# Decision Tree-Based Foot Orthosis Prescription for Patients with Pes Planus

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## Abstract

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## 1. Introduction

## 2. Related Study

## 3. Methodology

#### 3.1. CART Algorithm

#### 3.2. Dataset Description

#### 3.3. Dataset Splitting

#### 3.4. Pruning

#### 3.5. Evaluation Metrics

## 4. Results

## 5. Discussion

## 6. Limitations

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Graphical representation of the CART model after pruning. Note: Gini is a metric that quantifies the purity of the node/leaf. A sample is the number of data. The value represents the number of samples included in the GP and ASOHC at a given node. The color indicates the class to which the majority of samples of each node belong (GP: orange and ASOHC: purple). Darker colors mean lower Gini scores.

**Table 1.**Clinical characteristics of patients with the two types of foot orthoses in the training and test datasets.

Characteristics | Training Dataset (n = 292) | Test Dataset (n = 126) | |||

Name | Description | GP (n = 146) | ASOHC (n = 146) | GP (n = 71) | ASOHC (n = 55) |

Age (year) | Age | 6.52 ± 4.01 | 8.24 ± 3.85 | 6.38 ± 3.31 | 7.41 ± 4.37 |

HIR (0 or 1) | Hip internal rotation angle (>$45{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$: abnormal (0), ≤$45{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$: normal (1)) | 0 (n = 110) 1 (n = 36) | 0 (n = 144) 1 (n = 2) | 0 (n = 55) 1 (n = 16) | 0 (n = 52) 1 (n = 3) |

TMA-L (degree) | Transmalleolar angle on the left side | −1.93 ± 5.46 | −0.78 ± 2.92 | −2.03 ± 5.12 | −0.22 ± 2.23 |

IASTJ-L (degree) | Inversion angle of the subtalar joint on the left side | 37.82 ± 7.88 | 38.64 ± 7.02 | 38.09 ± 7.62 | 38.45 ± 8.10 |

EASTJ-L (degree) | Eversion angle of the subtalar joint on the left side | 16.21 ± 3.91 | 18.29 ± 4.26 | 15.63 ± 3.92 | 17.45 ± 3.51 |

EASTJ-R (degree) | Eversion angle of the subtalar joint on the right side | 14.49 ± 4.21 | 16.86 ± 4.42 | 14.82 ± 4.55 | 15.95 ± 4.52 |

FFRF-R (degree) | forefoot to rearfoot angle on the right side | 0.02 ± 0.26 | 0.12 ± 0.58 | 0.07 ± 0.59 | 0.27 ± 0.89 |

RCSPA-L (degree) | RCSP angle on the left side | −5.08 ± 2.45 | −9.19 ± 3.75 | −5.29 ± 2.95 | −9.30 ± 3.33 |

RCSPA-R (degree) | RCSP angle on the right side | −4.58 ± 2.00 | −8.12 ± 3.39 | −4.62 ± 2.51 | −8.18 ± 3.38 |

Rules | |||
---|---|---|---|

GP | 1 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years | |

2 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, FFRF-R ≤ $1.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

3 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = abnormal, RCSPA-R ≤ $-6.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $10.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

4 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = abnormal, RCSPA-R ≤ $-6.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $15.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

5 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = abnormal, RSCPA-R ≤ $-6.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $15.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

6 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, IASTJ-L ≤ $46.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

7 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, IASTJ-L ≤ $46.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $11.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, RCSPA-R ≤ $-4.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

ASOHC | 1 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = Normal | |

2 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

3 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, FFRF-R ≤ $1.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

4 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = abnormal, RCSPA-R ≤ $-6.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $10.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

5 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, HIR = abnormal, RCSPA-R ≤ $-6.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $15.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

6 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, IASTJ-L ≤ $46.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

7 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, IASTJ-L ≤ $46.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $11.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ | ||

8 | RCSPA-L ≤ $-7.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, Age ≤ 12 years, RCSPA-L ≤ $-5.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, TMA-L ≤ $-1.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, IASTJ-L ≤ $46.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-L ≤ $14.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, EASTJ-R ≤ $11.0{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$, RCSPA-R ≤ $-4.5{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

Class | Accuracy (%) | Precision (%) | Sensitivity (%) | F1 Score (%) |
---|---|---|---|---|

GP | 80.16 | 89.66 | 73.24 | 80.62 |

ASOHC | 80.16 | 72.06 | 89.09 | 79.67 |

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**MDPI and ACS Style**

Jung, J.-Y.; Yang, C.-M.; Kim, J.-J. Decision Tree-Based Foot Orthosis Prescription for Patients with Pes Planus. *Int. J. Environ. Res. Public Health* **2022**, *19*, 12484.
https://doi.org/10.3390/ijerph191912484

**AMA Style**

Jung J-Y, Yang C-M, Kim J-J. Decision Tree-Based Foot Orthosis Prescription for Patients with Pes Planus. *International Journal of Environmental Research and Public Health*. 2022; 19(19):12484.
https://doi.org/10.3390/ijerph191912484

**Chicago/Turabian Style**

Jung, Ji-Yong, Chang-Min Yang, and Jung-Ja Kim. 2022. "Decision Tree-Based Foot Orthosis Prescription for Patients with Pes Planus" *International Journal of Environmental Research and Public Health* 19, no. 19: 12484.
https://doi.org/10.3390/ijerph191912484