300. The top two sub-figures (

**A1**,

**A2**) show type I subjects and type II subjects respectively before DTW. The bottom two sub-figures (

**B1**,

**B2**) show type I subjects and type II subjects respectively after DTW.

**Figure 11.**Examples of RR segments removed and preserved after DTW processing for NSR005 and CHF224. The top two sub-figures (

**A1**,

**A2**) show two segments from NSR005 removed and preserved respectively after DTW, while bottom sub-figures (

**B1**,

**B2**) show two segments from CHF224 removed and preserved respectively after DTW. Herein, segment length N was fixed as 300.

**Figure 12.**Results of SampEn before and after DTW processing for NSR and CHF groups using m = 1 and 2, r = 12 ms, and N = 300. Herein, subjects are divided into two types: type I in (

**A**) with segments no less than 90, and type II in (

**B**) with segments less than 90. The symbol ‘*’ means statistical significance p < 0.01.

**Figure 13.**ROC curve plots with AUC values of type I subjects for heart failure detection before and after DTW processing. Herein, embedding dimension m was set as 1, physical threshold r = 12 ms, and segment length N = 300.

**Figure 14.**(

**A**) Distribution ranges of SampEn with traditional threshold between NSR and CHF groups for Datast0 and type I after DTW. ‘*’means there is a significant difference between NSR and CHF groups. (

**B**) ROC curve plots with AUC values of Dataset0 and type I subjects after DTW processing for heart failure detection. Herein, embedding dimension m was set as 1, traditional threshold r = 0.10, and segment length N = 300.

**Table 1.**Statistical results of the numbers of RR interval recordings, RR intervals and RR segments from the 54 NSR and 29 CHF RR Interval Databases for original dataset, dataset with fast HR sequence selection, dataset after DTW calculation as well as subject extraction.

Variables | NSR Group | CHF Group |
---|---|---|

No. of RR interval recordings | 54 | 29 |

No. of RR intervals | 5,790,504 | 3,312,195 |

No. of RR intervals after removing greater than 2 s | 5,780,148 | 3,306,394 |

No. of RR intervals after removing abnormal heartbeats | 5,738,937 | 3,102,120 |

No. of RR segments (N = 300) after removing abnormal heartbeats | 19,101 | 10,324 |

No. of RR intervals after fast HR sequence selection | 632,100 | 775,200 |

No. of RR segments (N = 300) after fast HR sequence selection | 2107 | 2584 |

No. of RR segments (N = 300) after DTW calculation | 1718 | 2411 |

No. of RR segments (N = 300) for type I subjects | 625 | 1921 |

No. of RR segments (N = 300) for type II subjects | 1093 | 490 |

**Table 2.**Results of SampEn from the parameter combination of embedding dimension m = 1 and 2, physical threshold r = 12 ms, and segment length N = 300. Herein, three datasets are used: Dataset0 with all RR segments preserved, Dataset1 with only fast HR sequences preserved, and Dataset2 with DTW processing added. P-value measured the statistical significance between the NSR and CHF groups at each combination of (m, r). Data are expressed as number or mean ± standard deviation (SD). ‘*’: statistical significance P < 0.01.

SampEn of Dataset0 | SampEn of Dataset1 | SampEn of Dataset2 | |||||||
---|---|---|---|---|---|---|---|---|---|

NSR | CHF | p-Value | NSR | CHF | p-Value | NSR | CHF | p-Value | |

m = 1 | 1.06 ± 0.22 | 0.72 ± 0.28 | 7 × 10^{−8} * | 0.70 ± 0.13 | 0.46 ± 0.11 | 8 × 10^{−321} * | 0.72 ± 0.12 | 0.46 ± 0.10 | 2 × 10^{−319} * |

m = 2 | 0.97 ± 0.21 | 0.63 ± 0.28 | 2 × 10^{−8} * | 0.59 ± 0.12 | 0.38 ± 0.09 | 3 × 10^{−297} * | 0.61 ± 0.11 | 0.38 ± 0.09 | 8 × 10^{−302} * |

**Table 3.**Sensitivity, specificity and accuracy results of SampEn using Dataset0, Dataset1 and Dataset2 respectively. In the parameter combination, embedding dimension m was set as 1, physical threshold r = 12 ms, and segment length N = 300.

Metric | Equally-Weighted Se and Sp | Highly-Weighted Se | Highly-Weighted Sp | ||||||
---|---|---|---|---|---|---|---|---|---|

Dataset0 | Dataset1 | Dataset2 | Dataset0 | Dataset1 | Dataset2 | Dataset0 | Dataset1 | Dataset2 | |

c | 0.72 | 0.57 | 0.59 | 1.86 | 0.93 | 0.92 | 0.40 | 0.26 | 0.26 |

J(%) | 43.35 | 49.14 | 53.83 | 1.80 | 9.71 | 11.17 | 16.86 | 12.36 | 12.59 |

Se(%) | 60.31 | 75.39 | 79.10 | >99.0 | >99.0 | >99.0 | 17.85 | 13.31 | 13.52 |

Sp(%) | 83.05 | 73.75 | 74.74 | 2.80 | 10.68 | 12.17 | >99.0 | >99.0 | >99.0 |

Acc(%) | 75.07 | 74.65 | 77.28 | 36.55 | 59.35 | 62.87 | 70.53 | 51.82 | 49.12 |

**Table 4.**Sensitivity, specificity and accuracy results of SampEn before and after DTW processing. Subjects with RR segment number $\ge $90 (type I) and RR segment number <90 (type IIII) are set as contrast here. In the parameter combination, embedding dimension m was set as 1, physical threshold r = 12 ms, and segment length N = 300.

Metric | Equally-Weighted Se and Sp | Highly-Weighted Se | Highly-Weighted Sp | |||
---|---|---|---|---|---|---|

Before DTW | After DTW | Before DTW | After DTW | Before DTW | After DTW | |

type I | ||||||

c | 0.59 | 0.61 | 0.74 | 0.74 | 0.35 | 0.48 |

J(%) | 66.49 | 78.93 | 46.66 | 58.05 | 32.00 | 60.93 |

Se(%) | 88.26 | 91.41 | >99.0 | >99.0 | 32.96 | 61.89 |

Sp(%) | 78.24 | 87.52 | 47.65 | 59.04 | >99.0 | >99.0 |

Acc(%) | 84.85 | 90.46 | 81.56 | 89.20 | 55.41 | 71.01 |

type II | ||||||

c | 0.41 | 0.41 | 1.16 | 1.18 | 0.24 | 0.24 |

J(%) | 10.24 | 12.72 | 3.05 | 2.84 | 2.30 | 2.35 |

Se(%) | 20.86 | 21.22 | >99.0 | >99.0 | 3.24 | 3.27 |

Sp(%) | 89.38 | 91.49 | 3.95 | 3.66 | >99.0 | >99.0 |

Acc(%) | 65.86 | 69.74 | 36.60 | 33.23 | 66.17 | 69.43 |

**Table 5.**Sensitivity, specificity and accuracy results of SampEn with traditional threshold before and after data refinement processing. Dataset0 refers to original RR interval databases, and type I after DTW refers to subjects with RR segment number ≥90 after both fast HR sequence selection and DTW calculation. In the parameter combination, embedding dimension m was set as 1, traditional threshold r = 0.10, and segment length N = 300.

Metric | Equally-Weighted Se and Sp | Highly-Weighted Se | Highly-Weighted Sp | |||
---|---|---|---|---|---|---|

Dataset0 | Type I after DTW | Dataset0 | Type I after DTW | Dataset0 | Type I after DTW | |

c | 0.68 | 1.57 | 2.76 | 1.75 | 0.89 | 1.35 |

J(%) | 37.13 | 75.18 | 1.74 | 47.49 | 0.24 | 50.21 |

Se(%) | 60.57 | 90.06 | >99.0 | >99.0 | 1.24 | 51.17 |

Sp(%) | 76.56 | 85.12 | 2.74 | 44.48 | >99.0 | >99.0 |

Acc(%) | 70.95 | 88.85 | 36.51 | 86.61 | 64.70 | 62.92 |

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## Share and Cite

**MDPI and ACS Style**

Xiong, J.; Liang, X.; Zhao, L.; Lo, B.; Li, J.; Liu, C. Improving Accuracy of Heart Failure Detection Using Data Refinement. *Entropy* **2020**, *22*, 520.
https://doi.org/10.3390/e22050520

**AMA Style**

Xiong J, Liang X, Zhao L, Lo B, Li J, Liu C. Improving Accuracy of Heart Failure Detection Using Data Refinement. *Entropy*. 2020; 22(5):520.
https://doi.org/10.3390/e22050520

**Chicago/Turabian Style**

Xiong, Jinle, Xueyu Liang, Lina Zhao, Benny Lo, Jianqing Li, and Chengyu Liu. 2020. "Improving Accuracy of Heart Failure Detection Using Data Refinement" *Entropy* 22, no. 5: 520.
https://doi.org/10.3390/e22050520