Combined surgery, that is, silicone oil removal (SOR) or pars plana vitrectomy (PPV) with concomitant cataract surgery, has become a common practice for treating vitreoretinal disorders. Given that nuclear sclerotic cataract is a frequent complication that occurs after PPV,1,2 especially with silicone oil (SO) tamponade,3 and that the surgical risk of phacoemulsification is greater in vitrectomized eyes,2,4 a combined operation may be considered even when the cataract is not severe.5 In addition, recent developments in surgical technology have led to the widespread recognition of combined surgery as a reliable and effective option for treating vitreoretinal diseases.6,7 However, it is difficult to obtain the expected refractive outcomes in these patients. A variable degree of myopic shift after combined surgery has been reported in a few studies,8,9 which brings up concerns over the choice of combined surgery for both patients and surgeons. Furthermore, the type of vitreoretinal disease has also been reported to be closely associated with refractive outcomes.8,10,11
Another important factor affecting refractive outcomes after combined surgery is the intraocular lens (IOL) formula selection. In recent years, several new formulae have emerged that use new methodologies and additional preoperative eye parameters to calculate IOL power.12 Comparisons of formula performance have been intensively investigated and confirmed in regular cataract surgery.13–15 However, evidence on the performance of these new formulae in combined surgery is sparse.16–18 Meanwhile, most previous studies evaluated only one or two conventional formulas, used limited sample sizes, and enrolled one or two types of vitreoretinal pathology.16–18 The performance of new formulas and the Wang–Koch (WK) adjustment methods in this population remains elusive.
In this study, we compared the efficacy of novel (Barrett Universal II [BUII], Emmetropia Verifying Optical [EVO], and Kane) and conventional formulae (Haigis, Hoffer Q, Holladay 1, and SRK/T) using WK adjustment in patients who underwent SOR or PPV with concomitant cataract surgery. In addition, the effectiveness of these formulae in treating various vitreoretinal pathologies was also assessed.
This is a single-center retrospective case-series study conducted in accordance with the Declaration of Helsinki. This study was approved by the ethical committee of the First Hospital, affiliated with the Army Medical University (Southwest Hospital), Chongqing, China (Batch number: [B] KY2021149). Owing to the nature of the study, the requirement for informed consent was waived.
Patients who underwent uneventful PPV or SOR combined with cataract surgery for vitreoretinal diseases at our institute between July 2015 and April 2021 were screened for eligibility. Only patients with monofocal IOLs were enrolled in this study. The exclusion criteria were as follows: 1) lens displacement, ocular trauma, keratopathy, glaucoma, or uveitis; 2) second SO tamponade due to the return of initial vitreoretinal pathology; 3) operative record of scleral buckling; 4) operative record of corneal refractive surgery; 5) significant opacification of the posterior capsule affecting refraction; 6) age younger than 20 years; and 7) poor medical record or follow-up duration less than three months. This study only enrolled the right eye if a patient had both eyes that matched the criteria, according to Hoffer et al.19 Finally, 301 eyes from 301 patients who underwent PPV or SOR with concomitant cataract surgery were enrolled.
Based on the preoperative diagnosis, eligible patients were separated into four categories. Group 1: Patients diagnosed with SO-filled eyes after PPV who underwent SOR with concomitant cataract surgery. Group 2: Patients diagnosed with epiretinal membrane (ERM). Group 3: Patients diagnosed with macular hole (MH). Group 4: Patients diagnosed with primary retinal detachment (RD).
Two surgeons (X.L. and Y.L.), fully experienced in vitreoretinal and cataract surgeries, performed all surgeries under local anesthesia. In all cases, microincision phacoemulsification plus IOL implantation was performed first, in the same setting as single cataract surgery. In Group 1, a 23-gauge SOR was subsequently performed. In Groups 2, 3, and 4, a 25-gauge PPV was performed after cataract surgery. Specifically, the internal limiting membrane was peeled using the Eckardt forceps and a special dye (brilliant blue) in Groups 2 and 3. Sterilized air, SO (5,000 cSt), or perfluoropropane (C3F8) was used to fill the vitreous cavity at the end of the surgery.
The following information was obtained from the patient's medical files: age, sex, preoperative diagnosis, use of SO, sterilized air, or C3F8 tamponade, ocular biometric measurements before surgery (axial length [AL], corneal power, keratometry [K] value, and anterior chamber depth) gathered using the IOLMaster 500 (Carl Zeiss, Oberkochen, Germany), best-corrected visual acuity, and power of the IOL implanted. Postoperative subjective refraction was evaluated by an ophthalmologist for at least three months after the combined surgery.
Formula Calculation and Outcome Measurements
Intraocular lens power was computed using SRK/T, Holladay 1, Haigis, and Hoffer Q integrated inside the IOLMaster 500. BUIIA, KaneB, and EVOC were computed using publicly accessible web sites. All formulas were evaluated in a genuine clinical setting using the User Group for Laser Interference Biometry (ULIB)D constants. Supplemental Digital Content 1 (see Table S1, https://links.lww.com/IAE/B989) summarizes the IOL constants used for all IOLs and formulas. All patients had their BUII, Kane, EVO, Haigis, Hoffer Q, Holladay 1, and SRK/T computed, and only patients whose AL was > 26 mm were assessed using the conventional formulae with the initial (WK1) and secondary (WK2) linear versions of the WK adjustment.
The following procedure was performed to determine the precision of the formula: First, the discrepancy between the postoperative spherical equivalent and expected preoperative spherical equivalent based on a formula for the implanted IOL was the refractive prediction error (PE). We then optimized the lens constant to eliminate the mean PE by changing each eye's PE by the same amount as the average PE, according to Wang et al.20 The arithmetic average of all PEs was used to calculate the mean prediction error (ME). Thereafter, both the middle value of the absolute errors, referred to as the median absolute error (MedAE), and the average value of the absolute errors, referred to as the mean absolute error (MAE), were computed. In addition, the fraction of cases within a certain interval (±0.25 diopters [D], ±0.50 D, ±0.75 D, and ±1.00 D) of PE was also evaluated. To further assess the efficacy of these formulae, we used the IOL Formula Performance Index (FPI), a new ranking method for formula accuracy, suggested by Wolfgang Haigis (personal communication, 2015) and optimized by Hoffer et al.21 The FPI was computed as follows:
It depends on the following four variables: 1) PE SD; 2) MedAEs; 3) the absolute value of the AL bias, which is the correlation slope (m) between PE and AL, is used to counteract the possibility of erroneous decreases in error owing to the negative sign of the slope; 4) the coefficient of proportion, which is the reciprocal of the fraction of cases having a PE within ±0.50 D, is shown by n10−1, and the number is increased by 10. The better the formula, the higher the FPI value.
All statistical analyses were performed using IBM SPSS Statistics for Windows (version 26.0, IBM Corp, Armonk, New York) in accordance with the published protocol.20,21 For all computations and statistical analyses, the visual acuity of each patient was transformed to the logarithm of the minimum angle of resolution value. The Shapiro–Wilk and Kolmogorov–Smirnov tests were used to examine the data distribution. The demographic and clinical traits of various patient groups were compared using the Kruskal–Wallis and chi-square tests for continuous and categorical data sets, respectively. Owing to the abnormal distribution of the data in this research, we used the Wilcoxon signed-rank test to evaluate whether the ME was statistically distinct from 0. To compare the absolute PE of various formulae, the Kruskal–Wallis and Friedman tests were applied for unpaired and paired data sets, respectively. The proportion of cases within a certain PE interval for various formulae was compared using Cochran's Q test. The P values were adjusted using Bonferroni's post hoc correction for multiple comparisons. Statistical significance was set at P < 0.05.
Our study enrolled 301 eyes from 301 patients who underwent uneventful PPV or SOR combined with cataract surgery. Among them, 155 patients were diagnosed with SO-filled eyes after PPV (Group 1), 83 with ERM (Group 2), 41 with MH (Group 3), and 22 with RD (Group 4) before combined surgery. The mean age and AL of the patients were 58.27 ± 9.49 years (20–85 years) and 25.52 ± 2.94 mm (21.69–34.92 mm), respectively. The IOLs used in the cohort were Lenstec Softec HD (n = 133), Lenstec Softec 1 (n = 123), Alcon AcrySof SN60WF (n = 21), Zeiss CT ASPHINA 509M (n = 14), and Zeiss CT ASPHINA 603P IOL (n = 10). During the combined surgery, 27 patients underwent SO tamponade, 244 underwent sterilized air tamponade, and 30 underwent C3F8 tamponade. Comparing demographic and clinical characteristics among different diagnostic groups, we found no significant difference in sex, keratometry 1, keratometry 2, or anterior chamber depth (P = 0.186, P = 0.068, P = 0.154, or P = 0.206, respectively), but there were significant differences in age, axial length, and preoperative best-corrected visual acuity (all P < 0.01). Patient demographic characteristics are presented in Table 1.
Table 1. -
Demographic and Clinical Characteristics of Patients
||58.27 ± 9.49
||53.44 ± 8.63
||64.69 ± 7.50
||61.22 ± 8.23
||61.55 ± 7.90
|Female, n (%)
|Preoperative Snellen BCVA
|Postoperative Snellen BCVA
|Preoperative logMAR BCVA
||0.87 ± 0.53
||0.98 ± 0.55
||0.59 ± 0.40
||0.91 ± 0.42
||1.03 ± 0.69
|Postoperative logMAR BCVA
||0.48 ± 0.37
||0.56 ± 0.39
||0.29 ± 0.28
||0.60 ± 0.35
||0.48 ± 0.38
||25.52 ± 2.94
||25.80 ± 2.93
||25.03 ± 3.01
||26.40 ± 3.13
||23.99 ± 1.56
||43.66 ± 1.39
||43.44 ± 1.47
||43.82 ± 1.45
||44.04 ± 1.33
||43.60 ± 1.68
||44.71 ± 1.51
||44.51 ± 1.67
||44.78 ± 1.45
||45.16 ± 1.52
||44.57 ± 1.70
||3.29 ± 0.38
||3.31 ± 0.35
||3.21 ± 0.42
||3.35 ± 0.38
||3.32 ± 0.39
|IOL power, D
||14.98 ± 7.35
||14.40 ± 7.26
||16.37 ± 7.04
||12.07 ± 8.18
||19.01 ± 4.10
‡Statistically significant (P < 0.05).
ACD, anterior chamber depth; K1, keratometry 1; K2, keratometry 2.
Prediction Outcomes in Total
The new formulas (BUII, EVO, and Kane) displayed significantly lower MAE (0.65 D), MedAE (0.39–0.41 D), and a greater proportion of PE within ±0.25 D (31.56%–33.55%), ±0.50 D (57.81%–59.14%), ±0.75 D (74.42%–76.08%), and ±1.00 D (82.72%–84.72%) than traditional formulas (Table 2, Figure 1A, and see Figure S1A, Supplemental Digital Content 8, https://links.lww.com/IAE/B996). No statistically significant difference was found in MedAE among BUII, Kane, EVO, and Haigis (P > 0.05). Barrett Universal II exhibited the minimum MedAE (0.39 D) and the supreme proportion of patients having a PE within ±0.25 D (33.55%) and ±0.50 D (59.14%); the MedAE of BUII was significantly lower than those of Holladay 1 (0.59 D, P < 0.01), Hoffer Q (0.57 D, P < 0.01), and SRK/T (0.51 D, P = 0.004). These results indicated that the new formulas displayed greater accuracy than the conventional formulas, and BUII showed the best performance.
Table 2. -
Prediction Outcomes of Various Intraocular Lens Formulas in Total (N = 301)
||±0.25 D (%)
||±0.50 D (%)
||±0.75 D (%)
||±1.00 D (%)
±0.25 D (%), ±0.50 D (%), ±0.75 D (%), ±1.00 D (%) = percentage of eyes within ±0.25 D, ±0.50 D, ±0.75 D, or ±1.00 D of prediction error. Formulas are ranked by FPI value.
Prediction Outcomes in Different Axial Lengths
Previous studies have shown that AL is highly correlated with refractive outcomes after combined surgery. Therefore, we performed a subgroup analysis to evaluate the performance of each formula in patients with different ALs. When eyes were categorized as normal (21.00–26.00 mm, n = 194) and long AL (>26.00 mm, n = 107), the ME and MedAE of each formula are summarized in Table 3. With a normal AL, all conventional formulas showed a significant myopic shift (all P < 0.05). We found a substantial difference in MedAE across the seven formulas (P < 0.01), and BUII and EVO showed substantially lower MedAE compared with Holladay 1 and Hoffer Q (all P < 0.05; Table 3). With a long AL, all conventional formulas exhibited a significant hyperopic shift (0.35–0.58 D, all P < 0.05). Compared with SRK/T, Holladay 1, and Hoffer Q, the new formulas (BUII, EVO, and Kane) showed substantially lower MedAE (all P < 0.01).
Table 3. -
Mean Error/Median Absolute Error for Each Formula in Different Axial Length, Vitreoretinal Pathology, and Tamponade Subgroups
| Normal (21–26 mm, n = 194)
| Long (>26 mm, n = 107)
| SO-filled eyes (n = 155)
| Epiretinal membrane (n = 83)
| Macular hole (n = 41)
| Primary retinal detachment (n = 22)
| SO (n = 27)
| Sterilized air (n = 244)
| C3F8 (n = 30)
*Comparison between mean error and zero.
†Statistically significant (P < 0.05).
In addition, we applied the WK adjustment method to evaluate whether the postoperative hyperopia of traditional formulas in patients with long AL could be corrected. As a result, we found that WK adjustment could correct postoperative hyperopia in long eyes and that the WK2 adjustment formulas were less aggressive in producing a myopic outcome than the WK1 adjustment formulas (Table 4, Figure 2). Furthermore, the WK2 adjustment significantly reduced the MedAE of SRK/T and Holladay 1 (P = 0.019 and P < 0.001) and exhibited a substantially superior proportion of patients with PE within a certain interval (Figure 1B, see Figure S1B, Supplemental Digital Content 8, https://links.lww.com/IAE/B996). In addition, we found no statistically significant difference between BUII, EVO, Kane, Holladay 1 formula with WK2 adjustment, and SRK/T formula with WK2 adjustment in prediction accuracy (all P > 0.05), indicating that Holladay 1 and SRK/T formulae with WK2 adjustment performed on par with the new formulae in long eyes.
Table 4. -
Prediction Outcomes of Various Intraocular Lens Formulas in Patients With Axial Length > 26 mm (N = 107)
||±0.25 D (%)
||±0.50 D (%)
||±0.75 D (%)
||±1.00 D (%)
±0.25 D (%), ±0.50 D (%), ±0.75 D (%), ±1.00 D (%) = percentage of eyes within ±0.25 D, ±0.50 D, ±0.75 D, or ±1.00 D of prediction error.
Formulas are ranked by FPI value.
*Comparison between ME and zero.
†Statistically significant (P < 0.05).
WK1, first linear version of Wang–Koch axial length adjustment; WK2, second linear Wang–Koch axial length adjustments.
These results showed that the novel formulae exhibited favorable performance in eyes with both normal and long AL, and the WK2 adjustment could correct postoperative hyperopia and improve the performance of traditional formulae in patients with long AL.
Prediction Outcomes in Different Vitreoretinal Pathologies
Considering the potential impact of vitreoretinal pathology on refractive outcomes, subgroup analysis was conducted according to the vitreoretinal pathology type. In patients with SO-filled eyes (Group 1), the new formulae showed substantially lower MedAE than Holladay 1, SRK/T, and Hoffer Q (all P < 0.05) (Table 3, see Table S2, Supplemental Digital Content 2, https://links.lww.com/IAE/B990). Among them, Kane exhibited the smallest MAE (0.62 D), MedAE (0.45 D), and the supreme proportion of patients having a PE within ±0.50 D (55.48%) and ±1.00 D (85.81%) (Figure 3A, see Figure S2A, Supplemental Digital Content 9, https://links.lww.com/IAE/B997). In patients with ERM (Group 2), no substantial difference in prediction accuracy was found between the seven formulae (P = 0.054) (see Table S3, Supplemental Digital Content 3, https://links.lww.com/IAE/B991). Among them, BUII had the minimum MAE (0.49 D) and the supreme proportion of patients having a PE within ±0.25 D (45.78%), ±0.50 D (69.88%), and ±0.75 D (83.13%) (Figure 3B, see Figure S2B, Supplemental Digital Content 9, https://links.lww.com/IAE/B997). In patients with MH (Group 3), the new formulas showed significantly lower MedAE compared with Holladay 1 and Hoffer Q (all P < 0.05) (see Table S4, Supplemental Digital Content 4, https://links.lww.com/IAE/B992). Among them, BUII showed a comparatively lower MedAE (0.32 D) and the greatest proportion of patients within ±0.50 D (75.61%) of PE (Figure 3C, see Figure S2C, Supplemental Digital Content 9, https://links.lww.com/IAE/B997). In patients with RD (Group 4), none of the seven formulas showed a statistically significant improvement in prediction accuracy (P = 0.075) (Figure 3D, see Table S5, Supplemental Digital Contents 5, https://links.lww.com/IAE/B993 and see Figure S2D, Supplemental Digital Content 9, https://links.lww.com/IAE/B997).
When the prediction accuracy of each formula was compared between the different types of vitreoretinal pathology, the RD group exhibited the worst prediction accuracy for all formulas (all P < 0.01) (Figure 4A). These results indicated that the new formulas displayed favorable accuracy in the SO-filled eyes, ERM, and MH groups; however, in the RD group, the new formulas did not significantly improve the prediction outcomes.
Prediction Outcomes in Different Intraocular Tamponades
Previous studies have also reported that intraocular tamponade is highly correlated with refractive outcomes after combined surgery. Therefore, we performed a subgroup analysis according to intraocular tamponade during combined surgery. The ME and MedAE of each formula in different tamponade subgroups are summarized in Table 3. With SO tamponade, all formulas showed a slight hyperopic shift (0.16–0.22 D, all P > 0.05). When the prediction accuracy of each formula was compared between the different types of intraocular tamponade, the SO tamponade subgroup exhibited the greatest MedAE for all seven formulas (all P < 0.01, Fig. 4B). These results indicated that different intraocular tamponades filled during combined surgery also affected refractive outcomes.
The primary challenge of combined surgery is the occurrence of highly variable refractive errors, leading to unsatisfactory surgical outcomes.8,9,22 Some studies have reported less favorable refractive outcomes after combined surgery.23,24 Therefore, our study aimed to assess the efficacy of new and conventional formulae with WK adjustment in patients who underwent SOR or PPV with concomitant cataract surgery and evaluate the performance of these formulae in different types of vitreoretinal pathology.
Several studies have shown that vitreoretinal pathology is an important factor affecting refractive outcomes after combined surgery.8,10,11 In this study, we compared the prediction accuracy of these formulae for different types of vitreoretinal pathology. We found that the RD group exhibited the worst refractive outcomes of all formulas, and even the new formulas failed to improve the prediction accuracy. Similar results have been reported in several studies that investigated patients with RD who underwent phacovitrectomy. The underestimation of AL measurements and the effect of intraocular tamponade on IOL position were important reasons for unsatisfactory refractive outcomes in patients with RD after combined surgery. Axial length underestimation could be caused by several factors, including inadequate fixation with visual axis deviation, the subretinal fluid's effect on the reflectivity of the retinal pigment epithelium, and disruption caused by the detached retina.25,26 Some studies showed that postoperative refractive outcomes were not significantly improved, and the fraction of patients having a PE within ±1.00 D was only 75.8%, although the longer AL measurement value was selected for IOL power calculation in bilateral AL measurement preoperatively.24,26 These results indicate that, in addition to AL underestimation, there are other important factors affecting refractive outcomes after combined surgery in patients with RD. In addition, intraocular tamponade (gas or SO) filled during the combined surgery was an important factor in unsatisfactory refractive outcomes in patients with RD.27,28 Nobuhiko et al27 investigated the effect of gas tamponade on the IOL position and refractive outcomes after phacovitrectomy. They found that the “vitrectomy with gas tamponade” group showed a greater postoperative myopic shift compared with the “vitrectomy without gas tamponade” group, which may be due to the buoyancy and surface tension of the gas pushing the IOL and causing forward fixation of the IOL.
Patients with vitreoretinal pathology have a comparatively higher proportion of high myopia (roughly 35% in our research), which makes calculating IOL power more challenging.4 In recent decades, several methods for calculating IOL power for eyes with high myopia have been established.29–31 For highly myopic eyes undergoing regular cataract surgery, both new and conventional formulae with WK adjustment have demonstrated acceptable prediction accuracy. However, their efficiency in long eyes undergoing combined surgery has not been well-established.13,14,29,31 Efstathios et al16 were the first to assess the efficacy of new and conventional formulae in patients undergoing phacovitrectomy for ERM. They found no significant difference in prediction accuracy between the new and traditional formulas. Diogo et al17 observed similar results when assessing the efficacy of various formulae in patients who underwent combined PPV and cataract surgery for vitreomacular interface disorders.
However, only patients with normal AL (21.00–27.00 mm) were included in these two studies.16,17 In this study, we investigated the performance of new and conventional formulae with WK adjustment in cases with long eyes undergoing combined surgery. As a result, we found that WK adjustment could correct the hyperopic shift of conventional formulae. In addition, the WK2 adjustment considerably enhanced the efficacy of SRK/T and Holladay 1 and exhibited comparable performance with the new formulae.
However, our study has certain limitations. First, the number of patients with RD in the sample was modest, which limited the subanalysis of this group of patients. Second, we did not assess the three latest formulae (the radial basis function, Olsen, and Holladay 2). Third, the surgeries were conducted by two surgeons (X.L. and Y.L.), which may be a confounding factor affecting the results. Fourth, patients' demographic and clinical characteristics differed significantly among diagnostic groups in our study, which may have skewed the results. Fifth, in addition to the related diseases mentioned in the exclusion criteria of this study, other underlying ocular comorbidities may also be a potential bias. Sixth, the absence of a control group also reduces the credibility of the results. Finally, our study is a retrospective case-series study that reports the clinical characteristics and outcomes of some groups of patients. Further prospective comparative studies based on larger samples with a control group are necessary to corroborate the results of our study. Despite these limitations, our study represents a real-world scenario and is more applicable than single-surgeon studies.
In conclusion, our study revealed that new formulae performed better than conventional formulae in patients who underwent combined surgery, and the BUII formula offered the best overall performance. In long eyes, Holladay 1 and SRK/T with WK2 adjustment offered satisfactory accuracy on par with the new formulae. For patients with SO-filled eyes, ERM, and MH, the new formulas showed satisfactory prediction accuracy. However, patients with RD showed the least favorable refractive outcomes, and the new formulas failed to significantly improve the prediction accuracy. Therefore, when planning to perform combined PPV and cataract surgery for patients with RD, surgeons should exercise caution when determining the IOL power. For patients with RD with macular-off, a two-step strategy for PPV and cataract surgery may be a better option. In the future, we will focus on how to enhance refractive outcomes after combined surgery in this population.
Other Cited Materials
- A. BUII: Barrett Universal II Formula. Available at: http://calc.apacrs.org/barrett_universal2015/. Accessed August 10, 2022.
- B. Kane: Available at: https://www.iolformula.com/. Accessed August 10, 2022.
- C. EVO: Emmetropia Verifying Optical Formula. Available at: www.evoiolcalculator.com/calculator.aspxAccessed August 10, 2022.
- D. ULIB: User Group for Laser Interference Biometry. Available at: http://ocusoft.de/ulib/c1.html. Accessed August 10, 2022.
This work was supported by the National Science Foundation of China (81770972) and Natural Science Foundation of China (81970843).
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