Accurate intraocular lens (IOL) power calculation is fundamental to achieving the desired refractive outcome following cataract surgery. Since the implantation of the first IOL by Sir Harold Ridley in 1949, it has been recognized that merely inserting a lens is insufficient; precise power estimation is critical to optimize postoperative visual outcomes.¹˒² Advances in cataract surgery techniques and increasing patient expectations for spectacle independence have further underscored the importance of reliable IOL power prediction.³

Several biometric parameters influence IOL power calculation, including axial length (AL), keratometry (K) and anterior chamber depth (ACD). Variations in AL and corneal power can significantly alter refractive outcomes, making the choice of calculation formula crucial.⁴˒⁵ In extreme biometric ranges, traditional formulas may become less reliable, leading to refractive surprises.⁶˒⁷

Formulas such as Holladay 1 have long been used to calculate IOL power based on AL, K values and a constant and remain a dependable benchmark in clinical practice.⁸ More recently, the Haigis formula was introduced, which incorporates ACD in addition to AL and K, potentially improving accuracy in eyes with short or long AL.⁹

With the advent of optical biometry, the precision of AL measurement has improved considerably, yet the choice of formula remains a major determinant of postoperative accuracy.¹⁰˒¹¹ Comparative studies have demonstrated that newer-generation formulas, including Haigis, may provide superior predictability in certain subgroups, while Holladay 1 continues to be widely trusted.¹²˒¹³

Despite numerous reports comparing multiple formulas, direct head-to-head evaluations between Holladay 1 and Haigis remain limited. Understanding their relative performance is essential for guiding clinical decision-making, particularly in routine cataract practice where achieving emmetropia is the primary goal. This study therefore aims to compare the accuracy and reliability of the Holladay 1 and Haigis formulas by analyzing predicted versus achieved postoperative refractions in our patient population.

OBJECTIVE

To compare the intraocular lens (IOL) power calculation using the Holladay 1 and Haigis formulae.

Study design and setting: This was a hospital-based, descriptive, observational and comparative study conducted in the Department of Ophthalmology at a tertiary care centre. The study period was 18 months for data collection and 6 months for analysis (July 2023 – June 2025).

Study population: All patients above 20 years of age attending the ophthalmology outpatient department (OPD), diagnosed with visually significant cataract and undergoing phacoemulsification with IOL implantation, were considered eligible.

Inclusion criteria:

1. Patients older than 20 years of age.
2. Presence of visually significant cataract.
3. Eyes suitable for phacoemulsification.
4. Willingness to participate in the study and provide informed consent.

Exclusion criteria:

1. Eyes with co-existing ocular pathology significantly altering vision.
2. History of previous intraocular or corneal surgery.
3. Presence of corneal pathology or opacity.
4. Complicated or traumatic cataract.
5. Pediatric cataract.
6. Eyes with retinal pathology.
7. Patients unwilling to provide informed consent.

Sample size: The minimum sample size was calculated to be 174 eyes, based on standard statistical formulae, with power set at 80% and a 95% confidence interval. The sample size was derived from differences in mean IOL power values predicted by different formulas reported in earlier literature.

Sampling technique: Simple random sampling was used to select eligible patients.

Study procedure: After obtaining informed consent, a detailed case history and comprehensive ophthalmic examination were performed. Biometric measurements were obtained using A-scan ultrasound biometry and an autorefractometer. For each patient, the intraocular lens (IOL) power was calculated using Holladay 1 and Haigis formulae.

Outcome measures: The predicted postoperative refractive outcomes from each formula were compared with the actual postoperative refraction measured at follow-up visits. The mean prediction error and mean absolute error were calculated for both formulas.

Instruments used:

1. Slit lamp
2. Snellen visual acuity chart
3. A-scan biometer
4. Autorefractometer

Holladay 1 formula: Introduced in 1988, the Holladay 1 formula is a third-generation theoretical model for intraocular lens (IOL) power calculation. It predicts the effective lens position (ELP) primarily using axial length (AL) and keratometry (K), combined with a surgeon-specific constant (“surgeon factor”). This constant refines the calculation and improves predictability across average eyes. While Holladay 1 has been widely applied in routine cataract surgery, its accuracy may decrease in extreme biometric situations, such as very short or very long eyes.

Haigis formula: The Haigis formula is a fourth-generation model that extends the predictive accuracy by incorporating anterior chamber depth (ACD) in addition to AL and K. It employs three individualized constants (a0, a1, a2):

• a0 corresponds to the manufacturer’s IOL constant,
• a1 relates to the measured preoperative ACD and
• a2 is linked to axial length.
•  

This three-constant system allows the Haigis formula to more precisely predict the postoperative effective lens position. The formula has been shown to perform reliably across a wide spectrum of eyes, particularly those with unusual biometry such as very short or long axial lengths, or shallow/deep anterior chambers.

Statistical analysis: Data were entered into Microsoft Excel and analyzed using SPSS version 24.0 (IBM, USA). Quantitative variables were expressed as mean ± standard deviation. The mean refractive prediction errors between Holladay 1 and Haigis were compared using paired t-tests. A p-value of <0.05 was considered statistically significant and p <0.001 was considered highly significant.

A total of 174 eyes of 174 patients were included in the study. The mean age of the study population was 56.8 ± 5.33 years (range 49–67 years). The majority of patients (50.6%) were in the 51–60 years age group, followed by 39.7% above 60 years and 9.8% below 50 years. The gender distribution was nearly equal, with females comprising 50.6% and males 49.4%. Laterality was evenly distributed, with right and left eyes contributing 50% each.

With respect to systemic comorbidities, 21.3% of patients had diabetes mellitus, 13.2% had hypertension, 5.2% had ischemic heart disease (IHD) and 8.6% had chronic obstructive pulmonary disease (COPD).

Biometric evaluation revealed a mean keratometric (K) value of 43.37 ± 1.43 D, mean corneal astigmatism of –1.31 ± 0.30 D, anterior chamber depth of 3.48 ± 0.59 mm, axial length of 23.53 ± 1.27 mm and mean intraocular lens (IOL) power of 22.97 ± 1.70 D.

Using the Holladay 1 formula, the mean absolute estimation error was 0.84 ± 0.38, estimation error –0.12 ± 0.84 and prediction error 1.56 ± 0.14. The proportion of eyes achieving refraction within the target range (EWTR) was 70.26 ± 6.14%.

Using the Haigis formula, the mean absolute estimation error was 0.87 ± 0.47, estimation error –0.29 ± 1.06 and prediction error 1.49 ± 0.36. The EWTR achieved was 68.37 ± 9.31%.

Direct comparison between Holladay 1 and Haigis revealed no statistically significant differences across all outcome measures. The absolute estimation error (0.84 vs 0.87, p = 0.61), estimation error (–0.12 vs –0.29, p = 0.33), prediction error (1.56 vs 1.49, p = 0.24) and EWTR (70.26% vs 68.37%, p = 0.28) were comparable. However, Holladay 1 showed a slightly higher proportion of eyes within the target refraction, suggesting marginally better predictability.

Table 1. Baseline demographic and clinical characteristics (n = 174)

Table 2. Biometric variables

Table 3. Outcomes with Holladay 1 and Haigis formulas

Table 4. Comparative analysis (Holladay 1 vs Haigis)

In our study, the mean age was 56.8 ± 5.3 years, with most patients between 51–60 years. The gender distribution was nearly equal, with females comprising 50.6% and males 49.4%. Kaya et al.¹⁴ reported a higher mean age (68.4 years) and female predominance (68%), though both studies reflect typical cataract populations. We found an equal distribution of right and left eyes (50% each). Kaya et al.¹⁴ also reported similar distribution (47% right vs. 53% left), confirming that laterality does not influence intraocular lens (IOL) power outcomes.

In our study, 21.3% had diabetes, 13.2% hypertension, 5.2% ischemic heart disease and 8.6% COPD. These systemic conditions, though clinically important, do not directly alter biometric predictability but highlight the real-world surgical profile. The mean keratometry was 43.37 D, mean AL 23.53 mm, mean corneal astigmatism –1.31 D and mean anterior chamber depth (ACD) 3.48 mm. Kaya et al.¹⁴ reported comparable results with mean K = 43.66 D and AL = 23.3 mm, confirming our study population represents medium axial length eyes where formula selection has greatest impact.

The Holladay 1 formula produced a mean absolute estimation error (AEE) of 0.84 ± 0.38, mean estimation error (ME) –0.12 ± 0.84, prediction error 1.56 ± 0.14 and 70.26% eyes within target refraction (EWTR). The Haigis formula showed an AEE of 0.87 ± 0.47, ME –0.29 ± 1.06, prediction error 1.49 ± 0.36 and EWTR 68.37%. On direct comparison, Holladay 1 achieved a slightly higher EWTR, but the differences in AEE, ME and prediction error were not statistically significant (all p > 0.05). This suggests both formulas provide comparable accuracy in medium axial length eyes, with Holladay 1 showing marginally better consistency. Our results are consistent with Dervin et al.¹⁵, who found low AEE with Holladay 1 in medium-long eyes and Narvaez et al.¹⁸, who also reported Holladay 1 as reliable in average axial lengths. Eleftheriadis et al.²⁰ confirmed Holladay 1 performed better than SRK/T and Hoffer Q in eyes with AL around 23 mm.

Conversely, several studies demonstrate advantages of Haigis under specific biometric profiles. Stoprya et al.¹⁶ and Kim et al.¹⁷ showed that Haigis is superior in short eyes (AL < 22 mm), while Xu et al.¹⁹ reported Haigis’s benefit in primary angle-closure glaucoma. Eom et al.²¹ demonstrated Haigis outperformed Hoffer Q in patients with shallow anterior chambers (ACD < 2.40 mm). These findings align with our conclusion that Haigis is more suited to extreme biometry, whereas Holladay 1 is more reliable in medium AL eyes. Our study reinforces that both Holladay 1 and Haigis formulas are clinically effective, but their performance depends on biometric context. Holladay 1 is reliable for medium axial lengths, while Haigis offers advantages in short AL and shallow ACD eyes. Hence, tailoring formula selection to patient biometry rather than relying on a single universal formula is crucial to minimizing refractive surprises and improving surgical outcomes.

This study demonstrates that both Holladay 1 and Haigis formulas provide clinically acceptable refractive outcomes in cataract surgery patients with medium axial lengths. Holladay 1 achieved slightly better predictability in terms of eyes within target refraction, while Haigis showed comparable results across all error parameters. These findings highlight that no single formula is universally superior and that the choice of formula should be guided by biometric profiles: Holladay 1 for medium axial lengths and Haigis for shorter axial lengths or shallow anterior chambers. Adopting a tailored approach to formula selection can minimize refractive surprises and optimize postoperative outcomes.

Limitations

This study has certain limitations. Being a single-center study, the findings may not be generalizable to other populations with different biometric characteristics. Most of the included eyes were within the medium axial length range, limiting extrapolation to short or long eyes where formula performance often differs. Only Holladay 1 and Haigis formulas were compared, while newer generation formulas such as Barrett Universal II or Olsen were not included. In addition, postoperative outcomes were assessed in the short term, without evaluating long-term refractive stability.

IEC Approval: Taken

Funding: Nil

Conflict of Interest: Nil

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