A total of 113 cataract extraction and IOL implantation cases were analyzed. The demographic and anatomic variables of all patients were shown in Table 1.1. The mean age was 67.12± 11.01, while the female/male ratio was 44/36. The mean AL was 23.69 ± 0.87 mm and the mean ACD was 3.21 ± 0.35 mm. The mean implanted IOL power was 21.10 ± 2.47D and the mean postoperative 1st-month SE was -0.42 ± 0.30D. The subgroup according to AL (Table 1.2) revealed that the majority of eyes (88.5%) were intermediate eyes, while the subgroup according to IOL power (Table 1.3) showed that we frequently implanted medium power lenses (78.8%). The eyes with normal axial length were divided into three groups (Table 1.4): shallow eyes (31%), normal eyes (49%), and deep eyes (20%).
Table 1.1 The demographic and anatomic variables of all patients
Variables
|
Value
|
Patients/Eyes
|
80/113
|
Eyes: OS/ OD
|
51/62
|
Female/ Male
|
44/36
|
|
Mean ± SD
|
Age (yrs)
|
67.12± 11.01
|
AL (mm)
|
23.69 ± 0.87
|
ACD (mm)
|
3.21 ± 0.35
|
LT (mm)
|
4.46 ± 0.41
|
WTW (mm)
|
11.93 ± 0.29
|
Implanted IOL power (D)
|
21.10 ± 2.47
|
Post-op first week SE (D)
|
-0.37 ± 0.30
|
Post-op first month SE (D)
|
-0.42 ± 0.30
|
OS, left eye; OD, right eye; AL, axial length; ACD, anterior chamber depth; LT, lens thickness; WTW, white-to-white; IOL, intraocular lens; SE, spherical equivalent; D, diopter; SD, standard deviation.
Table 1.2 Subgroup analysis according to AL
|
Frequency
|
Percent (%)
|
Short Eye (≤ 22 mm)
|
2
|
1.8
|
Intermediate Eye (22-25 mm)
|
100
|
88.5
|
Long Eye (≥ 25 mm)
|
11
|
9.7
|
Total
|
113
|
100.0
|
AL, axial length.
Table 1.3 Subgroup analysis according to IOL Power
|
Frequency
|
Percent
|
Low Power (≤ 18 D)
|
16
|
14.2
|
Medium Power (18.50-24.00 D)
|
89
|
78.8
|
High Power (≥ 24.50 D)
|
8
|
7.1
|
Total
|
113
|
100.0
|
Table 1.4 ACD Groups of Eyes with Intermediate Length (N= 100)
ACD Groups
|
Frequency
|
Percent (%)
|
≤3 mm
|
31
|
31
|
3.01- 3.49 mm
|
49
|
49
|
≥3.5 mm
|
20
|
20
|
Total
|
100
|
100
|
ACD, anterior chamber depth
The minimum, maximum, and mean values of implanted IOL power and recommended IOL power to achieve emmetropia of each formula were indicated in Table 2. The range of the implanted IOL power was between 15D and 27D. The mean IOL power of the Kane formula (21.02 ± 2.45D) was closer to the mean implanted IOL power (21.10 ± 2.47D) when compared to the other formulas. The Barret Universal II and the Ladas Super formulas had the lowest SD value (2.45), while the Hoffer Q formula had the highest SD value (2.72).
Cumulative percentages within ±0.25D, ±0.50D, ±0.75D, and ±1.00D in addition to the mean PE, MAE, and MedAE for each formula were reported in Table 3 and the binary comparison of AEs was presented in Table 4. When MAEs were compared, SRK/T and Barrett Universal II formulas had the lowest values (0.30D and 0.31D, respectively) while Holladay 2 formula had the greatest value (0.41D). There were significant differences between SRK/T and Holladay 2, Hoffer Q, Haigis, and Ladas Super Formula (p<0.05), but not between SRK/T and the new generation formulae (Kane, p=0.440; Barret Universal II, p=0.882; T2, p= 0.063). For Barret Universal II the difference was statistically significant compared to Holladay 2, Hoffer Q, Haigis, Kane, and Ladas Super Formula (p<0.05), but not in comparison to SRK/T (p=0.882) and T2 (p=0.289). SRK/T, Kane, T2, and Ladas Super Formula had the lowest SD of PE (0.33 and 0.35, respectively) while Hoffer Q had the highest SD of PE (0.40). According to the MedAE, the lowest and the greatest values were achieved by SRK/T (0.25D), Kane (0.27D), Barret Universal II (0.27D), and Hoffer Q (0.39D), respectively.
Table 2. Descriptive statistics of implanted IOL and recommended IOL diopter to achieve emmetropia of each formula for all patients (N= 113)
|
Minimum
|
Maximum
|
Mean ± SD
|
Implanted IOL power (D)
|
15.00
|
27.00
|
21.10 ± 2.47
|
Recommended IOL power to achieve emmetropia (D)
|
|
|
|
SRK/T
|
14.74
|
26.72
|
20.75 ± 2.46
|
Holladay 2
|
14.55
|
27.18
|
20.97 ± 2.64
|
Hoffer Q
|
14.39
|
27.44
|
20.88 ± 2.72
|
Haigis
|
14.73
|
27.09
|
20.96 ± 2.61
|
Kane
|
15.00
|
27.00
|
21.02 ± 2.45
|
Barrett Universal II
|
14.79
|
26.68
|
20.73 ± 2.45
|
T2
|
14.8
|
26.8
|
20.79 ± 2.53
|
Ladas Super Formula
|
14.76
|
26.86
|
20.81 ± 2.50
|
D, diopter; IOL, intraocular lens; SRK/T, Sanders-Retzlaff-Kraff/theoretical; SD, standard deviation
Table 3. Prediction Errors of each formula for all patients (N= 113)
Formula
|
SRK/T
|
Holladay 2
|
Hoffer Q
|
Haigis
|
Kane
|
Barrett Universal II
|
T2
|
Ladas Super Formula
|
Mean Prediction Error (D)± SD
|
-0.19± 0.33
|
-0.35± 0.38
|
-0.27± 0.40
|
-0.30± 0.39
|
-0.20± 0.35
|
-0.16± 0.37
|
-0.19± 0.35
|
-0.24± 0.35
|
Mean Absolute Error (D)± SD
|
0.30± 0.23
|
0.41± 0.30
|
0.40± 0.27
|
0.40± 0.29
|
0.32± 0.25
|
0.31± 0.26
|
0.33± 0.24
|
0.34± 0.25
|
Median Absolute
Error (D)
|
0.25
|
0.37
|
0.39
|
0.35
|
0.27
|
0.27
|
0.29
|
0.29
|
Prediction error
(% of eyes)
|
|
|
|
|
|
|
|
|
±0.25 D
|
50.4
|
34.5
|
33.6
|
35.4
|
46.0
|
49.6
|
45.1
|
44.2
|
±0.50 D
|
83.2
|
64.6
|
68.1
|
68.1
|
82.3
|
79.6
|
81.4
|
77.0
|
±0.75 D
|
93.8
|
87.6
|
88.5
|
86.7
|
93.9
|
93.8
|
94.2
|
92.9
|
±1.00 D
|
100
|
93.8
|
98.2
|
98.2
|
98.2
|
98.2
|
99.1
|
98.2
|
D, diopter; SRK/T, Sanders-Retzlaff-Kraff/theoretical; SD, standard deviation
Table 4. Binary comparison of AE values of formulas for all patients (N=113)
|
SRK/T
|
Holladay 2
|
Hoffer Q
|
Haigis
|
Kane
|
Barrett Universal II
|
T2
|
Ladas Super Formula
|
SRK/T
|
|
0.000*
|
<0.001*
|
<0.001*
|
0.440
|
0.882
|
0.063
|
0.019*
|
Holladay 2
|
<0.001*
|
|
0.754
|
0.841
|
<0.001*
|
<0.001*
|
<0.001*
|
<0.001*
|
Hoffer Q
|
<0.001*
|
0.754
|
|
0.952
|
<0.001*
|
<0.001*
|
<0.001*
|
<0.001*
|
Haigis
|
<0.001*
|
0.841
|
0.952
|
|
<0.001*
|
<0.001*
|
<0.001*
|
0.001*
|
Kane
|
0.440
|
<0.001*
|
0.001*
|
<0.001*
|
|
0.048*
|
0.633
|
0.240
|
Barrett Universal II
|
0.882
|
<0.001*
|
<0.001*
|
<0.001*
|
0.048*
|
|
0.289
|
0.003*
|
T2
|
0.063
|
<0.001*
|
<0.001*
|
<0.001*
|
0.633
|
0.289
|
|
0.518
|
Ladas Super Formula
|
0.019*
|
<0.001*
|
<0.001*
|
0.001*
|
0.240
|
0.003*
|
0.518
|
|
SRK/T, Sanders-Retzlaff-Kraff/theoretical.
Examining the percentages of eyes within ±0.50D prediction error (Figure 1) the values are between 64.6% and 83.2%. SRK/T obtained the highest percentage of ±0.50 D (83.2%), followed by Kane (82.3%) and T2 (81.4%) while Holladay 2 reported the lowest percentage (64.6%), followed by Hoffer and Haigis (68.1%). SRK/T was also the formula that achieved the largest percentage of eyes within ±0.25D (50.4%) and ±1.00D (100%). From the new generation formulae, Barret Universal II yielded the largest percentage of eyes within ±0.25D (49.6%), while T2 obtained the largest percentage of eyes within ±1.00D (99.1%). Subgroup analysis could not be performed due to the low number of short/long eyes and low/high IOL power. There were no significant correlations between each formula's recommended IOL power for emmetropia, postoperative 1st-month SE, and age.
Descriptive characteristics within the 3 ACD groups were presented in Table 5. There was a significant difference between the 2 groups (shallow and normal eyes) for LT (p=0.001, p=0.033). The greatest mean LT was observed in shallow eyes (4.69 mm) while the lowest mean LT was noticed in deep eyes (4.14 mm). Even if the axial length was between 22 and 25 mm, the groups with the highest mean AL, listed in order, were: deep eyes (23.95 mm), normal eyes (23.62 mm), and shallow eyes (23.21 mm). Refractive prediction errors, MAE, MedAE, and the percentages of eyes within ±0.25D, ±0.50D, ±0.75D, and ±1.00D for each ACD subgroup were included in Table 6. The lowest MAE and MedAE were noted in Barret Universal II (0.26D, and 0.20D, respectively) for shallow eyes, and SRK/T for normal eyes (0.30D, and 0.21D, respectively), and deep eyes (0.29D, and 0.22D, respectively) while the highest MAE and MedAE were observed in traditional formulae for all the ACD subgroups. Cumulative percentages of AE groups of each three ACD subgroups are also shown in Figure 2, Figure 3 and Figure 4. The percentage of eyes within ±0.50D was higher for the Ladas Super Formula for shallow eyes (87.1%), SRK/T and T2 Formula for normal eyes (83.7%), SRK/T and Ladas Super Formula for deep eyes (85%). There was a statistically significant difference between formulas just in the first group represented by shallow eyes (p<0.05). A positive correlation between the prediction error and ACD was found for the following formulae: SRK/T (p=0.31), Hoffer Q (p=0.001), and T2 (p=0.014).
Table 5. Descriptive Data within the ACD Subgroups
|
ACD (mm)
|
Lens Thickness (mm)
|
AL (mm)
|
Group 1: ACD ≤3 mm (N= 31)
|
|
|
|
Mean ± SD
|
2.81± 0.19
|
4.69± 0.35
|
23.21± 0.67
|
Range
|
2.16- 3.00
|
4.00- 5.38
|
22.16- 24.34
|
Group 2: ACD 3.01- 3.49 mm (N= 49)
|
|
|
|
Mean ± SD
|
3.24±0.15
|
4.39± 0.37
|
23.62± 0.66
|
Range
|
3.02- 3.49
|
3.64- 4.91
|
22.03- 24.99
|
Group 3: ACD ≥3.5 mm (N= 20)
|
|
|
|
Mean ± SD
|
3.70± 0.18
|
4.14± 0.29
|
23.95± 0.63
|
Range
|
23.01- 24.98
|
3.58– 4.79
|
23.01- 24.98
|
Table 6. Prediction Errors of each formula for ACD groups
Formula
|
SRK/T
|
Holladay 2
|
Hoffer Q
|
Haigis
|
Kane
|
Barrett Universal II
|
T2
|
Ladas Super Formula
|
Group 1
(ACD of ≤3 mm, N= 31)
|
|
|
|
|
|
|
|
|
Mean Prediction Error (D)± SD
|
-0.31± 0.27
|
-0.48± 0.33
|
-0.51± 0.25
|
-0.41± 0.29
|
-0.23± 0.26
|
-0.20± 0.33
|
-0.32± 0.25
|
-0.27± 0.24
|
Mean Absolute Error (D)± SD
|
0.35± 0.21
|
0.51± 0.28
|
0.51± 0.25
|
0.43± 0.26
|
0.27± 0.21
|
0.26± 0.28
|
0.34± 0.21
|
0.30± 0.20
|
Median Absolute
Error (D)
|
0.30
|
0.48
|
0.51
|
0.43
|
0.24
|
0.20
|
0.28
|
0.27
|
Prediction error
(% of eyes)
|
|
|
|
|
|
|
|
|
±0.25 D
|
45.2
|
19.4
|
12.9
|
29.0
|
54.8
|
64.5
|
41.9
|
45.2
|
±0.50 D
|
80.6
|
51.6
|
48.4
|
71.0
|
83.9
|
83.9
|
80.6
|
87.1
|
±0.75 D
|
93.5
|
80.6
|
83.9
|
83.9
|
96.8
|
96.8
|
96.8
|
96.8
|
±1.00 D
|
100
|
93.5
|
100
|
100
|
100
|
96.8
|
100
|
100
|
Group 2
(ACD 3.01- 3.49 mm, N= 49)
|
|
|
|
|
|
|
|
|
Mean Prediction Error (D)± SD
|
-0.17± 0.35
|
-0.32± 0.37
|
-0.22± 0.37
|
-0.26± 0.38
|
-0.17± 0.39
|
-0.14± 0.40
|
-0.18± 0.37
|
-0.34± 0.37
|
Mean Absolute Error (D)± SD
|
0.30± 0.25
|
0.37± 0.32
|
0.34± 0.26
|
0.36± 0.30
|
0.34± 0.26
|
0.34± 0.26
|
0.31± 0.26
|
0.34± 0.26
|
Median Absolute
Error (D)
|
0.21
|
0.29
|
0.29
|
0.28
|
0.26
|
0.28
|
0.26
|
0.29
|
Prediction error
(% of eyes)
|
|
|
|
|
|
|
|
|
±0.25 D
|
51
|
42.9
|
46.9
|
44.9
|
49
|
46.9
|
49
|
46.9
|
±0.50 D
|
83.7
|
69.4
|
73.5
|
69.4
|
79.6
|
79.6
|
83.7
|
73.5
|
±0.75 D
|
91.8
|
89.8
|
91.8
|
85.7
|
89.8
|
89.8
|
91.8
|
91.8
|
±1.00 D
|
100
|
93.9
|
98
|
98
|
98
|
98
|
98
|
98
|
Group 3
(ACD of ≥3.5 mm, N= 20)
|
|
|
|
|
|
|
|
|
Mean Prediction Error (D)± SD
|
-0.16± 0.35
|
-0.36± 0.39
|
-0.18± 0.47
|
-0.35± 0.48
|
-0.29± 0.42
|
-0.23± 0.35
|
-0.10± 0.36
|
-0.34± 0.40
|
Mean Absolute Error (D)± SD
|
0.29± 0.24
|
0.43± 0.30
|
0.41± 0.28
|
0.48± 0.34
|
0.40± 0.30
|
0.35± 0.23
|
0.31± 0.20
|
0.44± 0.28
|
Median Absolute
Error (D)
|
0.22
|
0.39
|
0.41
|
0.38
|
0.41
|
0.36
|
0.31
|
0.40
|
Prediction error
(% of eyes)
|
|
|
|
|
|
|
|
|
±0.25 D
|
55
|
35
|
25
|
25
|
30
|
40
|
45
|
35
|
±0.50 D
|
85
|
60
|
80
|
60
|
75
|
70
|
80
|
85
|
±0.75 D
|
95
|
90
|
90
|
90
|
90
|
95
|
100
|
95
|
±1.00 D
|
100
|
100
|
95
|
95
|
95
|
100
|
100
|
100
|
D, diopter; SRK/T, Sanders-Retzlaff-Kraff/theoretical; SD, standard deviation