Comparative accuracy of Barrett true-K and Haigis-L formulas for intraocular lens power calculation in post-laser-assisted in situ keratomileusis cataract surgery

Study design and ethical considerations

This study was a retrospective, comparative, observational clinical study conducted at a tertiary eye care centre in South Gujarat, India, between October 2024 and May 2025. The centre functions as a regional referral facility for cataract and refractive surgery and is equipped with advanced diagnostic and surgical infrastructure. The study adhered to the principles of the Declaration of Helsinki and was approved by the Institutional Ethics Committee of Shree Bharatimaiya College of Optometry and Physiotherapy. Written informed consent had been obtained from all patients at the time of surgery for the use of anonymised clinical data for research purposes.

Study population

Clinical records of patients with a documented history of LASIK who subsequently underwent phacoemulsification with posterior chamber monofocal IOL implantation were reviewed. Eligible patients were ≥45 years of age, had undergone myopic or hyperopic LASIK at least 1 year before cataract surgery and presented with a visually significant age-related cataract and a normal posterior segment examination. A minimum post-operative follow-up of 1 month was required.

Eyes were included only if regular corneal astigmatism was ≤2.0 dioptres. Exclusion criteria comprised prior corneal refractive procedures other than LASIK (photorefractive keratectomy (PRK), small incision lenticule extraction, radial keratotomy, phototherapeutic keratectomy), previous intraocular surgery (vitrectomy, trabeculectomy and keratoplasty), corneal ectasia, central corneal scarring, irregular or decentred ablation patterns, ocular comorbidities affecting visual outcome (glaucoma, diabetic retinopathy, age-related macular degeneration), significant systemic disease influencing vision and implantation of toric or multifocal IOLs.

A total of 60 eyes from 40 patients met the eligibility criteria and were included. When both eyes of a patient were eligible, both were analysed and statistical adjustment for inter-eye correlation was performed.

Group allocation and IOL power calculation

Eyes were divided into two groups based on the IOL power calculation formula used. Group 1 comprised 30 eyes calculated using the Barrett true-K total keratometry (TK) formula, incorporating TK (anterior and posterior corneal power) available on the IOLMaster 700. Group 2 comprised 30 eyes calculated using the Haigis-L formula. Allocation was based on consecutive case availability during the study period and was not randomised.

Pre-operative evaluation

All patients underwent a standardised pre-operative assessment that included measurement of uncorrected and best-corrected distance visual acuity using Snellen charts with conversion to logMAR, manifest refraction and optical biometry using the IOLMaster 700 (Carl Zeiss Meditec, Germany) to obtain axial length, keratometry, anterior chamber depth and lens thickness.

Detailed corneal assessment was performed using Scheimpflug–Placido tomography (Sirius system) to evaluate anterior and posterior corneal curvature, pachymetry and ablation centration. Eyes demonstrating significant irregularity or decentred ablation were excluded. Slit-lamp biomicroscopy, intraocular pressure measurement using rebound tonometry (iCare TA01i, Finland) and dilated fundus evaluation with optical coherence tomography when indicated were performed in all cases.

The intended post-operative target refraction for all eyes was emmetropia (0.00 dioptres), and the same target was applied irrespective of corneal curvature profile.

Surgical technique

All procedures were performed by a single experienced surgeon under topical anaesthesia using a standardized phacoemulsification technique. A 2.8-mm clear corneal incision was created, followed by continuous curvilinear capsulorhexis, nucleus emulsification, cortical aspiration and implantation of a foldable hydrophobic acrylic aspheric non-toric monofocal IOLs (AcrySof IQ, Alcon, USA) into the capsular bag. Post-operative treatment consisted of topical antibiotics and corticosteroids tapered over 4 weeks.

Post-operative care and follow-up

Post-operative examinations were conducted on day 1, day 10 and at 1 month. At each visit, uncorrected and best-corrected distance visual acuity, manifest refraction, spherical equivalent (SE) and residual refractive astigmatism were recorded. Vector analysis of astigmatism was performed using the Alpins method. Intraocular pressure, wound integrity, IOL centration and anterior segment status were also assessed.

Outcome measures

The primary outcome measure was refractive PE, defined as the achieved post-operative SE minus the predicted SE. Positive values indicated hyperopic error and negative values indicated myopic error. Secondary outcome measures included mean absolute error (MAE), the proportion of eyes within ±0.25, ±0.50 and ±1.00 dioptres of the intended refraction, post-operative uncorrected and best-corrected visual acuity (BCVA) and residual astigmatism parameters derived from vector analysis.

Statistical analysis

Data were analysed using the Statistical Package for the Social Sciences version 26.0 (IBM Corp., Armonk, NY, USA). Distribution normality was assessed using the Shapiro– Wilk test. Continuous variables were compared using paired or independent t-tests for normally distributed data and Wilcoxon signed-rank or Mann–Whitney U tests for nonparametric data. Categorical variables were analysed using the Chi-square or Fisher’s exact test.

To account for inter-eye correlation and baseline differences, generalised estimating equations (GEE) and analysis of covariance (ANCOVA) were applied. Results are presented as mean ± standard deviation or median with interquartile range, along with 95% confidence intervals (CI). A P < 0.05 was considered statistically significant.

Study population and surgical subgroups

A total of 60 eyes from 40 patients were included in this retrospective comparative analysis. Thirty eyes were evaluated using the Barrett true-K TK formula (Group 1) and thirty eyes using the Haigis-L formula (Group 2). All eyes had a documented history of corneal refractive surgery and underwent uneventful phacoemulsification with posterior chamber IOLs implantation.

With respect to the type of prior refractive surgery, 44 eyes (73.3%) had undergone myopic LASIK, while 16 eyes (26.7%) had undergone hyperopic LASIK. The distribution of myopic versus hyperopic LASIK eyes was comparable between the two formula groups (χ² = 0.18, P = 0.67), indicating the absence of selection bias related to refractive surgery type.

Baseline demographic and biometric characteristics

Baseline demographic and biometric parameters are summarised in Table 1. The two groups were statistically comparable in terms of axial length, mean keratometry, anterior chamber depth, baseline corneal astigmatism and pre-operative SE (all P > 0.05), confirming appropriate baseline equivalence.

The only statistically significant baseline difference was age, with the Barrett true-K TK group being younger than the Haigis-L group (54.9 ± 9.6 years vs. 61.3 ± 6.5 years; mean difference 6.4 years, 95% CI 2.2–10.6; P = 0.003). Given the potential influence of age on ELP prediction, all primary refractive outcome analyses were adjusted for age using ANCOVA. For patients contributing bilateral eyes, GEE with an exchangeable correlation structure was applied. Adjustment did not materially alter the magnitude or direction of inter-formula differences, confirming that outcome differences were primarily formula-dependent [Figure 1].

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Figure 1:

Baseline demographic and biometric comparability between Barrett true-K total keratometry and Haigis-L groups, demonstrating similarity across key parameters except age. SD: Standard deviation, ACD: Anterior chamber depth.

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Visual acuity outcomes

Between-group comparison

At 1 month postoperatively, mean UDVA was significantly superior in the Barrett true-K TK group (0.04 ± 0.08 logMAR) compared with the Haigis-L group (0.12 ± 0.19 logMAR; mean difference −0.08 logMAR, 95% CI −0.14 to −0.02; P = 0.021). The calculated effect size (Cohen’s d = 0.55) indicates a moderate and clinically meaningful advantage favouring Barrett true-K TK.

Post-operative BCVA was excellent and comparable between groups (0.01 ± 0.03 logMAR in both; P = 0.82), confirming that both formulas achieved similar best-corrected visual potential and that observed differences were predominantly refractive rather than optical-quality related.

Categorical analysis demonstrated a higher proportion of eyes achieving UDVA ≥20/20 (73% vs. 60%) and UDVA ≥20/40 (93% vs. 87%) in the Barrett group, although these differences did not reach statistical significance [Table 2 and Figure 2].

Table 2: Post-operative visual acuity outcomes.

Outcome	Barrett true-K TK	Haigis-L	P-value
UDVA (logMAR)	0.04±0.08	0.12±0.19	0.021
BCVA (logMAR)	0.01±0.03	0.01±0.03	0.82
UDVA ≥20/20 (%)	73	60	0.27
UDVA ≥20/40 (%)	93	87	0.44

UDVA: Uncorrected distance visual acuity, BCVA: Best-corrected visual acuity, TK: Total keratometry. A P value of <0.05 was considered statistically significant.

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Figure 2:

Comparison of post-operative uncorrected distance visual acuity between formulas, showing superior uncorrected visual outcomes with Barrett true-K total keratometry.

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Refractive accuracy and PE

PE was defined as the achieved post-operative SE minus the predicted SE, with negative values indicating a myopic outcome.

The MAE was significantly lower with Barrett true-K TK (0.34 ± 0.12 D) compared to Haigis-L (0.54 ± 0.21 D; mean difference −0.20 D, 95% CI −0.33 to −0.07; P = 0.038). The large effect size (Cohen’s d = 1.09) reflects a substantial improvement in refractive precision with Barrett true-K TK.

Both formulas demonstrated a mild myopic bias; however, the magnitude of bias was greater with Haigis-L (−0.29 ± 0.41 D) than with Barrett true-K TK (−0.18 ± 0.27 D), suggesting a higher tendency toward IOL under-powering with Haigis-L in post-LASIK eyes.

The proportion of eyes achieving refractive outcomes within ±0.50 D of target was 80% (95% CI 63–91%) in the Barrett group compared with 63% (95% CI 44–79%) in the Haigis-L group. Corresponding proportions within ±1.00 D were 97% and 90%, respectively. The cumulative distribution curve [Figure 3] demonstrated a steeper slope for Barrett true-K TK, indicating tighter clustering and reduced variability of refractive outcomes [Table 3].

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Figure 3:

Cumulative distribution of refractive prediction error, illustrating tighter clustering and reduced variability with Barrett true-K total keratometry.

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Residual astigmatism and vector analysis

Mean residual refractive astigmatism was slightly lower in the Barrett group (0.32 ± 0.21 D) compared with the Haigis-L group (0.39 ± 0.25 D), although this difference did not reach statistical significance (P = 0.21).

Vector analysis revealed smaller centroid displacement and reduced scatter of J0 and J45 components in the Barrett true-K TK group. While intergroup differences were not statistically significant, this pattern suggests greater directional stability of astigmatic outcomes, which is clinically relevant in post-LASIK corneas where even small vector misalignments may adversely affect uncorrected visual quality [Table 4; Figures 4 and 5].

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Figure 4:

Centroid vector analysis of residual refractive astigmatism. The X-axis represents the horizontal astigmatic component (J0, diopters) and the Y-axis represents the oblique astigmatic component (J45, diopters). The plot illustrates the mean vector (centroid) and distribution of astigmatic components for both Barrett true-K TK and Haigis-L groups, demonstrating smaller vector displacement and tighter clustering in the Barrett true-K TK group.

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Figure 5:

Double-angle vector plot of residual astigmatism highlighting reduced scatter with Barrett true-K total keratometry.

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Subgroup analysis: Axial length and LASIK type

Across all axial length categories, Barrett True-K TK consistently demonstrated lower MAE compared with Haigis-L. This advantage was preserved in short, medium and long eyes [Table 5]. In myopic LASIK eyes, MAE was 0.33 ± 0.11 D with Barrett true-K TK versus 0.53 ± 0.20 D with Haigis-L, representing the subgroup with the greatest relative benefit. In contrast, hyperopic LASIK eyes exhibited higher variability with both formulas (0.36 ± 0.12 D vs. 0.56 ± 0.23 D), indicating reduced predictability regardless of calculation method [Figure 6].

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Figure 6:

Subgroup comparison of mean absolute error (diopters) (Y-axis) vs subgroups axial length categories and laser-assisted in situ keratomileusis type (X-axis).

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Outliers and safety analysis

Large refractive outliers (>1.00 D PE) occurred in one eye (3%) in the Barrett group and three eyes (10%) in the Haigis-L group, reinforcing the greater clinical reliability of Barrett true-K TK. No intraoperative or post-operative complications were observed in either group [Table 6].

Safety outcomes

No intraoperative complications such as posterior capsule rupture or zonular dehiscence were observed. Post-operative recovery was uneventful, with no cases of cystoid macular oedema, corneal oedema or endophthalmitis. All IOLs remained well centred at 1 month. Mild, transient corneal oedema and temporary elevation of intraocular pressure were noted in a few eyes but resolved spontaneously within the 1^st post-operative week and did not differ between groups.

Interpretation of findings

Refractive accuracy, as reflected by MAE, represents the most clinically meaningful indicator of IOL calculation performance in post-refractive eyes. In the present study, Barrett true-K TK achieved a significantly lower MAE (0.34 ± 0.12 D) compared with Haigis-L (0.54 ± 0.21 D; P = 0.038) [Table 3]. This difference translated into a higher proportion of eyes achieving refractive outcomes within ±0.50 D and ±1.00 D of the intended target refraction, as demonstrated by the cumulative distribution curve [Figure 3].

Post-operative UDVA was also significantly better in the Barrett true-K TK group [Table 2 and Figure 2], whereas BCVA was excellent and comparable between groups. This finding indicates that the observed inter-formula differences were primarily attributable to refractive accuracy rather than optical quality or surgical factors, reinforcing the clinical relevance of formula selection in post-LASIK cataract surgery.

Both formulas demonstrated a mild myopic PE; however, the magnitude of bias was greater with Haigis-L [Table 3]. This tendency toward under-powering has been previously reported with Haigis-L and may reflect its reliance on empirically derived regression models that are less capable of fully compensating for altered corneal biomechanics in post-refractive eyes.^[5,9]

Algorithmic considerations

The superior performance of Barrett true-K TK can be attributed to its theoretical optics-based design, which incorporates TK and a refined estimation of ELP without requiring historical refractive data.^[6,7] In contrast, Haigis-L applies corneal power adjustments derived from population-based regression formulas, which may be less robust in eyes with atypical corneal geometry following refractive surgery.^[5,9]

This distinction is clinically significant, particularly in real-world settings where pre-LASIK refractive and keratometric data are often unavailable or unreliable. In such circumstances, formulas that minimise dependence on historical data such as Barrett True-K TK offer a clear practical advantage.

Comparison with previous studies

The findings of this study are consistent with prior reports evaluating IOL calculation formulas in post-refractive eyes. Abulafia et al. demonstrated that Barrett True-K produced significantly lower PEs than Haigis-L and Shammas formulas in post-LASIK and post-PRK eyes, particularly when historical data were unavailable.^[10] Wang et al. similarly reported superior refractive accuracy with Barrett True-K compared with Haigis-L, emphasising its reliability in no-history scenarios.^[11]

Ferguson et al. showed that Barrett true-K performed as well as or better than multi-formula averaging strategies, supporting its use as a standalone formula.^[7] More recently, Salama et al. and Li et al. reported MAE values for Barrett true-K in the range of 0.30–0.40 D in post-myopic LASIK eyes, closely matching the outcomes observed in the present study .^{[8, 12]} Conversely, the higher MAE observed with Haigis-L in our cohort aligns with findings reported by Menon et al. in Indian eyes, where Haigis-L demonstrated reduced accuracy compared with newer-generation formulas.^[13]

Subgroup analysis: Axial length and LASIK type

Subgroup analysis revealed that Barrett true-K TK maintained superior refractive accuracy across all axial length categories, including short, medium and long eyes [Table 5 and Figure 6]. This finding is clinically important, as long axial length eyes are known to pose additional challenges for IOL power prediction due to altered ELP and increased sensitivity to biometric measurement errors.^[14]

With respect to LASIK type, the greatest relative benefit of Barrett true-K TK was observed in post-myopic LASIK eyes, where refractive predictability was highest [Table 5]. In contrast, post-hyperopic LASIK eyes demonstrated greater variability with both formulas, reflecting the inherent difficulty of IOL calculation in this subgroup due to steeper peripheral corneal profiles and altered corneal biomechanics.^[15] These results support a cautious interpretation of refractive outcomes in post-hyperopic LASIK eyes, even when advanced formulas are used.

Astigmatism outcomes and vector analysis

Although mean residual refractive astigmatism did not differ significantly between formulas [Table 4], vector analysis demonstrated smaller centroid displacement and reduced scatter of J0 and J45 components in the Barrett true-K TK group [Figures 4 and 5]. While these differences did not reach statistical significance, they suggest improved directional stability of astigmatic outcomes, which is clinically relevant in post-LASIK corneas where even small vector misalignments may adversely affect uncorrected visual quality.

These findings are consistent with previous studies highlighting the importance of incorporating posterior corneal power and total corneal astigmatism into IOL calculations.^[13,16] The integration of TK within the Barrett true-K TK algorithm likely contributes to this observed stability.

Clinical implications

From a clinical perspective, the results of this study underscore the importance of formula selection in post-refractive cataract surgery. Barrett true-K TK not only achieved superior refractive accuracy but was also associated with fewer large refractive outliers [Table 6], which are particularly impactful in highly demanding post-LASIK patients. The higher proportion of eyes achieving UDVA ≥20/20 further emphasises its value in meeting contemporary expectations for spectacle independence [Table 2; Figure 2].

In regions such as India, where pre-LASIK records are frequently unavailable and patient expectations for refractive precision are high, the robustness and independence of Barrett true-K TK from historical data make it especially advantageous.^[12]

Strengths and limitations

The strengths of this study include a direct head-to-head comparison of two widely used formulas, uniform surgical technique performed by a single experienced surgeon and comprehensive evaluation of refractive accuracy, visual outcomes and astigmatic vector behaviour. Adjustment for age-related differences using ANCOVA and GEEs further strengthened the validity of the findings [Table 1 and Figure 1].

Limitations include the retrospective design, relatively small sample size and short follow-up period of 1 month, which may not fully capture long-term refractive stability. In addition, only two formulas were evaluated; newer-generation formulas and artificial intelligence-based calculators were not included, limiting the breadth of comparison.

Future directions

Future studies should be prospective, multicentric and adequately powered to include a broader range of modern formulas, longer follow-up and patient-reported outcome measures such as visual quality, glare and satisfaction. Such data would complement refractive accuracy metrics and provide a more comprehensive understanding of functional outcomes.