Spherical equivalent prediction analysis in intraocular lens power calculations using Barrett Universal II formula variations

Using true AL and optional parameters enhances the BUII formula's precision and accuracy, significantly improving refractive outcomes in eyes with short ALs.

Abstract

Purpose:

To evaluate the prediction accuracy of the Barrett Universal II (BUII) intraocular lens (IOL) formula variations, including optional biometric parameters and sum-of-segments (SOS) axial length (AL) modification, for IOL power calculation in cataract surgery.

Setting:

Single-center academic university hospital.

Design:

Retrospective case series.

Methods:

1340 eyes of 1340 patients undergoing uneventful cataract surgery were analyzed using 5 BUII variants: with only 1 optional parameter (lens thickness [BUII LT] or white-to-white [BUII WTW]), 2 optional parameters (BUII STD), without optional parameters (BUII WØ), and adjusted for SOS AL (BUII TAL). A single swept-source optical biometer (ARGOS) was used. Spherical equivalent prediction error (SEQ-PE, trueness), SD (precision), and absolute SEQ-PE (accuracy) were calculated with the online Eyetemis tool. Statistical comparisons were conducted using robust statistical methods across the entire cohort and subgroups based on AL: short (<22.0 mm), average (22.0 to 24.99 mm), and long (≥25.0 mm).

Results:

All formula variations showed high refractive accuracy. BUII TAL provided superior precision and best accuracy, particularly outperforming other variants in short eyes (P < .01). For average and long eyes, accuracy and precision differences between the modified BUII TAL and standard BUII STD were minimal and not statistically significant. The percentage of eyes within ±0.50 diopters prediction error was highest for BUII TAL and BUII STD (80%), slightly outperforming other variants.

Conclusions:

BUII formula variants demonstrated excellent refractive prediction accuracy. SOS adjustment and optional biometric parameters notably improved precision and accuracy, especially in short eyes.

Modern cataract surgery patients have increasingly high expectations regarding visual outcomes and spectacle independence.¹ Thus, cataract surgery has evolved from a basic vision-restorative procedure to an advanced refractive intervention, and the demand for precise intraocular lens (IOL) power calculations has intensified.^2–4 Among current formulas, the vergence-based Barrett Universal II (BUII) formula is widely regarded as a high-performing option, particularly for patients with extreme axial lengths (ALs) where achieving accurate refractive outcomes remains challenging.⁵

The BUII formula uses mandatory biometric inputs including AL, keratometry (K), and anterior chamber depth (ACD). In addition, it allows optional inputs such as lens thickness (LT) and white-to-white corneal diameter (WTW) that may further refine predictive accuracy.^3,6 However, evidence regarding the impact of these optional parameters on improving refractive outcomes remains limited.⁶

Eyes are often classified by AL as short (<22.0 mm), average (22.0 to 24.99 mm), or long (≥25.0 mm).⁷ Patients with extreme AL frequently experience suboptimal postoperative refractive outcomes due to limitations of traditional IOL calculation formulas in these ranges.^8,9 In contrast to the traditional AL measurements, which are based on a single refractive index for the entire eye, the sum-of-segments (SOS) AL approach addresses this limitation by summing segment-specific optical path lengths, thereby potentially improving accuracy.^10–12 A recent modification of the BUII formula can now account for SOS AL, aiming to increase IOL power calculation accuracy.

This study aimed to evaluate and compare the refractive prediction accuracy of the BUII formula across multiple variants in uneventful cataract surgery, and to assess whether incorporating optional biometric parameters and SOS-derived AL further improves outcomes in short, average, and long eyes. We aim to provide evidence-based recommendations for enhancing IOL power calculations and improving postoperative visual outcomes in cataract surgery patients.

METHODS

Participants Eligibility

This single-center retrospective study adhered to the tenets of the Declaration of Helsinki and was approved by the Coimbra University Hospital Ethics Committee. We reviewed cases of patients who underwent uneventful phacoemulsification cataract surgery at Coimbra University Hospital between January 2022 and March 2023. Only 1 eye per patient was included. Subgroup analyses were planned for short (AL <22.0 mm), average (22.0 to 24.99 mm), and long eyes (AL ≥25.0 mm).

Inclusion criteria were (1) patients aged 18 years or older who underwent uneventful cataract surgery with implantation of a single-piece hydrophobic acrylic IOL (AcrySof SN60AT, Alcon Laboratories, Inc.) and (2) postoperative corrected distance visual acuity (CDVA) ≥20/30 with subjective refraction performed at least 21 days postoperatively.

Exclusion criteria were eyes with incomplete biometric data, those measured by ultrasonic (contact) biometry, any combined or complicated cataract surgeries, history of corneal refractive surgery (eg, laser in situ keratomileusis, photorefractive keratectomy, and radial keratotomy), presence or suspicion of corneal ectasia (eg, keratoconus or related disorders), and ocular comorbidities other than cataract that could influence visual acuity.

Preoperative and Postoperative Assessments

All patients underwent a thorough preoperative examination. Biometric measurements were obtained under mesopic conditions using a single swept-source optical biometer (ARGOS, Alcon Laboratories, Inc.). The following biometric data were collected: standard AL, SOS AL, K, ACD, LT, and WTW. SOS AL is measured by summing the optical path lengths of each ocular segment (cornea, anterior chamber, lens, and vitreous) using segment-specific refractive indices, providing a “true” AL measurement.¹¹

All cataract surgeries were performed by experienced surgeons using a 2.75 mm clear corneal incision and in-the-bag 1-piece IOL implantation. Patients were examined at 1 week and 1 month postoperatively. Manifest refraction at the late postoperative visit (≥21 days) was used to calculate the spherical equivalent (SEQ) refraction. CDVA and the SEQ of the manifest refraction were recorded.

IOL Power Calculation

Manifest spherical equivalent was calculated as SEQ = sphere + ½ cylinder (diopters, D). For each eye, the prediction error in spherical equivalent (SEQ-PE) was defined as the postoperative refractive SEQ minus the predicted refractive SEQ. We computed SEQ-PEs for 5 versions of the BUII formula: BUII WØ (using only the mandatory inputs, without optional parameters), BUII LT (with lens thickness), BUII WTW (with white-to-white), BUII STD (with both LT and WTW), and BUII TAL (using the true AL from SOS AL in place of standard AL). All formulas were calculated using a single A-constant value of 118.75, which is the standard value used at our institution for the AcrySof SN60AT IOL on the ARGOS platform. No further formula-specific optimization was performed because the mean error in all formula variants with this A-constant was below 0.05 D (Table 2).

Table 2.

Values of SEQ-PE, precision, and absolute SEQ-PE of each formula variation in the full dataset (n = 1340)

Statistic	Group	Trimmed mean	Mean	SD	Min	Q1	Q2 (median)	Q3	Max
SEQ-PE (trueness) (D)	STD	−0.016	−0.031	0.415	−1.440	−0.300	−0.010	0.281	1.240
	TAL	−0.025	−0.038	0.416	−1.490	−0.296	−0.025	0.270	1.280
	WØ	0.001	−0.014	0.426	−1.520	−0.285	0.010	0.300	1.380
Precision of SEQ-PE (D)	STD	0.306	0.335	0.246	0.001	0.154	0.289	0.464	1.424
	TAL	0.304	0.333	0.249	0.000	0.140	0.285	0.465	1.465
	WØ	0.312	0.341	0.256	0.001	0.148	0.291	0.476	1.521
Absolute SEQ-PE (D)	STD	0.306	0.335	0.247	0.000	0.150	0.290	0.460	1.440
	TAL	0.303	0.334	0.251	0.000	0.140	0.285	0.460	1.490
	WØ	0.312	0.341	0.256	0.000	0.149	0.290	0.475	1.520

SEQ-PE = spherical equivalent prediction error; STD = Barrett Universal II with LT and white-to-white; Q1/Q2/Q3 = quartile thresholds for 25% (Q1), 50% (Q2), and 75% (Q3) of data; TAL = true axial length; WØ = without optional parameters

Statistical Analysis

Data were analyzed using the ESCRS Eyetemis online analysis tool (www.eyetemis.com) with the “paired SEQ-PE” option. This tool follows ISO standards for accuracy (assessing trueness and precision) and uses robust statistical methods to compare outcomes while adjusting for heteroscedasticity.¹³ Prediction errors from IOL formulas often exhibit non-Gaussian, long-tailed distributions. To enable valid statistical testing, the Eyetemis platform applies robust methods that trim 10% of extreme values from each end of the distribution.¹⁴ This allows for appropriate use of parametric tests while minimizing the impact of outliers. However, trimmed means may underestimate variability and make differences between formulas that seem smaller. For this reason, we also report untrimmed metrics, such as median absolute errors and prediction error thresholds, to better reflect clinical performance.

To compare formulas, we first performed a robust 1-way analysis of variance (trimmed means) to assess overall differences across the 5 formula variants. For post hoc analysis, pairwise comparisons between formulas were performed using robust 2-sample t tests. To reduce the risk of type I error from multiple comparisons, P values were adjusted using the Holm correction method, as implemented within the Eyetemis platform.

Evaluating Trueness (Mean Prediction Error)

To assess systematic error (distance of prediction errors from zero), the trimmed mean SEQ-PE of each formula was compared with zero using a 1-sample robust t test. In addition, trimmed means were compared between every pair of formulas using robust 2-sample t tests, adjusting P values with the Holm correction option.^14,15

Evaluating Precision (SD)

To compare the spread of errors among formulas, we examined the dispersion of SEQ-PE for each formula. For each pair of formulas, the robust 2-sample t test was applied to the 10% trimmed mean absolute deviation of SEQ-PEs.^14,15

Evaluating Accuracy (Mean Absolute Error)

To compare overall prediction accuracy, we used robust 2-sample tests to compare the trimmed means of the absolute SEQ-PEs between formulas.¹⁴ In addition, we analyzed the proportion of eyes within certain absolute prediction error thresholds (±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D). Differences in these proportions across all 5 formulas were assessed with the Cochran Q test for related samples.¹⁶ If Cochran Q indicated a significant difference, pairwise comparisons between formulas were performed using the McNemar test for correlated proportions, with appropriate adjustment for multiple comparisons.¹⁷

For subgroup analysis, eyes were categorized by AL into short (<22 mm), average (22 to 24.99 mm), and long (≥25.0 mm) groups. To better assess the impact of SOS AL, we compared the 2 best-performing and most clinically relevant formula configurations, Barrett STD, and Barrett TAL, in each subgroup. Given the large number of formula combinations and relatively smaller sample sizes in the short and long AL subgroups, we limited detailed subgroup analysis to the 2 most clinically relevant versions: BUII TAL and BUII STD. These configurations are the most representative of real-world biometry use. In practice, clinicians do not typically omit individual optional parameters nor do they toggle formula configurations based on parameter availability. Thus, hybrid configurations (eg, BUII WTW or BUII LT only) are artificial and unlikely to inform clinical decisions. Including all 5 formulas in each subgroup would also reduce statistical power and increase the risk of type I and II error.

Power Analysis

We conducted a Monte Carlo simulation (1000 iterations) to estimate the power of our sample to detect differences in mean absolute error between formula groups. Assuming a significance level of α = 0.05, an effect size of 0.10 D (difference in mean absolute SEQ-PE) and a conservative standard deviation of 0.26 D, the simulation indicated a power of approximately 0.90 (90%) to detect such differences.

RESULTS

General Analysis

A total of 1340 eyes of 1340 patients were included. The mean age was 74.40 ± 7.80 years, and 61.7% of patients were female. Preoperative biometric characteristics are summarized in Table 1. Descriptive statistics and outcomes for BUII STD, BUII TAL, and BUII WØ are provided in Table 2. Outcomes for BUII LT and BUII WTW are presented in Supplementary Table 1 (available at http://links.lww.com/JRS/B495).

Table 1.

Preoperative biometric data in the full dataset (n = 1340)

Parameter	Mean ± SD (range)
AL (mm)	23.36 ± 1.08 (20.87, 29.73)
ACD (mm)	3.32 ± 0.39 (2.12, 4.36)
K1 ant (D)	43.66 ± 1.55 (38.00, 49.04)
K2 ant (D)	44.54 ± 1.59 (38.97, 50.28)
Km ant (D)	44.10 ± 1.54 (38.48, 49.63)
LT (mm)	4.59 ± 0.42 (3.12, 6.00)
WTW (mm)	11.85 ± 0.41 (10.51, 13.36)

ACD = anterior chamber depth; AL = axial length; Km = mean keratometry; LT = lens thickness; WTW = white-to-white

SEQ-PE (Trueness)

The mean SEQ-PE ranged from −0.038 D (most myopic bias) to −0.014 D (most hyperopic bias). BUII TAL had a mean error of −0.038 D, which was slightly myopic and statistically different from zero (P = .026). However, this bias (less than half of a diopter) is clinically negligible. When comparing trueness between formulas, all pairwise comparisons of trimmed mean SEQ-PE were statistically significant (P < .05) except for the comparison between BUII STD and BUII TAL, which had equivalent trueness (P = .803). Trimmed means (trimming the highest and lowest 10% of errors) showed similar patterns. Table 2 and Figure 1A illustrate the SEQ-PE distributions for each formula.

Figure 1.

Comprehensive statistical analysis and heatmaps. SEQ-PE (A), precision of SEQ-PE (B), absolute SEQ-PE (C), and percentage of eyes falling within a specific diopter range (D). The asterisk (*) indicates significant differences within groups. Heatmaps provide adjusted P values for paired comparisons. SEQ-PE = spherical equivalent prediction error

Precision of SEQ-PE

The standard deviations (spread) of the prediction errors ranged from 0.333 D (BUII TAL, highest precision) to 0.341 D (BUII WØ, lowest precision). 10% trimmed means followed similar trends. Pairwise comparisons showed that BUII TAL's precision was significantly better than that of BUII WØ (P < .001). BUII STD (0.335 D) also had a significantly tighter error distribution than BUII WØ (P < .05). Differences between TAL and STD were not statistically significant at the 0.05 level. These precision outcomes are detailed in Table 2 and Figure 1B.

Absolute SEQ-PE (Accuracy)

The mean of the absolute prediction error ranged between 0.334 D (BUII TAL) and 0.341 D (BUII WØ). BUII TAL yielded the lowest mean absolute error (highest accuracy), followed closely by BUII STD. Robust comparisons indicated that BUII TAL had significantly lower absolute error than BUII WØ (P < .01). BUII STD likewise showed significantly lower absolute error than BUII WØ (P < .01). There was no significant accuracy difference between BUII TAL and BUII STD (P = .27). Figure 1C presents the absolute SEQ-PE distributions per formula.

Overall refractive prediction success rates were high for all formulas. Figure 1D shows the percentage of eyes within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D of target for each formula. At the ±0.50 D threshold, 80% of eyes were within target for both BUII STD and BUII TAL—the highest of any formula—compared with 78% for BUII WØ. At the ±0.25 D threshold, BUII STD and BUII TAL each hit 44%, slightly higher than BUII WØ (42%). These differences across formulas were statistically significant by Cochran Q (P < .01). Post hoc McNemar tests revealed that the inclusion of both optional parameters (STD) or use of SOS AL (TAL) yielded a modest but statistically higher fraction of eyes within 0.50 D and 0.25 D compared with the no-optionals formula (P < .05 for each comparison vs BUII WØ). Beyond ±0.50 D, all formulas performed similarly.

Subgroup Analysis: Short Eyes

This subgroup comprised 86 eyes with AL <22.0 mm. The mean SEQ-PE was −0.057 D for BUII TAL and +0.007 D for BUII STD (Table 3). Neither formula exhibited a statistically significant mean bias in short eyes (P = .314 and P = .649, respectively, for difference from zero), indicating that both remained largely accurate in trueness even in this challenging subgroup (Figure 2A). Trimmed means (10%) showed consistent patterns.

Table 3.

Values of SEQ-PE, precision, and absolute SEQ-PE of BUII TAL and BUII STD by AL subgroup

Parameter	Statistic	Group	Trimmed mean	Mean	SD	Min	Q1	Q2 (median)	Q3	Max
Short AL (n = 86)	SEQ-PE (trueness)	TAL	−0.046	−0.057	0.379	−1.040	−0.284	0.003	0.188	0.745
		STD	0.023	0.007	0.428	−1.210	−0.204	0.040	0.289	1.045
	Precision of SEQ-PE (D)	TAL	0.277	0.300	0.229	0.024	0.102	0.238	0.444	0.994
		STD	0.307	0.337	0.261	0.002	0.133	0.260	0.501	1.233
	Absolute SEQ-PE (D)	TAL	0.275	0.297	0.240	0.000	0.095	0.253	0.446	1.040
		STD	0.309	0.338	0.259	0.000	0.116	0.283	0.498	1.210
Average AL (n = 1176)	SEQ-PE (trueness)	TAL	−0.015	−0.031	0.414	−1.490	−0.290	−0.015	0.280	1.280
		STD	−0.010	−0.027	0.411	−1.440	−0.285	0.000	0.290	1.240
	Precision of SEQ-PE (D)	TAL	0.302	0.332	0.2485	0.000	0.147	0.280	0.460	1.475
		STD	0.302	0.331	0.244	0.000	0.155	0.290	0.450	1.430
	Absolute SEQ-PE (D)	TAL	0.301	0.332	0.250	0.000	0.145	0.280	0.460	1.490
		STD	0.301	0.331	0.2452	0.000	0.150	0.288	0.450	1.440
Long AL (n = 78)	SEQ-PE (trueness)	TAL	−0.163	−0.134	0.468	−0.995	−0.460	−0.205	0.090	1.130
		STD	−0.176	−0.142	0.454	−0.945	−0.430	−0.180	0.080	1.080
	Precision of SEQ-PE (D)	TAL	0.319	0.355	0.303	0.003	0.122	0.268	0.523	1.293
		STD	0.304	0.340	0.300	0.001	0.104	0.254	0.474	1.256
	Absolute SEQ-PE (D)	TAL	0.379	0.401	0.272	0.005	0.160	0.360	0.560	1.130
		STD	0.373	0.393	0.264	0.000	0.170	0.370	0.580	1.080

AL = axial length; BUII = Barrett Universal II; LT = lens thickness; SEQ-PE = spherical equivalent prediction error; STD = Barrett Universal II with LT and white-to-white; Q1/Q2/Q3 = quartile thresholds for 25% (Q1), 50% (Q2), and 75% (Q3) of data; TAL = true axial length; WØ = without optional parameters; WTW = white-to-white

Figure 2.

Comprehensive statistical analysis and heatmaps for short eyes. SEQ-PE (A), precision of SEQ-PE (B), absolute SEQ-PE (C), and percentage of eyes falling within a specific diopter range (D). The asterisk (*) indicates significant differences within groups. Heatmaps provide adjusted P values for paired comparisons. SEQ-PE = spherical equivalent prediction error

Precision in short eyes also differed: BUII TAL had a precision of 0.300 D vs 0.337 D for BUII STD. The difference in precision was statistically significant (P < .01), favoring BUII TAL (Figure 2B).

For accuracy, the mean absolute SEQ-PE in short eyes was 0.297 D with BUII TAL compared with 0.338 D with BUII STD. This reduction in mean absolute error for BUII TAL was statistically significant (P < .01, Figure 2C). In addition, BUII TAL achieved 85% of short eyes within ±0.50 D, compared with 70% with BUII STD.

Subgroup Analysis: Average Eyes

In the 1176 eyes with average AL (22.0 to 24.99 mm), BUII TAL and BUII STD performed very similarly. The mean SEQ-PEs were −0.031 D (TAL) and −0.027 D (STD); neither had a significant bias (P = .244 and P = .415, respectively). Precision was essentially identical (0.332 D vs 0.331 D for TAL and STD, P = .55). The mean absolute errors were 0.332 D (TAL) and 0.331 D (STD), with no significant difference (P = .60). Trimmed means (10%) also showed similar trends across formulas. In both cases, approximately 80% of eyes were within ±0.50 D. These data are in Table 3 and Supplementary Figure 1 (available at http://links.lww.com/JRS/B495).

Subgroup Analysis: Long Eyes

This subgroup included 78 eyes with AL ≥25.0 mm. BUII TAL and BUII STD again showed comparable results. The mean SEQ-PEs were −0.134 D (TAL) and −0.142 D (STD), which were slightly myopic and statistically different from zero (P = .011 and P = .007, respectively). Precision was 0.355 D (TAL) vs 0.340 D (STD), with no significant difference (P = .96). The mean absolute SEQ-PEs were 0.401 D (TAL) and 0.393 D (STD), also with no significant difference (P = .31). Once again, overall trends persisted after 10% data trimming. In long eyes, 68% (TAL) and 70% (STD) were within ±0.50 D, which was not a statistically meaningful difference (Table 3 and Supplementary Figure 2, available at http://links.lww.com/JRS/B495).

DISCUSSION

In this study, we compared the refractive prediction precision and accuracy of the BUII formula in its standard form (with or without optional parameters) vs a modified form using SOS AL (Barrett “True AL”). We found small but significant differences in performance metrics across these formula variations. Overall, BUII TAL consistently demonstrated the highest precision and accuracy, followed by BUII with both optional variables included. In subgroup analyses, this benefit was most pronounced in short eyes: In eyes with AL <22 mm, BUII TAL showed significantly better precision and accuracy than BUII STD (P < .01). In average and long eyes, by contrast, BUII TAL and BUII STD performed nearly indistinguishably. Incorporating the SOS AL and optional biometric parameters thus provided additional predictive value primarily in shorter eyes, likely by improving the estimation of effective lens position in eyes where standard assumptions are less accurate.¹⁸

SOS AL values are longer in short eyes and shorter in long eyes than composite AL.¹⁹ A recent study by Miyamoto and Kamiya validated the Barrett True AL formula by comparing its predictive accuracy with the standard BUII and other biometry methods.²⁰ They found no statistically significant differences in overall prediction accuracy among formulas, but the Barrett TAL formula achieved lens constant results closest to zero error.²⁰ More recently, a study by Hata et al. further evaluated the BUII TAL approach using segmented AL measurements and confirmed a modest but statistically significant improvement in refractive accuracy compared with the traditional BUII, particularly in achieving outcomes within ±0.25 D and ±0.50 D of target.²¹ This growing body of evidence suggests that using SOS AL can reduce systematic refractive error without requiring extensive surgeon-specific constant adjustments. Our findings align with that implication: BUII TAL had virtually zero mean error and outperformed the standard formula in short eyes where constant offsets often fail to fully correct the nonlinearity in axial extremes. The improved performance of BUII TAL in short eyes is consistent with the known amplification of AL-related prediction errors in this group.²² In short eyes, even small errors in AL estimation can produce disproportionately large refractive surprises. Shorter AL also amplifies the impact of any AL measurement error.²³ Therefore, the benefit of using SOS AL, which more closely approximates the true anatomical AL by segmenting optical path lengths, is expected to be more pronounced in short eyes, as demonstrated by Kato and colleagues.²² By contrast, average and long eyes already have AL values close to the true anatomical length, so the additional precision gained from segmentation is proportionally less relevant. This aligns with our findings in which the difference between formulas narrowed as AL increased. Device-specific differences also matter; previous research has shown that ACD and AL can vary slightly between biometers, impacting IOL power calculations.²⁴ We mitigated that by using a single device for all eyes.

Our measures of trueness indicated that all formula versions were very close to zero mean error. The standard Barrett (no optional variables) had virtually no mean bias, and adding LT/WTW or using SOS AL did not introduce any notable systematic shifts. The small myopic bias observed with BUII LT and TAL in the overall data (∼0.02 to 0.03 D) was statistically significant due to the large sample size but is not clinically meaningful. Notably, in short eyes, both TAL and STD retained no significant bias. In subgroup analyses, the advantage of TAL over STD in precision was only significant for short eyes (P < .01), with no difference for average or long eyes. This pattern suggests that for normal and long eyes, the Barrett formula's prediction variability is already low and not further improved by extra parameters, whereas short eyes benefit from the refined input.

We observed 80% of eyes within 0.50 D of target for the best-performing versions (TAL, STD). This is broadly comparable with the 84% to 90% within 0.50 D reported by Sorkin et al. for a mix of modern formulas in a large series, using a similar analytic approach.¹⁵ It is worth emphasizing that the differences between formulas in our study, while statistically significant, were on the order of a few hundredths of a diopter in absolute error. Such small differences may not manifest in a noticeable refractive difference for individual patients. This underlines that the BUII, even without optional data, is already an excellent formula across ALs, consistent with recent literature.^8,12

When comparing Barrett with other formulas, the Kane formula is often cited as one of the most accurate across all ALs.^3,9,25 Kane, which also uses AL, K, ACD, LT, and optional inputs (such as central corneal thickness and patient sex) powered by an AI-derived algorithm, has shown outstanding performance in many studies.²⁶ Interestingly, Li et al. found that adding corneal thickness to the Kane formula did not improve accuracy in short eyes, whereas adding LT did yield some benefit in those with shallow ACD and steep corneas.²⁵ A recent multicenter study by Kenny et al. found, however, that the ZEISS AI calculator outperformed Barrett, Pearl-DGS, and Kane formulas in prediction accuracy, while using segmented AL offered no added benefit over traditional AL in any of the tested formulas.²⁷ For extremely long eyes (>30 mm), previous research indicates that formulas such as Kane, BUII, and the EVO 2.0 combined with AL adjustments (eg, Wang-Koch modification) produce the best outcomes and mitigate hyperopic errors.²⁸ Our long-eye subset was not in the ultra-long range, but Barrett performed excellently, and the lack of difference with TAL suggests that beyond a certain length, the challenge may shift more to effective lens position prediction and other factors than AL measurement per se.

The strengths of our study include (1) one of the largest sample sizes (1 eye per patient, N = 1340) evaluating this research topic (true SOS AL and inclusion of optional biometric variables), providing robust statistical power; (2) use of a single modern swept-source biometer (ensuring consistency in AL and other measurements across all cases); (3) evaluation of the Barrett formula with and without optional inputs and with SOS AL, allowing a focused comparison within the same formula framework; and (4) the use of the ESCRS Eyetemis platform for analysis, which used trimmed mean statistics and robust hypothesis testing as recommended for IOL formula comparisons by ESCRS guidelines, ensuring reproducibility and reducing the influence of outliers.^15,29

One limitation is the relatively small number of short-eye and long-eye cases, which may be underpowered for detecting very subtle differences. Future studies with larger cohorts of extreme AL would further validate the observed trends. In addition, our study evaluated only 1 IOL model (AcrySof SN60AT)—while this controlled for lens constant differences, it means our adjusted constants are specific to that lens. The outcomes might differ slightly with other IOL designs. Also, all formulas were calculated using a single A-constant of 118.75 because formula-specific optimization was not performed (notably mean error was already under 0.05 D for all formula variations). Further per-formula optimization would likely not change our results. This approach enhances the real-world relevance of our results because most surgeons rely on a fixed A-constant in clinical settings. Finally, we did not compare the Barrett variants with other formula families (eg, Kane, Hill-RBF, and Olsen) in this report. Such comparisons would be valuable to see whether the small improvements observed here translate into a material advantage over competing formulas.

In conclusion, modifying the BUII formula with SOS AL and including optional biometric variables can further increase the precision and accuracy of refractive outcomes, most notably in short eyes where traditional calculations are less reliable. For eyes of average length, the standard BUII formula without optional inputs already performs at a very high level, and additional data apparently confer little advantage. Ongoing innovations, such as machine learning-enhanced formulas and ray-tracing approaches, may continue to improve refractive prediction in difficult eyes. Future research should focus on validating these results in broader populations and determining whether the observed gains in short eyes can be replicated with other new formulas.

WHAT WAS KNOWN

• The Barrett Universal II formula is a leading IOL power calculation formula that generally provides excellent refractive accuracy across a range of axial lengths (ALs).

• Optional biometric parameters (such as lens thickness and white-to-white corneal diameter) and improved AL measurements (sum-of-segments [SOS] true AL) have been proposed to improve formula predictions, but evidence of their added benefit has been limited or mixed.

• Short eyes (with AL under 22 mm) are known to be challenging for IOL power prediction, often showing higher prediction errors with conventional formulas, indicating a gap in optimal calculation methods for these cases.

WHAT THIS PAPER ADDS

• In a large cohort, we demonstrate that a Barrett Universal II formula adjusted with SOS AL (Barrett TAL) and one including both optional parameters yield slightly better refractive outcomes than the standard Barrett II formula, with the improvement most pronounced in short eyes. In eyes <22 mm AL, the Barrett TAL variant significantly reduced prediction error and variability compared with the standard formula.

• For average and long eyes, the inclusion of optional parameters or true AL did not meaningfully change outcomes.

• Our study applies trimmed-mean robust statistical analysis (as per recent ESCRS guidelines) for formula comparison and reinforces findings by Shammas et al. and others that using a “True AL” approach can benefit short eyes. It provides clinicians with evidence that using devices or formulas capable of SOS measurements can improve refractive targeting for short eyes, while reassuring that for most patients, current standard formulas are sufficient.