To assess whether incorporating a machine learning (ML) method for accurate prediction of postoperative anterior chamber depth (ACD) improves the refraction prediction performance of existing intraocular lens (IOL) calculation formulas.

A dataset of 4806 patients with cataract was gathered at the Kellogg Eye Center, University of Michigan, and split into a training set (80% of patients, 5761 eyes) and a testing set (20% of patients, 961 eyes). A previously developed ML-based method was used to predict the postoperative ACD based on preoperative biometry. This ML-based postoperative ACD was integrated into new effective lens position (ELP) predictions using regression models to rescale the ML output for each of four existing formulas (Haigis, Hoffer Q, Holladay and SRK/T). The performance of the formulas with ML-modified ELP was compared using a testing dataset. Performance was measured by the mean absolute error (MAE) in refraction prediction.

When the ELP was replaced with a linear combination of the original ELP and the ML-predicted ELP, the MAEs±SD (in Diopters) in the testing set were: 0.356±0.329 for Haigis, 0.352±0.319 for Hoffer Q, 0.371±0.336 for Holladay, and 0.361±0.331 for SRK/T which were significantly lower (p<0.05) than those of the original formulas: 0.373±0.328 for Haigis, 0.408±0.337 for Hoffer Q, 0.384±0.341 for Holladay and 0.394±0.351 for SRK/T.

Using a more accurately predicted postoperative ACD significantly improves the prediction accuracy of four existing IOL power formulas.

The estimation of postoperative intraocular lens (IOL) position is essential to IOL power calculations for cataract surgery. Norrby and Olsen have reported that inaccuracy in the prediction of the postoperative anterior chamber depth (ACD) is the number one source of error for postoperative refraction prediction.

It is so far largely unexplored whether inserting a more accurately predicted ELP into existing formulas improves refraction prediction accuracy. This is an important question because: (1) it provides a fast and efficient way to modify and improve on existing IOL formulas whose reliability has been tested extensively; (2) such research can provide supports for translating the continued improvements in accuracy in postoperative ACD prediction into better refraction predictions in published formulas. Several previous studies had modified the ELPs in existing formulas in order to achieve better refraction prediction results in certain cataract cases. Modification of ELP calculation in the Haigis formula for sulcus-implanted IOLs was reported to improve performance.

Since most recently published IOL formulas (eg, Barrett Universal II,

In previous work,

In this study, biometry records were collected using the same approach as for the development of the ML postoperative ACD prediction model at University of Michigan’s Kellogg Eye Center.

The inclusion criteria were: (1) patients who had cataract surgery (Current Procedural Terminology (CPT) code=66 984 or 66 982) but no prior refractive surgery and no additional surgical procedures at the time of cataract surgery. (2) The implanted lens was an Alcon SN60WF single-piece acrylic monofocal lens (Alcon, USA). Each case in the dataset corresponds to one operation of a single eye with preoperative and postoperative information. The preoperative information includes the measurements of the AL, lens thickness (LT), ACD, flat keratometry (K1), steep keratometry (K2), and the average keratometry which was calculated as

The dataset in total consisted of 4806 patients (

The analysis pipeline of the presented study.

We implemented four existing formulas (Haigis, Hoffer Q, Holladay, and SRK/T) in Python based on their publications.

In the first step, the most optimal ELP (denoted

After the computation of

On the testing set,

The A-constants for the formulas were optimised based on the training dataset so that the ME in refraction prediction was closest to zero. The A-constants were optimised separately for the unmodified formulas and formulas with a modified ELP estimate (see additional details in the A-constant optimisation section and

Linear regression analysis was used to assess the significance of the correlation between

The cases in the training and testing datasets had a similar distribution according to the summary statistics shown in

The summary statistics for the patient demographics for the training and testing dataset

Characteristic | Training set | Testing set |

Gender | Male: 2514 eyes (43.6%), | Male: 425 eyes (44.2%), |

Age at surgery (years) | 70.99±9.61 | 70.10±10.24 |

Preoperative K (D) | 43.85±1.64 | 43.90±1.66 |

Preoperative AL (mm) | 24.19±1.40 | 24.20±1.41 |

Preoperative LT (mm) | 4.54±0.45 | 4.53±0.45 |

Preoperative ACD (mm) | 3.24±0.41 | 3.26±0.41 |

Postoperative refraction (D) | −0.53±0.96 | −0.57±0.90 |

For the age at surgery, preoperative biometry, and postoperative refraction, the mean±standard deviation (SD) is shown in the table.

ACD, anterior chamber depth; AL, axial length; D, Diopter; K, keratometry; LT, lens thickness.

The Pearson correlation coefficients (R) between

The Pearson correlation coefficients (R) between

Index | Variable pairs | Haigis | Hoffer Q | Holladay1 | SRK/T |

1 | 0.751 | 0.676 | 0.698 | 0.636 | |

2 | 0.621 | 0.730 | 0.622 | 0.633 | |

3 | 0.532 | 0.544 | 0.534 | 0.524 |

The

Linear regression models were established based on the training set and the

The

Index | Methods | Haigis | Hoffer Q | Holladay1 | SRK/T |

1 | Formula LR | 0.377 | 0.541 | 0.579 | 0.394 |

2 | ML LR | 0.376 | 0.442 | 0.426 | 0.378 |

3 | Formula & ML LR |

The outlier cases were removed before calculating the above values. The largest

We tested the performance of four scenarios on the testing set and summarised the MAE and SD in

Performance in the testing set

Index | Methods | Haigis | Hoffer Q | Holladay1 | SRK/T |

1 | Original | 0.373±0.328 | 0.408±0.337 | 0.384±0.341 | 0.394±0.351 |

2 | Formula LR | 0.373±0.328 (0.0%) | 0.374±0.321 (8.3%) | 0.388±0.342 (−1.1%) | 0.391±0.345 (0.8%) |

3 | ML LR | 0.391±0.346 (−4.8%) | 0.454±0.375 (-21.4%) | 0.434±0.364 (−13.0%) | 0.397±0.344 (−1.5%) |

4 | Formula & ML LR |

The MAE ±SD and the percentage reduction in MAE compared with ‘Original’ for alternative linear models in the testing set. All MAE and SD were rounded to three decimal places. The percentage reduction was calculated as

We further compared the MAEs of ‘Original’ and ‘Formula & ML LR’ among patients with short, medium and long AL (

In this study, we applied a previously developed ML method for postoperative ACD prediction to an unseen dataset of 4806 cataract surgery patients to assess whether it was possible to improve the performance of existing IOL formulas (Haigis, Hoffer Q, Holladay, and SRK/T) by replacing each formula’s ELP estimate.

We computed three ELP-related quantities: the ML-predicted postoperative ACD (

Using a training dataset of 3845 patients, we sought to evaluate whether the machine-predicted postoperative ACD,

In this study, the A-constants were optimised separately when

Previous studies involving replacement of ELP in existing formulas have focused on special cases, such as sulcus implantation and postrefractive surgery eyes, where ELP estimates of traditional formulas would be expected to be inapplicable.

In summary, the results of this study demonstrate that an ML method for postoperative ACD prediction based on postoperative optical biometry can be incorporated into a variety of existing IOL power formulas to improve their accuracy in refraction prediction.

TL: data analysis, programming and writing of the manuscript. JS: data collection. NN: data collection, guidance on method development, and writing of the manuscript.

This work was supported by the Lighthouse Guild, New York, NY (JDS) and National Eye Institute, Bethesda, MD, 1R01EY026641-01A1 (JDS).

None declared.

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Data may be obtained from the Sight Outcomes Research Collaborative (SOURCE) repository for participating institutions and are not publicly available.

Not required.

Institutional review board approval was obtained for the study, and it was determined that informed consent was not required because of its retrospective nature and the anonymised data used in this study. The study was carried out in accordance with the tenets of the Declaration of Helsinki.