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The refractive accuracy of intraocular lens (IOL) formulas varies in eyes that undergo combined phacovitrectomy for different underlying vitreoretinal pathology. A total of 401 eyes that underwent uncomplicated phacovitrectomy (23–25 g) with implantation of a plate haptic IOL (CT Asphina 409 M) in the capsular bag between April 2020 and December 2022 were included in the study. Inclusion criteria were postoperative best corrected visual acuity of 0.4 LogMAR or better at least 8 weeks after surgery. The Barrett Universal II (BUII), Haigis, Hill-Radial Basis Function (Hill-RBFv3.0), Hoffer Q, Holladay I, Holladay II, Kane, K6, Pearl-DGS and SRK/T formulas were compared for their accuracy in mean absolute error (MAE). Furthermore, all formulas were additionally tested by using the prediction for an IOL power 0,5 or 1D above the IOL used (IOLdown). Wilcox-Holladay-Wang-Koch (WHWK) statistical tests with Holm correction were applied. The Barrett IOLdown formula showed the lowest refractive prediction error (0.03D; together with Hill IOLdown), lowest MAE (0.40D), lowest median absolute error (MedAE; 0.31D), lowest standard deviation of MAE (0.55D) and lowest root mean squared absolute error (RMSAE; 0,54D). Barrett IOLdown had the highest percentage of eyes with predicted error within ± 0.25D (41.6%), Kane IOLdown within ± 0.50D (70.5%) and ± 0.75D (89%) and Hill IOLdown within ± 1D (95.2%). Except for Haigis, Hoffer Q and Pearl-DGS, all other formulas showed a statistically significantly lower MAE after IOLdown modification. The newest formulas with IOLdown modification performed better than old generation formulas, with Barrett IOLdown exhibiting the best results.

It is difficult to accurately estimate species richness if there are many almost undetectable species in a hyper‐diverse community. Practically, an accurate lower bound for species richness is preferable to an inaccurate point estimator. The traditional nonparametric lower bound developed by Chao (1984, Scandinavian Journal of Statistics 11, 265–270) for individual‐based abundance data uses only the information on the rarest species (the numbers of singletons and doubletons) to estimate the number of undetected species in samples. Applying a modified Good–Turing frequency formula, we derive an approximate formula for the first‐order bias of this traditional lower bound. The approximate bias is estimated by using additional information (namely, the numbers of tripletons and quadrupletons). This approximate bias can be corrected, and an improved lower bound is thus obtained. The proposed lower bound is nonparametric in the sense that it is universally valid for any species abundance distribution. A similar type of improved lower bound can be derived for incidence data. We test our proposed lower bounds on simulated data sets generated from various species abundance models. Simulation results show that the proposed lower bounds always reduce bias over the traditional lower bounds and improve accuracy (as measured by mean squared error) when the heterogeneity of species abundances is relatively high. We also apply the proposed new lower bounds to real data for illustration and for comparisons with previously developed estimators.

This study investigated the underlying causes of the myopic outcomes of the optic-based newer formulas (Barrett Universal II, EVO 2.0, Kane, Hoffer-QST and PEARL-DGS) in long Korean eyes with Alcon TFNT intraocular lens (IOL) implantation. Postoperative data from 3100 randomly selected eyes of 3100 patients were analyzed to compare the reference back-calculated effective lens positions (ELPs) based on the Haigis formula using conventional axial length (AL) and Cooke-modified AL (CMAL) with the predicted ELP of each single- and triple-optimized Haigis formula applied to AL- and CMAL. Contrary to the AL-applied Haigis formula, the predicted ELP curve of the CMAL-applied, single-optimized Haigis formula, simulating the methods of the newer formulas, exhibited a significant upward deviation from the back-calculated ELP in long eyes. The relationship between the AL and anterior chamber depth in our long-eyed population differed from that in the base population of the PEARL-DGS formula. The myopic outcomes in long eyes appeared to stem from the substantial overestimation of the postoperative IOL position with AL modification, leading to the implantation of inappropriately higher-powered IOLs. This discrepancy may be attributed to the ethnic differences in ocular biometrics, particularly the relatively smaller anterior segment in East Asian patients with long AL.

PurposeTo investigate the accuracy of modern intraocular lens (IOL) power calculation formulas in eyes with axial length (AL) ≥ 26.00 mm.MethodsA total of 193 eyes with one type of lens were analysed. An IOL Master 700 (Carl Zeiss Meditec, Jena, Germany) was used for optical biometry. Thirteen formulas and their modifications were evaluated: Barrett Universal II, Haigis, Hoffer QST, Holladay 1 MWK, Holladay 1 NLR, Holladay 2 NLR, Kane, Naeser 2, SRK/T, SRK/T MWK, T2, VRF and VRF-G. The User Group for Laser Interference Biometry lens constants were used for IOL power calculation. The mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE) and the percentage of eyes with PEs within ± 0.25 D, ± 0.50 D and <  ± 1.00 D were calculated.ResultsThe modern formulas (Barrett Universal II, Hoffer QST, Kane, Naeser 2 and VRF-G) produced the smallest MedAE among all methods (0.30 D, 0.30 D, 0.30 D, 0.29 D and 0.28 D, respectively). The percentage of eyes with a PE within ± 0.50 D ranged from 67.48% to 74.85% for SRK/T and Hoffer QST, Naeser 2 and VRF-G, respectively.ConclusionsDunn’s post hoc test of the absolute errors revealed statistically significant differences (P < 0.05) between some of the newer formulas (Naeser 2 and VRF-G) and the remaining ones. From a clinical perspective the Hoffer QST, Naeser 2 and VRF-G formulas were more accurate predictors of postoperative refraction with the largest proportion of eyes within ± 0.50 D.

This study evaluates the accuracy of a newly developed intraocular lens (IOL) power calculation method that applies four different IOL power calculation formulas according to 768 biometric subgroups based on keratometry, anterior chamber depth, and axial length. This retrospective cross-sectional study was conducted in at Korea University Ansan Hospital. A total of 1600 eyes from 1600 patients who underwent phacoemulsification and a ZCB00 IOL in-the-bag implantation were divided into two datasets: a reference dataset (1200 eyes) and a validation dataset (400 eyes). Using the reference dataset and the results of previous studies, the Eom IOL power calculator was developed using 768 biometric subgroups. The median absolute errors (MedAEs) and IOL Formula Performance Indexes (FPIs) of the Barrett Universal II, Haigis, Hoffer Q, Holladay 1, Ladas Super, SRK/T, and Eom formulas using the 400-eye validation dataset were compared. The MedAE of the Eom formula (0.22 D) was significantly smaller than that of the other four formulas, except for the Barrett Universal II and Ladas Super formulas (0.24 D and 0.23 D, respectively). The IOL FPI of the Eom formula was 0.553, which ranked first, followed by the Ladas Super (0.474), Barrett Universal II (0.470), Holladay 1 (0.444), Hoffer Q (0.396), Haigis (0.392), and SRK/T (0.361) formulas. In conclusion, the Eom IOL power calculator developed in this study demonstrated similar or slightly better accuracy than the Barrett Universal II and Ladas Super formulas and was superior to the four traditional IOL power calculation formulas.

Purpose: The proper selection of an intraocular lens power calculation formula is an essential aspect of cataract surgery. This study evaluated the accuracy of artificial intelligence-based formulas. Design: Systematic review. Methods: This review comprises articles evaluating the exactness of artificial intelligence-based formulas published from 2017 to July 2023. The papers were identified by a literature search of various databases (Pubmed/MEDLINE, Google Scholar, Crossref, Cochrane Library, Web of Science, and SciELO) using the terms “IOL formulas”, “FullMonte”, “Ladas”, “Hill-RBF”, “PEARL-DGS”, “Kane”, “Karmona”, “Hoffer QST”, and “Nallasamy”. In total, 25 peer-reviewed articles in English with the maximum sample and the largest number of compared formulas were examined. Results: The scores of the mean absolute error and percentage of patients within ±0.5 D and ±1.0 D were used to estimate the exactness of the formulas. In most studies the Kane formula obtained the smallest mean absolute error and the highest percentage of patients within ±0.5 D and ±1.0 D. Second place was typically achieved by the PEARL DGS formula. The limitations of the studies were also discussed. Conclusions: Kane seems to be the most accurate artificial intelligence-based formula. PEARL DGS also gives very good results. Hoffer QST, Karmona, and Nallasamy are the newest, and need further evaluation.

To assess the contribution of each optional parameter to the IOL power calculation and evaluate the effect of omitting biometric variables (ACD, LT, WTW) using the VRF-G formula. A total of 501 eyes from 501 consecutive patients included in the study underwent cataract surgery with in-the-bag implantation of one-piece soft hydrophobic acrylic posterior chamber IOLs, AcrySof IQ SN60WF (Alcon Labs, Fort Worth, TX, USA). The primary calculation comprised five measured variables, and IOL power was recalculated for different combinations of omitting ACD, LT, and WTW. Outcome measurements included the difference in IOL power calculations between different omission combinations. Omitting any of the biometric variables resulted in a significant difference in the mean difference in IOL power calculation (ranging from 0.029 to 0.108 diopters), except for WTW omission alone (0.002 diopters). ACD proved to have the most impact, with its omission resulting in larger differences in power calculations (range: 0.177-0.248 diopters) compared to combinations where ACD was not omitted (range: 0.057-0.141 diopters). The shortest eyes were most affected by ACD omission. The study highlights the importance of ACD in IOL power calculations, particularly for shorter eyes. WTW and LT were found to be less important when using the VRF-G formula for IOL power calculations.

This study aimed to evaluate the accuracy of six intraocular lens (IOL) calculation formulas using total keratometry (TK) and standard keratometry (K) measurements from the IOLMaster 700 in various ocular subgroups. A total of 212 eyes were analyzed. The mean absolute error (MAE), standard deviation (SD) of prediction error, and the median absolute error (MedAE) were calculated for each formula. and the prediction accuracy was compared across different subgroups categorized by axial length (AL), anterior chamber depth (ACD), lens thickness (LT), and other ocular parameters. Results showed that the Barrett Universal II (BU II) formula consistently had the lowest MAEs and MedAEs in the overall sample and most subgroups. The BU II formula performed particularly well in subgroups with thin LT when using TK mode and in medium LT subgroups using K mode. Comparison between TK and K modes showed no consistent superiority, with each mode outperforming the other in specific subgroups. The accuracy of the BU II formula was not influenced by ocular parameters, suggesting its robustness across different patient groups. In conclusion, the BU II formula demonstrated superior accuracy compared to other formulas, especially in specific subgroups, and its performance remained consistent regardless of ocular measurement variations.

BackgroundScleral fixation of intraocular lenses has become a popular procedure for treating aphakia in the absence of capsular support. However, the lens formulas used to predict refractive outcomes were designed for in-the-bag lens placement. This study evaluates the accuracy of the SRK/T formula in predicting a target postoperative refraction when suturing a scleral-fixated intraocular lens (IOL) implant 3 mm posterior to the limbus.MethodsThis is a retrospective, case series including 20 eyes of 20 patients who underwent scleral fixation of Akreos AO60 IOLs (Bausch & Lomb, Rochester, NY) by a single surgeon at the OSU Wexner Medical Center. Preoperative measurements were performed with optical biometry, and IOL power was calculated with the SRK/T formula. Following surgery, the actual refractive spherical equivalent (SE) was performed and compared with the preoperative prediction. Prediction error (PE), defined as the deviation of actual postoperative SE refraction in diopters (D) from preoperative predicted SE refraction, was the primary outcome measure.ResultsThe mean attempted (predicted) SE was − 1.12 D (± 0.87). Mean achieved SE was − 0.96 D (± 1.04). Mean PE (actual postoperative SE versus predicted preoperative SE) was 0.16 D (± 0.69). A total of 9 eyes (45%) were within ± 0.5 D of the predicted SE, 16 eyes (80%) were within ± 1.0 D, and all 20 eyes (100%) were within ± 1.5 D.ConclusionIOL power calculation using the SRK/T formula with optical biometry demonstrates reliable postoperative refractive outcomes in patients undergoing scleral fixation of an IOL (Akreos AO60). Further studies are needed to refine the predictive value of the SRK/T and other formulas for application in scleral fixation of IOLs.

To compare the accuracy of a newly developed intraocular lens (IOL) power formula (VRF-G) with twelve existing formulas (Barret Universal II, EVO 2.0, Haigis, Hill-RBF 2.0, Hoffer Q, Holladay 1, Kane, Næeser 2, PEARL-DGS, SRK/T, T2 and VRF). Retrospective case series including 828 patients having uncomplicated cataract surgery with the implantation of a single IOL model (SN60WF). Using optimised constants, refraction prediction error of each formula was calculated for each eye. Subgroup analysis was performed based on the axial length (short ≤22.0mm; medium >22.0mm to <26.0mm; long ≥26.0mm). Main outcomes included mean prediction error (ME) mean (MAE) and median absolute error (MedAE), in diopters (D), and the percentage of eyes within ±0.25D, ±0.50D, ±0.75D and ±1.00D. Formulas absolute errors were statistically different among them (p<0.001), with Kane having the lowest MAE of all formulas, followed by EVO 2.0 and VRF-G, which had the lowest MedAE. The Kane formula had the highest percentage of eyes within ±0.25D (47.0%) and ±1.00D (97.7%) and the VRF-G formula had the highest percentage of eyes within ±0.50D (79.5%). For all AL subgroups, Kane, EVO 2.0 and VRF-G formulas had the most accurate performances (lowest MAE). New generation formulas may help us in achieving better refractive results, lowering the variance in accuracy in extreme eyes - Kane, EVO 2.0 and VRF-G formulas are promising candidates to fulfil that goal.