This was a retrospective, multicenter observational study. The study flowchart is shown in Figure 1 and comprises two datasets. The development set included patients scheduled for MRS at Zhongshan Ophthalmic Center (ZOC), Guangzhou, China, and was used for formula development. Subsequently, cataract patients with previous MRS history (LASIK/PRK) who underwent phacoemulsification and primary in-the-bag IOL implantation at ZOC and two other centers (Shenzhen Eye Hospital and Wuhan Aier Eye Hospital) were included for formula validation (validation set). All procedures in this study adhered to the tenets of the Declaration of Helsinki and were approved by the Institutional Review Board/Ethics Committee (2023KYPJ230). The requirement for informed consent was waived for the retrospective data collection.

Study flowchart. SMILE = small incision lenticule extraction; FS-LASIK = femtosecond lasers and laser assisted in situ keratomileusis; Kmean = mean keratometry; ARC = anterior corneal radius; PRC = posterior corneal radius; ELP = effective lens position; ME = mean arithmetic prediction error; MAE = mean absolute prediction error; MedAE = median absolute prediction error; RMSAE = root-mean-square absolute prediction error; FPI = formula performance index.

Inclusion criteria were as follows: (1) age over 18 years; (2) successful biometric measurements by IOLMaster 700 (Carl Zeiss Meditec AG). Exclusion criteria were: (1) a history of other ocular surgery or ocular trauma; (2) intraoperative or postoperative complications, such as IOL dislocation or posterior capsular rupture; (3) requirement for additional surgeries, such as corneal collagen cross-linking or capsular tension ring implantation; (4) lack of follow-up data at least 1 month after surgery (biometry by the IOLMaster 700 for the development set and subjective refraction for the validation set); and (5) postoperative best-corrected visual acuity worse than 20/40 for the validation set.

Patients’ demographics, biometric parameters (including AL, anterior and posterior keratometry, anterior chamber depth, lens thickness [LT], horizontal corneal diameter, and corneal thickness [CCT]), surgical information, and subjective refraction were obtained from electronic database. The B/F ratio was calculated as the ratio of posterior to anterior corneal curvature. The TCP was calculated using the following equation (Equation 1):

• $n_{\text{cornea}}$ : refractive index of cornea (1.376)

• $n_{\text{air}}$ : refractive index of air (1.0)

• $n_{\text{aqueous}}$ : refractive index of aqueous humor (1.336)

• ARC: anterior cornea radius (in meters)

• PRC: posterior cornea radius (in meters)

• CCT: corneal thickness (in meters)

The formula structure has been described in detail in our previous work. Briefly, the LISA calculator integrates thick-lens equations and artificial intelligence (AI) for IOL power calculation. The thick-lens optical framework was implemented building upon the foundational open-source framework of the PEARL-DGS formula (Debellemanière et al). We further developed and integrated additional modules, including toric IOL calculations, device-specific optimizations, and adjustments for long eyes. The AI component was developed independently using the database from ZOC. After back calculating the thick-lens ELP from postoperative refraction, we established the ELP prediction models using AI for ordinary cataract patients (LISA) and cataract patients with prior pars plana vitrectomy (LISA-PPV), respectively. For ordinary cataract patients, optical AL, ARC, aqueous humor depth (AQD; defined as the distance from the posterior corneal surface to the anterior lens surface), LT, and sex were included as predictors of ELP. Additional ELP models were developed for cases with missing AQD or LT.

Compared to the standard LISA formula, the LISA MRS versions specifically address the altered corneal curvature to optimize ELP prediction by estimating the theoretical preoperative ARC. Depending on data availability, two modes were developed:

LISA MRS-PRC: in this mode, TCP calculation remained consistent with the standard formula (Equation 1). The specific modification lay in the ELP prediction: the theoretical preoperative ARC was estimated from the postoperative PRC using a linear regression model derived from the development set (Equation 2).

2) LISA MRS (without PRC): To enable clinical application when posterior corneal measurements are unavailable, two specific adjustments were made. First, TCP was estimated from mean keratometry (Kmean) (Equation 3). Second, for ELP prediction, the theoretical preoperative ARC was estimated from postoperative ARC (Equation 4).

Apart from these mode-specific steps, all other settings were identical to the standard LISA formula.

The performance of LISA MRS was evaluated and compared with formulas which have PRC versions (Barrett True K, Emmetropia Verifying Optical [EVO], and Hoffer QST) and two classical formulas (Haigis-L and Shammas PL, assessed via the ASCRS online calculator*) in the validation set. The IOL constants were obtained from the IOLCon website*. To evaluate the prediction accuracy of each formula, we analyzed: (1) the mean and SD (SD) of arithmetic prediction error (ME); (2) the mean, median, and root-mean-square absolute prediction error (MAE, MedAE, RMSAE); (3) the percentage of eyes with a prediction error within ±0.25 D, ±0.50 D and ±1.0 D; (4) the formula performance index (FPI).

The Shapiro-Wilk test was applied to examine the normality of continuous variables. Data that followed a normal distribution were summarized as the mean and SD. Categorical variables were reported as frequencies and percentages. Changes in corneal parameters before and after myopic corneal refractive surgery were analyzed using the paired t -test. The association between postoperative PRC and preoperative ARC was initially explored with scatter plots, followed by Pearson’s correlation analysis and subsequent construction of a linear regression model. Analysis of trueness, precision, and accuracy of formulas was performed using the Eyetemis platform ( https://eyetemis.com ). We reported Holm-corrected P values for multiple comparisons between formulas, and unadjusted P values for pairwise comparisons between the standard and PRC versions of the same formula. All statistical analysis was performed using STATA (version 17; StataCorp). R software (version 4.3.0; R Foundation for Statistical Computing) and OriginPro 2023 (OriginLab) were used for graphing.

The development set included a total of 134 participants (134 eyes) scheduled for MRS. The mean age was 27.63 ± 5.95 years (range: 18 to 40 years). Among these eyes, 98 (73.13%) underwent SMILE and 36 (26.87%) received FS-LASIK. The mean preoperative AL was 25.73 ± 1.00 mm (range: 23.72 to 28.24 mm). The validation set included 225 cataract patients after MRS with a mean age of 53.18 ± 7.15 years. The mean AL was 28.24 ± 2.31 mm (range: 24.11 to 36.17 mm), and the mean simulated and posterior keratometry were 38.08 ± 2.12 and 5.71 ± 0.24 D, respectively. The most frequently used IOL models were ZCB00 (Johnson & Johnson Vision), SN60WF (Alcon), ZXR00 (Johnson & Johnson Vision), MX60 (Bausch + Lomb), and 920H (Rayner), accounting for over 65% of implanted lenses. The detailed distribution of all implanted IOL models is provided in Supplementary Materials (eTable 1).

The TCP decreased from 42.69 ± 1.30 D preoperatively to 37.42 ± 2.19 D postoperatively (eTable 2, mean difference, 5.28 ± 1.72 D, P <.001), and simulated keratometry decreased from 43.28 ± 1.33 to 38.56 ± 2.07 D (mean difference, 4.73 ± 1.54 D; P <.001). PRC also showed a small but statistically significant reduction (5.84 ± 0.21 vs 5.82 ± 0.21 D; mean difference, 0.019 ± 0.063 D; P <.001), and the B/F ratio declined from 0.88 ± 0.01 to 0.78 ± 0.03 ( P <.001). Notably, SMILE and FS-LASIK induced a similar change pattern in both anterior and posterior keratometry (both P >.05, eTable 2 and Figure 2 A). A strong linear relationship was observed between postoperative PRC and preoperative ARC, with a correlation coefficient of 0.91 ( P <.001). Based on this relationship, a linear regression model was established as follows (in mm): preoperative ARC = 0.87* postoperative PRC + 1.82 (Equation 2), with an R² of 0.82 ( Figure 2 B). Two additional regression models were established for the non-PRC version (LISA MRS): 1) TCP = 1.06 × Kmean-3.27 (in D, Equation 3); and 2) preoperative ARC = 0.34 × postoperative ARC + 4.86 (in mm, Equation 4).

Changes in posterior corneal radius before and after myopic corneal refractive surgery (A), and the relationship between preoperative anterior corneal radius and postoperative posterior corneal radius (B). SMILE = small incision lenticule extraction; FS-LASIK = femtosecond laser-assisted in situ keratomileusis.

Table 1 and Figure 3 summarize the prediction accuracy of the 10 formulas in the validation set. Most formulas showed a myopic prediction error ranging from −0.09 D (LISA MRS and LISA MRS-PRC) to −0.45 D (Haigis-L), except for Hoffer QST-PRC (−0.02 D). For precision of postoperative spherical equivalent prediction errors (SEQ-PEs), there were significant differeces between LISA MRS-PRC and Haigis-L, Hoffer QST, and Shammas PL, as well as between EVO-PRC and Haigis-L (all adjusted P value <.05, eFigure 1E). Regarding the accuracy of SEQ-PEs, statistical analysis revealed significant differences in the following comparisons: LISA MRS-PRC vs Hoffer QST; EVO-PRC vs Barrett True K and Hoffer QST; and EVO vs Hoffer QST. Furthermore, Haigis-L and Shammas-PL showed significantly lower accuracy than most other formulas (eFigure 1E). The FPI was highest for LISA MRS (with or without PRC, 0.43), followed by Hoffer QST (0.37), EVO and Hoffer QST-PRC (both 0.32), EVO-PRC and Barrett True K-PRC (both 0.30), and Barrett True K (0.26). LISA MRS-PRC and EVO-PRC both achieved the lowest MedAE (0.47 D). LISA MRS-PRC also yielded the lowest RMSAE (0.76 D) and the highest percentage of eyes within ±0.50 D of prediction error (52.00%), whereas EVO-PRC had the lowest MAE (0.58 D).

Table 1

Performance of IOL Power Calculation Formulas in Cataract Patients With Prior Myopic Corneal Refractive Surgery ( n = 225)

	ME(SD)	MAE	MedAE	RMSAE	±0.25D	±0.50D	±1D	FPI
Barrett True K	−0.25 (0.81) a	0.67	0.61	0.85	24.89	45.33	75.56	0.26
Barrett True K-PRC	−0.19 (0.77) a	0.63	0.54 b	0.79	24.00	46.67	80.00 c	0.30
EVO	−0.14 (0.78) a	0.60	0.49	0.79	31.56	50.22	77.33	0.32
EVO-PRC	−0.14 (0.77) a	0.58	0.47	0.78	34.67	51.56	77.78	0.30
Haigis-L	−0.45 (0.96) a	0.83	0.70	1.06	20.00	36.44	67.11	0.37
Hoffer QST	−0.15 (0.88) a	0.71	0.60	0.89	23.11	40.44	76.89	0.37
Hoffer QST-PRC	−0.02 (0.79)	0.61	0.50 b	0.79	28.44	50.22 c	80.44	0.32
LISA MRS	−0.09 (0.80) a	0.63	0.54	0.80	26.67	47.56	77.33	0.43
LISA MRS-PRC	−0.09 (0.76) a	0.60	0.47 b	0.76	29.33	52.00 c	79.11	0.43
Shammas PL	−0.38 (0.87) a	0.77	0.69	0.95	19.11	37.78	70.22	0.25

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