# Use of a Machine Learning Method in Predicting Refraction after Cataract Surgery

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Study Design

#### 2.2. Patients

#### 2.3. Preoperative, Postoperative Examinations, and Surgical Measurements

#### 2.4. IOL Power Calculation Formulas and Optimization of Constants

#### 2.5. Machine Learning

#### 2.6. Statistical Analysis

#### 2.7. Ethics Statement

#### 2.8. Data Availability

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Flow of prediction using the conventional intraocular lens (IOL) calculation formulas. (

**b**) Flow of prediction using machine learning methods.

**Figure 3.**Mean absolute prediction error of conventional IOL power calculation formulae. Mean absolute error for the Barrett Universal II formula, SRK/T formula, Holladay 1 formula, Hoffer Q formula, and Haigis formula were 0.2960, 0.3314, 0.3312, 0.3602, and 0.3210, respectively. The p-value by the Friedman test was < 0.0001. The SRK/T formula vs. the Barrett Universal II formula: p = 0.0002. The Holladay 1 formula vs. the Barrett Universal II formula: p = 0.0004. The Hoffer Q formula vs. the Barrett Universal II formula: p < 0.0001. The Haigis formula vs. the Barrett Universal II formula: p = 0.0013. (The p-values were calculated using the Wilcoxon signed-rank test and were adjusted using the Bonferroni correction).

**Figure 4.**Mean absolute prediction error value of the Barret Universal II formula and machine learning methods. Abbreviations: SVR, support vector regression; GBR gradient boosting regression; RFR, random forest regression; NN, neural network.

**Figure 5.**Mean absolute prediction error categorized according to the axial length. In the short-axis group, the mean absolute error for the Barrett Universal II formula, SVR, GBR, RFR, and NN were 0.3360, 0.2967, 0.3069, 0.2593, and 0.3085, respectively. In the middle-axis group, the mean absolute error for the Barrett Universal II formula, SVR, GBR, RFR, and NN were 0.2858, 0.2789, 0.2788, 0.2898, and 0.2821, respectively. In the long-axis group, the mean absolute error for the Barrett Universal II formula, SVR, GBR, RFR, and NN were 0.3045, 0.3153, 0.3008, 0.3089, and 0.2991, respectively. The p-value by the Friedman test was > 0.05 for all axial length subgroups.

**Figure 6.**Mean absolute prediction error of the SRK/T formula and machine learning methods. Mean absolute error for the SRK/T formula, SVR, GBR, RFR, and NN were 0.3314, 0.2877, 0.2929, 0.2964, and 0.2891, respectively. The p-value by the Friedman test was < 0.0001. The SVR formula vs. the SRK/T formula: p < 0.0001; GBR vs. the SRK/T formula: p < 0.0001; RFR vs. the SRK/T formula: p = 0.0001; NN vs. the SRK/T formula: p < 0.0001; (The p-values were calculated using the Wilcoxon signed-rank test and were adjusted using the Bonferroni correction).

Training Data | Test Data | p Value | |
---|---|---|---|

n | Total: 2831 YP2.2: 296 SZ-1: 260 W60R: 193 KS-SP: 28 NS60YG: 21 SN60WF: 125 SN6AT: 208 SN6AD: 79 SV25T: 38 ZCB00V: 463 TECNIS multi: 463 TECNIS symphony: 202 | Total: 500 YP2.2: 500 | |

Axial length | 24.02 ± 1.57 | 23.92 ± 1.35 | 0.1741 |

Average radius of the corneal curvature | 7.63 ± 0.27 | 7.62 ± 0.25 | 0.6757 |

ACD | 3.10 ± 0.41 | 3.10 ± 0.38 | 0.9293 |

LT | 4.57 ± 0.43 | 4.57 ± 0.43 | 0.5257 |

WTW | 11.74 ± 0.41 | 11.75 ± 0.41 | 0.5651 |

IOL power | 19.63 ± 4.25 | 19.55 ± 3.50 | 0.6942 |

Postoperative refraction | −0.13 ± 0.82 | −0.09 ± 0.92 | 0.3323 |

A Constants (for SRK/T) | SF (for Holladay 1) | pACD (for Hoffer Q) | a0, a1, a2 (for Haigis) | ||||
---|---|---|---|---|---|---|---|

YP2.2 | 119.2 | YP2.2 | 1.93 | YP2.2 | 5.792 | YP2.2 | −1.72, 0.277, 0.260 |

SZ-1 | 119.48 | ||||||

W60R | 119.49 | ||||||

KS-SP | 119.72 | ||||||

NS60YG | 120.88 | ||||||

SN60WF | 119.2 | ||||||

SN6AT | 119.16 | ||||||

SN6AD | 119.24 | ||||||

SV25T | 119.56 | ||||||

ZCB00V | 119.58 | ||||||

Tecnis multi | 119.63 | ||||||

Tecnis symphony | 119.19 |

Barrett Universal II Formula | SVR | RFR | GBR | NN |
---|---|---|---|---|

406/500 | 422/500 | 412/500 | 414/500 | 422/500 |

Axial Length | Corneal Curvature | ACD | LT | IOL Power | SRKT | |
---|---|---|---|---|---|---|

Mean | 0.131356521 | 0.181638074 | 0.204091 | 0.173306 | 0.075068989 | 0.234539 |

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**MDPI and ACS Style**

Yamauchi, T.; Tabuchi, H.; Takase, K.; Masumoto, H.
Use of a Machine Learning Method in Predicting Refraction after Cataract Surgery. *J. Clin. Med.* **2021**, *10*, 1103.
https://doi.org/10.3390/jcm10051103

**AMA Style**

Yamauchi T, Tabuchi H, Takase K, Masumoto H.
Use of a Machine Learning Method in Predicting Refraction after Cataract Surgery. *Journal of Clinical Medicine*. 2021; 10(5):1103.
https://doi.org/10.3390/jcm10051103

**Chicago/Turabian Style**

Yamauchi, Tomofusa, Hitoshi Tabuchi, Kosuke Takase, and Hiroki Masumoto.
2021. "Use of a Machine Learning Method in Predicting Refraction after Cataract Surgery" *Journal of Clinical Medicine* 10, no. 5: 1103.
https://doi.org/10.3390/jcm10051103