Theoretical and Clinical Comparison of the Hoffer Q and SRK/T Formulas

Jin Ho Jeong; Sung Gon Kim; Hye Jin Lee; Sun Ho Lee; Dong Min Cha

doi:10.3341/jkos.2014.55.1.85

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Jeong, Kim, Lee, Lee, and Cha: Theoretical and Clinical Comparison of the Hoffer Q and SRK/T Formulas

Original Article

J Korean Ophthalmol Soc 2014;55(1):85-92.

Published online: 7 September 2014

DOI: https://doi.org/10.3341/jkos.2014.55.1.85

Theoretical and Clinical Comparison of the Hoffer Q and SRK/T Formulas

Jin Ho Jeong, MD, PhD, Sung Gon Kim, MD, Hye Jin Lee, MD, Sun Ho Lee, MD, Dong Min Cha, MD

Department of Ophthalmology, Jeju National University School of Medicine, Jeju, Korea

Address reprint requests to Jin Ho Jeong, MD, PhD Department of Ophthalmology, Jeju National University Hospital, #15 Aran 13-gil, Jeju 690-767, Korea, Tel: 82-64-717-1362, Fax: 82-64-717-1102, E-mail: amario@naver.com

Received 12 April 201319 June 2013 Accepted 1 October 2013

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Purpose

To evaluate the biometric conditions causing increased disparity in the calculation of intraocular lens (IOL) power between the Hoffer Q and SRK/T formulas.

Methods

A prospective comparative study was conducted on 365 uneventful, cataract surgeries performed at a tertiary care center by one surgeon. The IOL power was calculated using both the Hoffer Q and SRK/T formulas with A-scan biometry. For a selected IOL power, the expected disparity between the 2 formulas (EDF) was measured and the EDF value was used to categorize the cases. The resultant error associated with each formula was determined at postoperative 6 weeks. KAL was defined as the product of mean corneal power (K) and axial length (AL). Postoperative errors of both formulas were calculated and their association with preoperative biometry measurements analyzed.

Results

In 17.8% of the cases, the EDF was larger than 0.4 D, possibly leading to different IOL diopter recommendations. The EDF value and the product of corneal curvature and axial length were significantly correlated (R² = 0.855, p ＜ 0.001). Multiple regression analysis of causative preoperative biometric factors on the postoperative formula errors showed that astigmatism, anterior chamber depth (ACD), and lens thickness (LT) were significantly associated with Hoffer Q error and SRK/T error.

Conclusions

Overall, both formulas performed very well when recommending the correct IOL power. The cause of disparity between the predicted refraction for the 2 formulas was more associated with KAL than K or AL alone. Astigmatism, ACD, and LT were the causative factors for the postoperative errors in both formulas.

Keywords: Effective lens position, Hoffer Q formula, IOL formula comparison, SRK/T formula

References

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Figure 1.

Distribution frequency was illustrated in histogram with normal distribution curve. In histogram, 37 cases (12.1%) had axial length shorter than 22 mm, and 239 cases (78.3%) ranged between 22 and 25 mm, and 29 cases (9.5%) were longer than 25 mm.

Figure 2.

For the selected IOL power, the disparity between the 2 formulas (expected disparity between formulas, EDF) was calculated by subtracting the expected refraction value obtained using the SRK/T formula from that obtained using the Hoffer Q formula. The 365 cases were divided into 3 groups according to their EDF value (A: EDF ＞ 0.4 D, B: -0.4 D ≤ EDF ≤ 0.4 D, C: EDF ＜ -0.4 D). The scatterplot of the corneal curvatures and axial lengths showed clear discrimination among the EDF subgroups. EDF subgroup A (red circle), B (green circle), C (blue circle).

Figure 3.

The EDF values were plotted against the axial length, and showed an R value of 0.417, by using a linear regression model (p = 0.000). The EDF values show large amplitude of variation even in middle axial length range (22-25 mm). ^* EDF (expected disparity between formulas) was calculated by subtracting the expected refraction value obtained using the SRK/T formula from that obtained using the Hoffer Q formula.

Figure 4.

The EDF^* values were plotted against the products of corneal curvature and axial length, and showed an r² value of 0.855, by using a quadratic curve estimation (p = 0.000). ^* EDF (expected disparity between formulas) was calculated by subtracting the expected refraction value obtained using the SRK/T formula from that obtained using the Hoffer Q formula.

Table 1.

Characteristics of preoperative biometric data and the power of IOL distribution

	Minimum	Maximum	Mean ± SD
Age (years)	40	91	71.09 ± 8.99
Axial length (mm)	19.18	31.47	23.44 ± 1.55
Spherical equivalent of refractive error (diopter)	-24.50	+10.50	-0.37 ± 3.85
Cylinder of refractive error (diopter)	0	+3.50	1.17 ± 0.73
Corneal curvature (diopter)	40.44	49.56	44.26 ± 1.60
Anterior chamber depth (mm)	2.00	4.29	3.14 ± 0.45
Power of IOL (diopter)	0.0	38.0	20.17 ± 4.44

Table 2.

Mean EDF^* and the number of subgroups stratified by axial length

Subgroup	A^*		B^†		C^‡
Axial length	EDF	(N)	EDF	(N)	EDF	(N)
＜22 mm	-0.80 ± 0.53	(9)	0.00 ± 0.18	(41)	0.55 ± 0.08	(4)
22-25 mm	-0.48 ± 0.05	(10)	0.00 ± 0.18	(242)	0.53 ± 0.09	(24)
＞25 mm	-0.41 ± 0.00	(1)	0.17 ± 0.20	(17)	0.54 ± 0.11	(17)
Total	-0.62 ± 0.39	(20)	0.00 ± 0.19	(300)	0.53 ± 0.10	(45)

Values are presented as mean ± SD.

EDF = expected disparity between formulas.

^* EDF ＞ 0.4 D

^† -0.4 D ≤ EDF ≤ 0.4 D

^‡ EDF ＜ -0.4 D.

Table 3.

The composition of Hoffer Q and SRK/T formula and Pearson correlation with biometric factors

Composition	Mean ± SD	K	AL	KAL^‡
ACDh^*	5.05 ± 0.44	-0.048 (0.360)	0.914 (0.000)	0.898 (0.000)
ACDt^†	5.10 ± 0.61	0.276 (0.000)	0.777 (0.000)	0.950 (0.000)
ACD	3.13 ± 0.45	-0.037 (0.482)	0.506 (0.000)	0.491 (0.000)

SD = standard deviation.

^* Effective lens position of Hoffer Q formula

^† Effective lens position of SRK/T formula

^‡ Defined as the product of mean corneal power (K) and axial length (AL).

Table 4.

The results of multiple regression analyses of Hoffer Q and SRK/T formula error against the preoperative biometric measurements with EDF

Adjusted R²	Error of Hoffer Q formula	Error of SRK/T formula
Adjusted R²	0.272	0.225
Significance
Mean keratometry	0.379	0.332
Astigmatism	0.000^*	0.000^*
Axial length	0.485	0.494
Anterior chamber depth	0.000^*	0.000^*
Lens thickness	0.005^*	0.004^*
EPL difference	0.066	0.072
Emmetropic power difference	0.215	0.160
EDF	0.278	0.014^*

^* Statistically significant.

Table 5.

Comparison of IOL formula accuracy using MAE amount

1) Mean absolute error (MAE) comparison between both formulae stratified by EDF^* subgroup using paired t-test
Group	MAE of Hoffer Q	MAE of SRK-T	N	Sig. (2-tailed)
A^*	0.45 ± 0.31 D	0.42 ± 0.38 D	20	0.534
B^†	0.29 ± 0.23 D	0.27 ± 0.23 D	300	0.149
C^‡	0.41 ± 0.33 D	0.42 ± 0.38 D	45	0.784
2) Mean absolute error (MAE) comparison between both formulae stratified by axial length using paired t-test
Axial length	MAE of Hoffer Q	MAE of SRK-T	N	Sig. (2-tailed)
＜22 mm	0.33 ± 0.26 D	0.35 ± 0.31 D	54	0.866
22-25 mm	0.29 ± 0.23 D	0.27 ± 0.23 D	276	0.155
＞25 mm	0.50 ± 0.36 D	0.44 ± 0.41 D	35	0.447
3) Percentage of eyes within 0.50 D, within 1.00 D or over 1.00 D of mean absolute errors (MAE) was calculated to compare the accuracy of formula
MAE of formula	＜0.50 D	≤1.00 D	＞1.00 D
Hoffer Q formula	295 (80.8%)	358 (98.1%)	7 (1.9%)
SRK/T formula	294 (80.5%)	359 (98.4%)	6 (1.6%)