Accuracy of Kane, Hill-RBF, and PEARL-DGS versus traditional IOL formulas in highly myopic eyes: a systematic review and meta-analysis

Abstract

Purpose

To evaluate the accuracy of Kane, Hill-RBF, and PEARL-DGS compared with traditional intraocular lens (IOL) formulas in highly myopic eyes undergoing cataract surgery.

Methods

A systematic review registered in PROSPERO (CRD420261372807) and conducted in accordance with PRISMA 2020 evaluated studies comparing Kane, Hill-RBF, and/or PEARL-DGS with conventional IOL formulas in highly myopic eyes. PubMed, Embase, and the Cochrane Library were searched from inception to April 8, 2026 using reconstructed database-specific strategies combining concepts for high myopia or long axial length, cataract surgery and IOL power calculation, and the formula names Kane, Hill-RBF, and PEARL-DGS. Two independent reviewers performed screening, data extraction, and adapted PROBAST-style risk-of-bias assessment, with disagreements resolved by a third reviewer. Eligible studies included original human clinical studies reporting postoperative refractive prediction outcomes in highly myopic eyes, preferentially defined as axial length (AL) > = 26.0 mm, or in separately extractable high-myopia subgroups. Random-effects quantitative synthesis was performed for the most comparable threshold endpoint when exact percentages and denominators were available. Primary outcomes included the proportion of eyes within +/-0.50 D of prediction error and mean absolute error (MAE), when reported using sufficiently comparable definitions. Secondary outcomes included MedAE, ME, SD of prediction error, RMSAE, and the proportions of eyes within +/-0.25 D and +/-1.00 D.

Results

The final included evidence set comprised 11 original comparative studies published online or in print from 2020 to 2026. Five studies were threshold-relevant in the narrative layer, 4 had numeric +/-0.50 D rows represented in the extraction seed, and 3 entered the pooled target-formula model. Across the included studies, Kane, Hill-RBF, and PEARL-DGS generally showed favorable refractive prediction performance in highly myopic eyes, but rankings varied by axial-length subgroup, formula version, biometry inputs, constant optimization, mean error zeroing, IOL design, and outcome family. Verified findings included a MedAE of 0.26 D for Kane in Cheng 2021, an MAE of 0.40 +/- 0.39 D with 71.44% within +/-0.50 D for Hill-RBF 2.0 in Chen 2021, and in Jiang 2025 a lowest overall MAE of 0.50 D for Hill-RBF 3.0 with the highest overall +/-0.50 D proportion of 69.57% for PEARL-DGS. For the exploratory cross-formula target benchmark, three independent studies contributed exact overall threshold rows, yielding a pooled proportion within +/-0.50 D of 70.90% (95% CI, 68.34% to 73.33%; I2 = 0.0%). A secondary Hill-RBF overall synthesis from two studies yielded 71.03% (95% CI, 68.35% to 73.58%; I2 = 0.0%). Because the main pooled model contains only 3 studies and combines architecture-distinct target formulas, I2 should be interpreted as a descriptive statistic with limited power rather than as evidence of biological or algorithmic homogeneity.

Conclusions

Current evidence supports Kane, Hill-RBF, and PEARL-DGS as reasonable front-line options for highly myopic eyes, and the threshold synthesis provides a cautious benchmark for currently extractable overall target-formula threshold performance. However, the evidence does not establish a single formula as uniformly best across all long-eye settings, nor does the 3-study pooled model constitute a formula ranking. Interpretation should remain anchored to threshold-based accuracy and to study-level differences in population definition, formula implementation, IOL design, and analytical handling.

Registration

This review was registered in PROSPERO under CRD420261372807.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12886-026-05048-5.

Introduction

Previous comparative studies and one related network meta-analysis provide the evidence base for this review [1–12]. Methodological sources on newer formula architecture and biometry inputs provide mechanistic context [13–20]. Accurate IOL power calculation remains challenging in highly myopic eyes for reasons that extend beyond geometric axial elongation alone. Long eyes may expose optical-biometry assumptions because axial length derived from a single group refractive index can differ from segmental or sum-of-segments estimates, particularly when the vitreous cavity is disproportionately enlarged [16, 17]. Highly myopic eyes may also show non-proportional relationships among axial length, anterior chamber depth, lens thickness, corneal power, and posterior corneal shape, which can make effective lens position or related anatomical-position estimates less stable than in average eyes [15]. In addition, the use of standard keratometry versus total keratometry or other posterior-corneal inputs can change the information available to formulas and may partly explain why formula rankings vary across long-eye cohorts [3, 14].

The clinical relevance of a +/-0.50 D benchmark is underscored by broader cataract literature showing that even contemporary formula performance leaves a substantial minority of eyes outside this threshold. A recent medium-long-eye artificial-intelligence formula study reported a contextual benchmark of 73.7% of eyes within +/-0.50 D [21]. This value is used here as a background comparator rather than as a direct high-myopia estimate: if contemporary AI formulas leave 26.3% of eyes outside +/-0.50 D in a less extreme long-eye cohort, separately evaluating highly myopic eyes is clinically warranted. Related biometry literature has emphasized that axial length, corneal power, and anterior-chamber-depth-related effective-lens-position uncertainty may contribute materially to IOL power error, with reported proportional contributions of approximately 36%, 22%, and 42%, respectively [22]. These proportions should be interpreted as general background on biometric and algorithmic error sources, not as fixed weights transferable to eyes with AL > = 26.0 mm or AL > = 30.0 mm, where posterior-pole morphology and axial-length measurement geometry may shift the balance of error.

Newer formulas such as Kane, Hill-RBF, and PEARL-DGS have attracted increasing attention, but they should not be treated as a single interchangeable artificial-intelligence category. The Kane formula is described as a theoretical-optics formula refined by regression and artificial-intelligence components [18]. Hill-RBF is a data-driven radial-basis-function pattern-recognition method with mathematical boundary or out-of-bounds checks intended to flag biometric patterns less represented in the training space [19]. PEARL-DGS is an open-source, machine-learning-based thick-lens formula-development framework that can incorporate sum-of-segments axial length and machine-learning prediction of theoretical internal lens position [20]. Ensemble-learning approaches such as the Nallasamy formula further illustrate that modern formula development is moving toward architecture-specific combinations of optical modeling, training data, and implementation constraints rather than a single undifferentiated “AI formula” class [13].

Related formula-development literature also highlights mechanisms that may shape future long-eye prediction accuracy, including stacking ensemble machine learning, updated formula calibration such as Hoffer QST, and population-specific artificial-intelligence estimation of effective lens position [13–15]. These studies are cited as methodological context only and were not added to the 11-study systematic-review evidence set.

The current clinical literature has reached a broad but incomplete consensus: newer formulas often perform favorably in long eyes, but their apparent advantage is modified by axial-length spectrum, comparator choice, formula version, optimization strategy, and outcome definition. This creates two practical controversies for clinicians. First, studies in very long eyes do not consistently show whether newer formulas or optimized Wang-Koch-adjusted traditional formulas should be preferred. Second, few datasets evaluate Kane, Hill-RBF, and PEARL-DGS head-to-head under harmonized reporting conditions. A review that separates consensus findings from these unresolved controversies is therefore more useful than a simple formula-ranking exercise.

This review was designed to address that need by organizing the evidence around a common clinical benchmark, the proportion of eyes within +/-0.50 D of prediction error, while preserving incompatible absolute-error families as separate outcomes. Because several studies differ in reporting structure and analytical handling, the present manuscript does not claim a completed pooled ranking. Instead, it maps the verified evidence, identifies which endpoints are most comparable, and clarifies where future quantitative synthesis would be defensible.

This systematic review was designed to evaluate the accuracy of Kane, Hill-RBF, and PEARL-DGS versus traditional IOL formulas in highly myopic eyes undergoing cataract surgery, to summarize comparative evidence on refractive prediction accuracy, and to identify key methodological sources of heterogeneity.

Methods

Protocol and registration

This systematic review was conducted in accordance with PRISMA 2020 and was registered in PROSPERO (CRD420261372807). The review question was defined a priori to evaluate the accuracy of Kane, Hill-RBF, and PEARL-DGS versus traditional intraocular lens (IOL) formulas in highly myopic eyes undergoing cataract surgery.

Eligibility criteria

Eligible studies were original human clinical studies of cataract surgery with IOL implantation that enrolled highly myopic eyes or provided a separately extractable high-myopia subgroup, evaluated at least one index formula of interest (Kane, Hill-RBF, or PEARL-DGS), included at least one conventional comparator formula, and reported postoperative refractive prediction outcomes. High myopia was preferentially defined as AL > = 26.0 mm.

Reviews, editorials, conference abstracts without sufficient data, animal studies, simulation-only studies, and studies without extractable postoperative refractive outcomes were excluded.

Information sources and search strategy

A systematic literature search was conducted in PubMed, Embase, and the Cochrane Library from database inception to April 8, 2026. The search strategy combined concepts for high myopia or long axial length, cataract surgery and IOL implantation, refractive prediction or IOL power calculation, and the formula names Kane, Hill-RBF, and PEARL-DGS. Reference lists of included studies and relevant review articles were also screened manually to identify additional reports. Original saved platform export queries and duplicate-removal logs were not available in the working directory at manuscript preparation. Therefore, Supplementary Appendix 1 provides reconstructed final search strategies, screening notes, and pooling-eligibility decisions to support transparency, while acknowledging that the exact database-export history cannot be reproduced verbatim. The reconstructed strategy is intended to make the search logic auditable, but it cannot guarantee forensic identity with historical database hit counts because live bibliographic databases may change through indexing updates and delayed record curation.

Selection process

Two reviewers independently screened titles and abstracts and then independently reviewed the full texts of potentially eligible articles. Records judged clearly irrelevant were excluded at title and abstract screening, whereas uncertain records were advanced to full-text assessment. Disagreements were resolved first by discussion and, when needed, by adjudication from a third reviewer. One primary reason for exclusion was assigned to each excluded full-text article.

Data collection process and outcomes

Two reviewers independently extracted data using a predefined standardized form, with disagreements resolved by discussion and then by a third reviewer when required. Data extraction included study design, country, sample size, high-myopia definition, axial length threshold, formula list and version, formula access year when reported, comparator formulas, biometry method and device generation, keratometry source, IOL model or IOL design, constant optimization, mean error zeroing, and outcome definitions. When available, extraction also recorded whether the study used standard keratometry or total keratometry, single-index or segmental/sum-of-segments axial length, and whether complex subgroups such as posterior staphyloma or previous corneal refractive surgery were separately extractable. Outcomes of interest included MAE, MedAE, ME, SD of prediction error, RMSAE when reported, and the proportions of eyes within +/-0.25 D, +/-0.50 D, and +/-1.00 D. When studies reported separately analyzable long-eye subgroups, those subgroup data were extracted separately while preserving the parent study identifier. Missing IOL model, denominator, or formula-version fields were coded as not reported or unavailable in the extractable source rather than left blank.

The primary outcomes were the proportion of eyes within +/-0.50 D of prediction error and MAE, when reported using sufficiently comparable definitions.

Risk of bias assessment

Two reviewers independently assessed methodological quality using an adapted PROBAST-style framework tailored to comparative IOL-formula prediction studies. The prespecified risk-of-bias domains were Participants/patient selection, Predictor/index-formula process, Outcome ascertainment, and Analysis integrity. Applicability concerns were judged separately for population applicability, formula applicability, and outcome applicability. Particular attention was paid to exact formula version, IOL constant optimization, mean error zeroing, measurement device, subgroup extractability, and whether analyses were performed on an eye-based or patient-based basis. Disagreements were resolved by discussion and, when required, by a third reviewer.

Statistical strategy

All included studies were eligible for structured qualitative synthesis. Quantitative synthesis was prespecified only when studies were sufficiently comparable in population definition, outcome reporting, and analytical methods. For the completed threshold model, logit-transformed random-effects proportion meta-analysis was implemented in a reproducible Python standard-library script, using DerSimonian-Laird tau2 and reporting pooled proportions with 95% confidence intervals. Statistical heterogeneity was evaluated using Cochran’s Q and the I2 statistic, but heterogeneity estimates from very small models were treated as descriptive and underpowered. No missing formula-specific threshold percentage, denominator, dispersion measure, or paired-comparison correlation was imputed. MAE, MedAE, RMSAE, and study-defined AE metrics were treated as distinct endpoints and were not pooled across incompatible summary metrics. Because threshold-based refractive accuracy was more consistently reported across the verified literature, the proportion of eyes within +/-0.50 D was prespecified as the most promising common endpoint for broader cross-study synthesis. Narrative synthesis was preferred whenever clinical, formula-level, IOL-design, calibration, or methodological heterogeneity prevented defensible pooling.

Subgroup and sensitivity analyses were planned according to axial length threshold, formula version, constant optimization, mean error zeroing, and special analytical contexts such as plate-haptic IOL implantation. When data permitted, additional sensitivity groupings were planned for swept-source OCT versus non-swept-source biometry, standard keratometry versus total keratometry, single-index versus segmental or sum-of-segments axial length, and online formula access period. These planned analyses were not forced when the extractable studies lacked aligned subgroup denominators, exact formula versions, or sufficient reporting of optimization and mean-error handling.

Reporting bias assessment

Assessment of reporting bias was planned only for pooled endpoints to which at least 10 studies contributed. When that threshold was met, funnel plots and Egger’s test were to be used to explore possible small-study effects or publication bias.

Certainty of evidence

A brief GRADE-style narrative approach was planned for the primary threshold endpoint, with attention to study design, risk of bias, inconsistency, indirectness, imprecision, and reporting-bias concerns. Incompatible nonpooled outcome families such as MAE, MedAE, RMSAE, and AE were not assigned a combined pooled-certainty rating unless future harmonized synthesis became possible.

Results

Study selection

The locked working library identified 13 records for screening. No citation-level duplicates remained in the final authoritative library, so 13 unique records underwent title and abstract screening. No records were excluded at the title and abstract stage because the current library had already been narrowed to directly relevant original studies before the analysis lock. All 13 reports were therefore sought for retrieval, retrieved, and assessed at the full-text level. Two studies were excluded after full-text review, leaving 11 studies in the systematic review. Five studies were threshold-relevant in the narrative layer for the proportion of eyes within +/-0.50 D of prediction error; 4 had numeric +/-0.50 D rows in the extraction seed, and 3 contributed exact overall target-formula rows with usable denominators to the pooled model.

The two full-text exclusions were assigned as follows: one study was excluded because separately extractable high-myopia outcomes against adequate traditional comparators were not confirmed (Chen 2024), and one study was excluded because the comparator structure did not match the prespecified target-versus-traditional review question (Zhu 2023). Within the retained working files, no included report was coded as a confirmed duplicate or overlapping cohort requiring removal.

Figure 1 presents a PRISMA 2020 flow diagram based on these locked working-library counts. Because the original raw database export and duplicate-removal logs were unavailable at manuscript preparation, the identification-stage nodes should be interpreted as a reconstructed library flow rather than a verbatim database-audit trail; the reconstructed search strategies and pooling-eligibility matrix are provided in Supplementary Appendix 1.

Fig. 1.

PRISMA 2020 flow diagram of study selection. PRISMA 2020 flow diagram based on the locked working-library counts available for this review: 13 records in the locked library, 0 duplicates removed, 13 records screened, 13 reports sought for retrieval and retrieved, 13 full texts assessed, 2 full-text exclusions (Chen 2024 and Zhu 2023), 11 studies included in the systematic review, 5 studies retained in the threshold-oriented evidence layer, and 3 studies entered in the pooled target-formula model. Because original raw database export logs were unavailable at manuscript preparation, the identification-stage nodes should be interpreted as a reconstructed library flow rather than a verbatim database-audit trail; additional search and pooling-eligibility details are provided in Supplementary Appendix 1.

Study characteristics

The final 11-study set published online or in print from 2020 to 2026 comprised 7 core comparative studies and 4 supplementary-only studies retained for contextual or sensitivity use. Studies were conducted across China, Japan, Spain, Poland, and other international long-eye cohorts, and most used retrospective comparative or retrospective case-series designs, although prospective evidence was also present.

Definitions of high myopia varied, although most studies used axial length thresholds around AL > = 26.0 mm. Some studies emphasized more extreme subgroups such as AL > = 30.0 mm, whereas others evaluated broader long-eye ranges above 26.0 mm. These differences mattered because eyes at or beyond 30.0 mm may be more likely to have posterior-pole anatomic irregularity, axial-length measurement axis mismatch, or effective-lens-position prediction instability than less extreme long eyes. Comparator rankings therefore should not be assumed to remain stable across all axial-length strata.

Across the final included set, the target formulas of interest were Kane, Hill-RBF, and PEARL-DGS, although not every study evaluated all three simultaneously. Earlier studies more commonly assessed Kane and Hill-RBF 2.0, whereas later studies increasingly included Hill-RBF 3.0 and PEARL-DGS. Comparator formulas frequently included SRK/T, Haigis, Holladay 1, Holladay 2, and Barrett Universal II, and several studies also examined Wang-Koch-adjusted traditional formulas or broader sets of contemporary formulas.

Biometry platform, keratometry strategy, IOL model, postoperative follow-up, constant optimization, and mean error handling were not harmonized across the evidence base. Extractable IOL details ranged from explicit special-design contexts, such as plate-haptic IOL implantation, to broader cataract cohorts in which the implanted model was not reported in the extractable source. IOL model opacity was treated as an interpretation and risk-of-bias issue rather than solved by inference, because IOL design and constant selection can affect effective lens position and formula calibration. For that reason, the 7 core studies were used to anchor the main comparative narrative, whereas 4 supplementary-only studies were retained to contextualize RMSAE-focused findings, keratometry-specific analyses, PEARL-DGS-only long-eye comparisons, and special-design sensitivity settings rather than to drive the pooled threshold model.

Qualitative synthesis

The qualitative synthesis was interpreted in two tiers and organized around the main questions that make this literature clinically difficult. The 7 core studies formed the main comparative evidence base for judging whether Kane, Hill-RBF, and PEARL-DGS consistently improved prediction accuracy over traditional formulas in highly myopic or long-eye cohorts. Four additional studies were retained as supplementary-only evidence because they mainly contributed RMSAE-structure context, keratometry-specific context, PEARL-DGS-only long-eye context, or a special plate-haptic IOL sensitivity context rather than directly strengthening the main comparative set.

Core comparative evidence

Across the 7 core studies, the evidence supported a cautious but consistent consensus: Kane, Hill-RBF, and PEARL-DGS generally demonstrated favorable refractive prediction performance in highly myopic eyes and often matched or outperformed older traditional formulas, but no single newer formula was uniformly superior across all cohorts and analytical settings. The main value of synthesizing these reports together is therefore not to declare an absolute winner, but to show where the favorable pattern is reproducible and where it breaks down.

Kane showed strong performance across multiple core studies. In Cheng 2021, the extraction seed verifies 370 eyes and a lowest overall Kane MedAE of 0.26 D [1]. In Jiang 2025, Kane achieved the lowest MAE in the super-long subgroup at 0.43 D and 70.97% of eyes within +/-0.50 D [6]. Hill-RBF also performed well in the core evidence base. Chen 2021 reported that Hill-RBF 2.0 had the lowest MAE at 0.40 +/- 0.39 D and the highest proportions within +/-0.50 D and +/-1.00 D at 71.44% and 94.59%, respectively [2]. In Jiang 2025, Hill-RBF 3.0 had the lowest overall MAE at 0.50 D and the lowest overall MedAE at 0.34 D, and in the long-axial-length subgroup it again had the lowest MAE at 0.43 D and the highest proportion within +/-0.50 D at 79.17% [6]. In Wei 2022, Hill-RBF 3.0 with total keratometry achieved 66.99% of eyes within +/-0.50 D and 87.38% within +/-0.75 D [3].

PEARL-DGS was increasingly competitive in the core evidence base, but the core studies did not show uniform dominance. In Jiang 2025, PEARL-DGS achieved the highest overall proportion of eyes within +/-0.50 D at 69.57% [6]. In Li 2026b, PEARL-DGS ranked near the top of a 12-formula comparison with an AE of 0.35 D, although Hoffer QST performed best overall at 0.33 D [7]. Because Li 2026b reported AE rather than MAE, it informed narrative ranking context rather than MAE-based synthesis.

The main controversy emerged at the boundary of long-eye anatomy and formula implementation. Cheng 2021 supported strong overall Kane MedAE performance in the extraction seed, and Jiang 2025 supported Kane performance in a super-long subgroup, whereas Vilaltella 2025 and Stopyra 2025 preserved the counterexample that optimized or adjusted traditional formulas could remain highly competitive. In Vilaltella 2025, a modified Holladay 1 Wang-Koch approach achieved the lowest MedAE after mean error zeroing [4]. In Stopyra 2025, SRK/T achieved the lowest RMSAE at 0.349 D and the highest proportion within +/-0.50 D at 84.97% [9]. These conflicting patterns are not treated here as contradictions to be averaged away; rather, they identify where future standardized subgroup analyses, especially for very long eyes, are most needed.

Supplementary-only evidence

The supplementary-only studies were interpreted as context rather than as equal-weight confirmatory evidence. Kinoshita 2025 was retained because it provided useful multicenter RMSAE-structure information, but the accessible evidence did not support placing it in the pooled threshold model and did not place PEARL-DGS in the best RMSAE-performing group [5]. Li 2026 (keratometry) was retained as keratometry-context evidence rather than as core pooled evidence because its main value was to show that formula ranking could shift in a keratometry-focused analysis rather than to strengthen the primary target-versus-traditional comparison [8]. Stopyra 2026 was retained as supplementary long-eye context because it contributed PEARL-DGS-relevant comparison against modified traditional formulas, but Kane and Hill-RBF were absent. Mo 2024 was retained only as a sensitivity-context study because the plate-haptic IOL design made the cohort too specific for the main pooled evidence base.

Taken together, the tiered qualitative synthesis supports cautious preference for newer formulas in highly myopic eyes while preserving the key nuance that the strongest comparative claims come from the core studies, whereas the supplementary-only studies are mainly useful for contextualizing edge cases, special designs, and non-primary outcome structures.

Quantitative synthesis

Quantitative synthesis was completed for the most comparable extractable threshold endpoint, the proportion of eyes within +/-0.50 D of prediction error. The main pooled analysis was restricted to one exact overall target-formula result per independent study because this rule minimized double counting and avoided mixing subgroup rows, comparator rows, or endpoint families. The primary pooled group included Chen 2021 (Hill-RBF 2.0), Wei 2022 (Hill-RBF 3.0 with total keratometry), and Jiang 2025 (PEARL-DGS), with events derived from reported percentages and denominators. Because these rows represent architecture-distinct formulas rather than a single homogeneous tool, the model is best understood as an exploratory cross-formula target benchmark for auditable threshold performance. The random-effects pooled proportion within +/-0.50 D was 70.90% (95% CI, 68.34% to 73.33%; Q = 1.0104; I2 = 0.0%; tau2 = 0.000000). This estimate should be read as a conservative benchmark for the currently auditable, comparator-aligned target-formula threshold data, not as a universal formula ranking or as evidence that all 11 studies were statistically interchangeable. With only 3 studies, the I2 value has low inferential power and should not be interpreted as proof that the formulas, cohorts, biometry platforms, or calibration contexts were homogeneous.

Five studies were threshold-relevant for this endpoint in the narrative layer: Cheng 2021, Chen 2021, Wei 2022, Jiang 2025, and Stopyra 2025. Four of these studies had numeric +/-0.50 D rows represented in the extraction seed: Chen 2021, Wei 2022, Jiang 2025, and Stopyra 2025. Exact overall target-formula rows with usable denominators were available from Chen 2021, Wei 2022, and Jiang 2025. Cheng 2021 and Stopyra 2025 were eligible for threshold-oriented narrative interpretation but not the pooled target-formula model: Cheng 2021 lacked comparator-aligned threshold rows in the extractable source, whereas Stopyra 2025 provided an exact SRK/T threshold row but not an exact PEARL-DGS threshold percentage. Among verified numeric results, Hill-RBF 2.0 reached 71.44% within +/-0.50 D in Chen 2021 [2], Hill-RBF 3.0 reached 66.99% in Wei 2022 [3] and 79.17% in the long-AL subgroup in Jiang 2025 [6], PEARL-DGS reached 69.57% overall in Jiang 2025 [6], Kane reached 70.97% in the super-long subgroup in the same study [6], and SRK/T reached 84.97% in Stopyra 2025 [9]. The secondary Hill-RBF overall synthesis, based on Chen 2021 and Wei 2022, yielded a pooled proportion within +/-0.50 D of 71.03% (95% CI, 68.35% to 73.58%; Q = 0.9014; I2 = 0.0%; tau2 = 0.000000). These findings support threshold accuracy as the clearest current anchor for broader synthesis while also showing that optimized traditional formulas may remain highly competitive in selected cohorts.

The difference between the 11 included studies and the 3-study pooled target-formula model was driven by both data availability and methodological incompatibility. Data-availability exclusions included unavailable denominator data, unavailable formula-level threshold rows, or absent exact PEARL-DGS threshold percentages. Methodological exclusions included studies whose main contribution was an AE, RMSAE, keratometry-context, mean-error-zeroed, or special IOL-design analysis that would not be comparable with the overall target-formula threshold endpoint. These exclusions were not treated as evidence loss to be repaired by statistical imputation; rather, they were treated as boundaries protecting the pooled estimate from incompatible outcome families and calibration contexts. Supplementary Appendix 1 lists the pooling status and exclusion rationale for each included study so that narrative inclusion and statistical pooling are not conflated.

Figure 2 presents the completed random-effects forest plot for the exploratory cross-formula target benchmark. Rows with exact subgroup percentages but without subgroup denominators were retained as contextual evidence and excluded from the pooled estimate.

Fig. 2.

Random-effects meta-analysis of +/-0.50 D threshold accuracy. Random-effects forest plot for the exploratory cross-formula target benchmark of the proportion of eyes within +/-0.50 D. The plot includes one exact overall target-formula result per independent study: Hill-RBF 2.0 from Chen 2021, Hill-RBF 3.0 from Wei 2022, and PEARL-DGS from Jiang 2025. Events were derived from reported percentages and denominators. The pooled proportion was 70.90% (95% CI, 68.34% to 73.33%; I2 = 0.0%; tau2 = 0.000000). Because this model contains only 3 studies and architecture-distinct formulas, I2 should be read descriptively rather than as evidence of formula homogeneity. Cheng 2021 was excluded from the pooled model because comparator-aligned threshold rows were unavailable in the extractable source, and rows with subgroup percentages but no subgroup denominators were excluded from pooling

SMD analysis for continuous absolute-error outcomes was assessed but not pooled because comparator-aligned dispersion data and paired-correlation information were insufficient across studies. Chen 2021 provides comparator-populated MAE means and SDs, but the formula comparisons are same-eye comparisons and paired correlations were unavailable. Jiang 2025 contributes extractable MAE values but lacks comparator-aligned dispersion in the current source. MedAE, RMSAE, and AE metrics are kept separate and interpreted narratively rather than pooled across incompatible definitions. Figure 3 therefore presents a nonpooled forest-style display of the currently verified MAE subset rather than a completed pooled MAE synthesis.

Fig. 3.

Nonpooled forest-style display of the currently verified MAE subset. Nonpooled forest-style display of the currently verified mean absolute error (MAE) subset in highly myopic eyes. The figure shows point estimates only for the verified MAE rows from Chen 2021 and Jiang 2025, including Barrett Universal II and EVO because they are part of the only clearly comparator-populated verified MAE subset. Jiang 2025 is displayed as currently verified winner-only subgroup context; NR denotes data not reported or not available in the extractable source, and subgroup denominators are not displayed as if they equaled the overall 115-eye cohort. No derived pairwise contrasts, confidence intervals, or pooled random-effects estimate are shown, and MAE is not merged with MedAE, RMSAE, or AE

Table 1 therefore presents the final 11-study set and explicitly distinguishes core studies from supplementary-only studies so that the narrative synthesis and pooled analysis are not conflated.

Table 1.

Included studies

study	inclusion_role	eyes	high_myopia_definition	target_formulas	key_contribution
Cheng 2021	Core	370	AL > = 26.0 mm	Kane; Hill-RBF 2.0	Kane had the lowest MedAE overall; comparator-aligned threshold rows were unavailable for pooling
Chen 2021	Core	1054	AL > = 26.0 mm	Kane; Hill-RBF 2.0	Hill-RBF 2.0 contributed an exact overall +/-0.50 D threshold row to the pooled model
Wei 2022	Core	103	AL > = 26.0 mm	Kane; Hill-RBF 3.0	Hill-RBF 3.0 with total keratometry contributed an exact overall +/-0.50 D threshold row
Vilaltella 2025	Core	72	AL > = 26.0 mm	Kane; Hill-RBF 3.0; PEARL-DGS	Mean-error-zeroed Wang-Koch-adjusted traditional formula context
Jiang 2025	Core	115	AL > = 26.0 mm	Kane; Hill-RBF 3.0; PEARL-DGS	PEARL-DGS contributed an exact overall +/-0.50 D threshold row; subgroup denominators were unavailable
Stopyra 2025	Core	153	Long eyes 26.00 to 29.47 mm	Kane; Hill-RBF 3.0; PEARL-DGS	SRK/T led on RMSAE and exact +/-0.50 D comparator context; PEARL-DGS threshold percentage was unavailable
Li 2026b	Core	255	Highly myopic eyes	Kane; PEARL-DGS	AE-based 12-formula comparison; not pooled with MAE or threshold outcomes
Kinoshita 2025	Supplementary only	326	AL > = 26.0 mm	Kane; Hill-RBF; PEARL-DGS	RMSAE-structure context; per-formula threshold rows were unavailable
Li 2026 (keratometry)	Supplementary only	302	Highly myopic eyes	Kane; PEARL-DGS	Keratometry-context evidence; formula-specific threshold values were unavailable
Stopyra 2026	Supplementary only	164	Long eyes > 26.00 mm	PEARL-DGS	PEARL-DGS-only long-eye context without Kane or Hill-RBF
Mo 2024	Supplementary only	693 (391 plate-haptic; 302 comparator)	Highly myopic eyes with plate-haptic IOLs	Kane; Hill-RBF 3.0; PEARL-DGS	Special IOL-design sensitivity context

Using the adapted PROBAST-style framework, all 11 studies included in the systematic review were assessed. The overall risk-of-bias pattern was mixed but predominantly some concerns rather than uniformly low risk. Participant-selection concerns usually reflected retrospective or single-center recruitment, eye-based samples, incomplete reporting of patient-level clustering, or high-myopia definitions that did not always isolate pathological-myopia features. Retrospective formula evaluation is common in IOL-calculation research and was not treated as misconduct or poor execution; it was rated cautiously because single-center calibration, ethnicity, surgeon constants, and eye-based sampling can limit external generalizability. Analysis-integrity concerns were more often related to formula-version opacity, incomplete reporting of IOL model, constant optimization or mean-error zeroing, subgroup denominators that could not be extracted, special IOL-design restriction, and the use of different outcome families across studies. Supplementary-only studies were assessed for risk of bias even when they did not enter the pooled model; their supplementary status affected pooling eligibility, not whether a risk-of-bias judgment was required. Stopyra 2026 was judged as some concerns across domains because it lacked Kane and Hill-RBF coverage for the main three-formula question, whereas Mo 2024 was judged high for analysis integrity and overall because the plate-haptic IOL design makes it a special-design sensitivity context rather than a generalizable main-analysis cohort. Because most reports did not provide patient identifiers or intraclass correlations, post hoc cluster adjustment for bilateral-eye inclusion was not mathematically defensible. These domain-level reasons explain why Figs. 4 and 5 show many “some concerns” judgments rather than a uniformly low-risk evidence base.

Fig. 4.

Risk-of-bias summary across all included studies. Graphical summary of domain-level judgments across the four core adapted PROBAST-style risk-of-bias domains: Participants/patient selection, Predictor/index-formula process, Outcome ascertainment, and Analysis integrity. The figure summarizes all 11 studies represented in Table 2; supplementary-only studies were assessed for risk of bias even though they were not pooled

Fig. 5.

Study-level risk-of-bias traffic-light plot for all included studies. Study-level traffic-light plot across the four core adapted PROBAST-style risk-of-bias domains: Participants/patient selection, Predictor/index-formula process, Outcome ascertainment, and Analysis integrity. The figure summarizes all 11 studies represented in Table 2; supplementary-only studies were assessed for risk of bias even though they were not pooled

Figure 4 summarizes the adapted PROBAST-style risk-of-bias profile across all 11 studies represented in Table 2. It is limited to the four core risk-of-bias domains and uses conservative review-level judgments rather than statistical imputation.

Table 2.

Adapted PROBAST-style risk of bias assessment

study	participants_patient_selection	predictor_or_index_formula_process	outcome_ascertainment	analysis_integrity	overall_judgment
Cheng 2021	Some concerns	Some concerns	Some concerns	Some concerns	High
Chen 2021	Some concerns	Some concerns	Some concerns	Some concerns	High
Wei 2022	Some concerns	Some concerns	Low	Some concerns	Some concerns
Vilaltella 2025	Some concerns	Low	Low	High	High
Jiang 2025	Low	Low	Low	Low	Low
Stopyra 2025	Some concerns	Some concerns	Some concerns	Some concerns	Some concerns
Li 2026b	Some concerns	Some concerns	Some concerns	Some concerns	Some concerns
Kinoshita 2025	Some concerns	Some concerns	Some concerns	Some concerns	Some concerns
Li 2026 (keratometry)	Some concerns	Some concerns	Some concerns	Some concerns	Some concerns
Stopyra 2026	Some concerns	Some concerns	Some concerns	Some concerns	Some concerns
Mo 2024	Some concerns	Some concerns	Some concerns	High	High

Figure 5 provides the complementary study-level traffic-light view for the same 11-study assessed set. Like Fig. 4, it is restricted to the four core risk-of-bias domains and does not extend beyond the finalized Table 2 judgments.

No reporting-bias analysis was performed because no pooled endpoint met the prespecified minimum of 10 contributing studies.

Figure 6 summarizes reporting-bias assessment eligibility across the main outcome families. The lead endpoint, % within +/-0.50 D, currently has 4 numeric studies represented in the extraction seed, while MAE has 2, MedAE has 4 represented studies with 3 numeric studies, RMSAE has 2 represented studies with 1 numeric study, AE has 1, % within +/-0.75 D has 2, and % within +/-1.00 D has 1. This 4-study numeric reporting-bias baseline differs from the 5-study threshold-relevant narrative layer because Cheng 2021 lacks comparator-aligned numeric threshold rows in the extractable source. Accordingly, no funnel plot or Egger analysis is shown at the current stage.

Fig. 6.

Publication-bias eligibility status for pooled endpoints. Cross-endpoint publication-bias eligibility status graphic summarizing the prespecified threshold of at least 10 contributing studies for funnel-plot and Egger assessment. The figure highlights the primary % within +/-0.50 D endpoint as the leading current candidate but shows that no outcome family currently reaches the threshold. Counts reflect studies represented in the current extraction seed rather than formula-level rows, and no funnel plot or Egger’s test is shown. Although 5 studies inform the threshold-oriented narrative layer overall, Cheng 2021 is excluded from the publication-bias baseline seed count because it lacks comparator-aligned numeric rows in the extractable source, leaving 4 directly quantified studies represented in the figure

Table 3.

Formula performance summary

study	best_supported_pattern	outcome_basis	main_interpretation
Cheng 2021	Kane	MedAE	Kane performed best overall and in the AL > = 30.0 mm subgroup
Chen 2021	Hill-RBF 2.0	MAE and +/-0.50 D	Hill-RBF 2.0 outperformed Kane and modern comparators in this cohort
Wei 2022	Hill-RBF 3.0 with total keratometry	+/-0.50 D and MedAE	Hill-RBF 3.0 was among the strongest formulas when total keratometry was used
Vilaltella 2025	Modified Holladay 1 Wang-Koch	Zeroed MedAE	An optimized traditional formula outperformed newer formulas after mean-error zeroing
Jiang 2025	Hill-RBF 3.0 overall; Kane in very long eyes	MAE; MedAE; +/-0.50 D	Best formula varied by axial-length subgroup
Stopyra 2025	SRK/T	RMSAE and +/-0.50 D	A traditional formula led on key endpoints in this long-eye cohort
Li 2026b	Hoffer QST; PEARL-DGS near top	AE	PEARL-DGS was competitive but not the single best formula
Kinoshita 2025	Wang-Koch-adjusted or best RMSAE group	RMSAE structure	Supplementary RMSAE-context evidence only
Li 2026 (keratometry)	Modern formulas overall	Keratometry-context pattern	Supplementary keratometry-context evidence only
Stopyra 2026	SRK/T-led long-eye pattern	Threshold and RMSAE context	Supplementary PEARL-DGS-only long-eye context
Mo 2024	Special-design sensitivity context	Plate-haptic IOL cohort	Supplementary sensitivity-context evidence only

Discussion

Main interpretation

The final 11-study evidence base supports a pragmatic rather than formula-dogmatic conclusion. Kane, Hill-RBF, and PEARL-DGS were generally associated with favorable refractive prediction accuracy in highly myopic eyes and often performed at least as well as, and sometimes better than, commonly used traditional formulas. However, the size of the advantage and the identity of the best-performing formula varied by cohort and by endpoint. The 4 supplementary-only studies reinforced that this is not a uniform winner-take-all literature, because contextual evidence from RMSAE-focused, keratometry-focused, PEARL-DGS-only, and special-design analyses did not always point in the same direction as the main core comparisons.

What this review adds

This review adds value by reorganizing a fragmented formula-comparison literature into clinically interpretable evidence layers. It separates core comparative studies from supplementary-context studies, prioritizes the proportion within +/-0.50 D as the clearest cross-study threshold endpoint, preserves MAE, MedAE, RMSAE, and AE as distinct outcome families, and makes formula version, optimization, mean-error zeroing, and biometry inputs central to interpretation rather than secondary details. This structure also enabled a focused pooled estimate for the currently extractable threshold benchmark while identifying which claims remain context-generating or require additional full-text extraction.

Why rankings differ across studies

The between-study inconsistency is clinically and methodologically plausible. Studies differed in the definition of high myopia, with some using AL > = 26.0 mm and others emphasizing more extreme subgroups such as AL > = 30.0 mm. They also differed in formula version, especially for Hill-RBF, in the use of total versus standard keratometry, and in whether outcomes were reported as MAE, MedAE, RMSAE, or threshold-based accuracy. These differences matter because formula rankings can shift when the population becomes more extreme, when different biometric inputs are used, or when one metric is more sensitive to outliers than another. Recent long-eye work specifically evaluating axial-length adjustment factors reinforces that the choice of AL adjustment is not interchangeable across formulas or axial-length strata and should be interpreted as an active modeling decision rather than a minor preprocessing step [23]. This issue applies differently across formula families: traditional vergence formulas often rely on external axial-length adjustments such as Wang-Koch-style modification, whereas newer hybrid or data-driven formulas such as Kane, Hill-RBF, and PEARL-DGS incorporate nonlinear calibration internally and cannot always be “adjusted” in the same external way.

Constant optimization, mean error handling, and exact formula version are additional sources of variation. In some studies, formulas were evaluated after mean error zeroing or with IOLCon-based optimization, whereas in others the reporting was incomplete. This is not a minor technical detail. Constant optimization and mean-error zeroing are related but not equivalent: optimization addresses systematic offsets tied to IOL model, surgeon, population, or calibration source, whereas mean-error zeroing is a post hoc analytical handling step that can change threshold performance and limit comparability with nonzeroed cohorts. Constant refinement is intended to remove systematic refractive offsets related to surgeon technique, IOL model, population, or surgical context; this principle is not limited to high myopia and has also been emphasized in complex settings such as sutureless scleral fixation with the Yamane technique [24]. That citation is used as a methodological analogue for constant refinement in complex refractive settings, not as a claim that Yamane fixation and in-the-bag cataract surgery in highly myopic eyes share the same mechanism of error. The strong showing of modified Holladay 1 Wang-Koch in Vilaltella 2025 and SRK/T in Stopyra 2025 underscores this point: newer formulas are often competitive or superior, but optimized traditional formulas may still perform extremely well in selected datasets.

The broader formula-development literature reinforces this mechanism-based interpretation. At the input level, standard keratometry versus total keratometry, single-index axial length versus segmental or sum-of-segments axial length, and measured versus inferred posterior-corneal information may expose different sources of error [14, 16, 17]. At the model level, radial-basis-function pattern recognition, hybrid theoretical-optics/regression models, and machine-learning-assisted thick-lens frameworks are not interchangeable algorithms and may respond differently to unusual long-eye anatomy [18–20]. At the implementation level, constant optimization, mean-error zeroing, formula version, and the population used for training or calibration may shift rankings without proving that one formula is universally superior. A post-lock AJO 2026 study comparing nine artificial intelligence-based formulas, including Hill-RBF 3.0, Kane, and PEARL-DGS, in long Caucasian eyes further supports the need to interpret newer AI formulas by cohort, formula version, and calibration context rather than as a single homogeneous class [25]. Its emphasis on Hill-RBF 3.0 also illustrates why formula-version opacity in earlier studies is an analysis-integrity concern. This 2026 study is discussed as contemporary context only; it was not added to the final included evidence set and does not alter the PRISMA counts, tables, or pooled analysis. Because several recent long-eye AI-formula reports arise from overlapping author groups and predominantly Caucasian long-eye cohorts, they are used here as context-generating evidence rather than independent confirmation of a universal formula ranking, and they are interpreted alongside Chinese, Japanese, Spanish, keratometry-specific, and special-IOL evidence.

These mechanisms also define theoretical applicability boundaries. Traditional vergence formulas in long eyes are especially sensitive to how axial length, corneal power, and effective lens position are represented; Wang-Koch adjustment, constant optimization, and mean-error zeroing can therefore change whether a traditional formula appears obsolete or competitive. Conversely, data-driven formulas such as Hill-RBF should not be interpreted as unconstrained extrapolation engines. Their apparent safety and accuracy depend on how closely the evaluated eye resembles the biometric domain used to train or validate the model, and out-of-bounds or warning behavior should be treated as clinically relevant information rather than a nuisance result. The current evidence base does not quantify exact failure thresholds for extreme axial length or very flat keratometry, so these concepts are interpreted as applicability boundaries rather than measured breakpoints.

Clinical implications

For clinical practice, the most defensible conclusion is pragmatic rather than formula-dogmatic. Kane, Hill-RBF, and PEARL-DGS appear to be reasonable front-line options for highly myopic eyes, particularly when the goal is to maximize the chance of postoperative prediction error within +/-0.50 D. At the same time, local performance should still be interpreted through the lens of available biometry, optimization workflow, and case mix. A department with stable optimization practices and strong historical performance from adjusted traditional formulas should not assume that a newer formula will automatically dominate in every subgroup.

The current evidence also suggests that threshold outcomes may be more clinically communicable than isolated absolute-error summaries. The proportion of eyes within +/-0.50 D maps more directly onto refractive counseling and postoperative expectations, and it is the most repeatable cross-study endpoint in the current library. For this reason, it is a stronger anchor for narrative comparison than any single MAE, MedAE, RMSAE, or AE result viewed in isolation.

Strengths of this review

This review has several strengths. It focuses specifically on highly myopic eyes rather than pooling them into broader cataract cohorts, it centers on formulas that are highly relevant to current practice, and it explicitly separates 7 core comparative studies from 4 supplementary-only studies so that contextual evidence is not over-weighted. It also preserves outcome-family boundaries rather than collapsing MAE, MedAE, RMSAE, and generic AE into a single misleading synthesis, and it treats borderline studies cautiously where threshold data are incomplete or where accessible evidence supports only supplementary rather than core use.

Limitations

The main limitations arise from both the underlying literature and the available extractable data. Most studies were retrospective, reporting standards were inconsistent, and not every study provided full details on exact formula version, IOL model, constant optimization, mean error zeroing, or subgroup definitions. Several otherwise relevant studies were excluded from specific quantitative models because denominator data, comparator-aligned threshold rows, continuous-outcome dispersion, or paired-correlation information were unavailable in the extractable sources. Unavailable fields were coded conservatively as not reported or unavailable in the extractable source. The reference base also contains a visible cluster of recent long-eye AI-formula reports from overlapping investigators; this reflects the current publication landscape but limits how strongly those reports can be treated as independent external validation across ethnicities, devices, and surgical settings.

A second limitation is endpoint incompatibility. Even when studies address the same clinical question, the use of MAE, MedAE, RMSAE, and study-defined AE metrics prevents straightforward pooling unless full-text methods confirm that the summaries are genuinely comparable and dispersion or paired-comparison information is available. For the same reason, some studies are more useful for structured narrative synthesis than for formal quantitative pooling. Pooling these outcome families by imputation or by treating them as interchangeable absolute-error measures would risk producing a more precise-looking but less valid result.

A third limitation is that the evidence for PEARL-DGS remains newer and somewhat less settled than the evidence for Kane or Hill-RBF. Recent studies suggest that PEARL-DGS is often competitive, but not uniformly dominant, and some accessible reports place other modern formulas ahead of it. That nuance is important and should be preserved in any submission version.

A fourth limitation is coverage of clinically important subtypes. The review is organized primarily around high myopia or long axial length, most commonly AL > = 26.0 mm, but highly myopic eyes are not a homogeneous anatomical category. The present evidence set does not allow systematic stratification by posterior staphyloma morphology, East Asian pathological-myopia phenotype, AL > = 30.0 mm extreme-long-eye status, or prior myopic LASIK/PRK. These factors may affect fixation, axial-length measurement, corneal power estimation, and the interpretation of effective lens position, but they remain insufficiently represented in the current extractable core evidence.

A fifth limitation is chronological and technological comparability. Studies published from 2020 to 2026 may differ not only in cohort composition but also in formula access date, silent online formula updates, biometry platform, and availability of swept-source OCT inputs. Earlier PCI-based or single-index axial-length studies are not directly equivalent to studies using IOLMaster 700, Argos, total keratometry, posterior-corneal information, or segmental/sum-of-segments axial length. Because many reports do not fully document formula version or access year, cross-year comparisons of Kane, Hill-RBF, and PEARL-DGS should be interpreted as study-specific implementations rather than immutable formula identities. The post-lock AJO 2026 report was therefore used to update discussion context, especially around Hill-RBF 3.0 and long Caucasian eyes, but was not retroactively inserted into the registered evidence set.

A final reproducibility limitation is that the original platform-specific database exports and duplicate-removal logs were unavailable at manuscript preparation. The reconstructed search strategies and study-accounting notes in Supplementary Appendix 1 preserve the logic of the search and screening process, but they cannot fully substitute for verbatim export histories. This limitation affects the auditability of the identification stage rather than the extracted study-level outcomes or the completed threshold model. It should therefore be interpreted as a limitation in exact historical provenance, not as permission to fabricate duplicate counts or to reopen the locked analysis window without rerunning the full screening, extraction, risk-of-bias, and pooling workflow.

Certainty of evidence

Using a brief GRADE-style narrative approach, the certainty of evidence for the primary threshold endpoint should presently be regarded as low. This reflects the predominance of retrospective observational designs, incomplete reporting of exact formula version, IOL model, optimization handling, and mean-error handling, heterogeneity in long-eye definitions and subgroup structure, and exclusion of some relevant studies from the pooled model because denominator or comparator-aligned threshold data were unavailable in the extractable sources. The 3-study threshold model improves auditability by excluding incompatible rows, but it remains an exploratory cross-formula benchmark whose small size limits precision, heterogeneity detection, and generalizability. No combined pooled-certainty rating was assigned to incompatible nonpooled outcome families such as MAE, MedAE, RMSAE, or AE.

Research priorities

Future comparative studies should report exact formula versions, formula access dates, biometer and keratometry details, IOL model, optimization source, mean error handling, and axial-length subgroup definitions in a standardized way. Studies that provide both threshold outcomes and compatible absolute-error summaries will be most useful for future evidence synthesis. Head-to-head datasets including Kane, Hill-RBF, PEARL-DGS, and optimized traditional comparators within the same highly myopic cohort would be particularly valuable, especially if they prespecify analyses for AL > = 26.0 mm and very-long-eye groups such as AL > = 30.0 mm.

Future work should also standardize the reporting of the proportion within +/-0.50 D, provide dispersion measures for MAE or MedAE, and document whether swept-source OCT, total keratometry, posterior-corneal inputs, segmental or sum-of-segments axial length, IOL constant optimization, and mean-error zeroing were used. Separately extractable data for posterior staphyloma, East Asian pathological-myopia phenotypes, and previous LASIK/PRK would help define the boundaries of formula applicability. These details would be required before extreme-axial-length, posterior-staphyloma, post-refractive-surgery, or device-generation subgroup meta-analyses could be interpreted defensibly.

Conclusion

In conclusion, the current evidence indicates that Kane, Hill-RBF, and PEARL-DGS are credible options for IOL power calculation in highly myopic eyes and often perform well against traditional formulas. However, the evidence base remains methodologically heterogeneous and does not support a universal rank order across all long-eye settings. Threshold-based accuracy, especially the proportion within +/-0.50 D, is presently the clearest common endpoint for harmonized synthesis.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

H.C. conceptualized the study, conducted the literature search, performed the statistical analysis, and wrote the main manuscript text. Y.W. contributed to the literature screening, data extraction, and risk of bias assessment. F.Q. designed and supervised the project, resolved disagreements during the review process, and critically revised the manuscript. All authors reviewed the manuscript.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

Ethics approval and informed consent were not required because this study was a systematic review and meta-analysis of previously published studies.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.