A validated nomogram based on age and biometric parameters provided an individualized, accurate tool for preoperative risk assessment of significant plate-haptic toric IOL rotation.
Abstract
Purpose:
To identify independent risk factors associated with significant postoperative rotation (≥10 degrees) of plate-haptic toric intraocular lenses (IOLs) and to develop and externally validate a predictive nomogram.
Setting:
2 independent eye centers in China.
Design:
Prospective observational study with a training cohort and an external validation cohort.
Methods:
805 eyes from 805 cataract patients with regular corneal astigmatism (≥0.75 diopter) who underwent phacoemulsification and plate-haptic toric IOL implantation between August 2021 and December 2024 were included. Patients from 1 center formed the training cohort, while patients from the second center served as the external validation cohort. Least absolute shrinkage and selection operator regression followed by multivariate logistic regression was used to identify predictors of significant toric IOL rotation (≥10 degrees at 2 weeks postoperatively). A predictive nomogram was developed and validated through receiver operating characteristic analysis, calibration curve, and decision curve analysis (DCA).
Results:
Age (odds ratio [OR] = 1.04, P = .002), anterior chamber depth (ACD) (OR = 7.71, P < .001), lens thickness (LT) (OR = 5.13, P < .001), and white-to-white (WTW) (OR = 2.36, P = .002) were identified as independent predictors. The nomogram demonstrated good discriminative performance with an area under the curve of 0.809 in the training cohort and 0.848 in the validation cohort. Calibration and DCA analyses confirmed the accuracy and clinical utility of the model.
Conclusions:
A validated nomogram based on age, ACD, LT, and WTW provides a useful tool for individualized preoperative risk assessment of significant toric IOL rotation, aiding surgical decision-making.
Corneal astigmatism (AST) of ≥1.5 diopters (D) is present in up to one-fifth of eyes undergoing cataract surgery, and toric intraocular lenses (IOLs) have therefore become the preferred option for simultaneously correcting cataract and preexisting corneal AST.1,2 Compared with other AST correction techniques, toric IOL implantation has become the preferred method in cataract surgery because of its predictable, safe, and effective refractive outcomes.3,4
Despite these advantages, the clinical success of toric IOLs hinges on postoperative rotational stability. A 1 degree misalignment negates roughly 3% of the intended astigmatic correction, and a rotation of ≥10 degrees can lead to visually disturbing residual AST that often necessitates secondary surgery.5
Numerous studies have investigated the factors that might influence toric IOL rotation, including ocular biometry, IOL design, and surgical technique.6–10 A larger white-to-white (WTW) distance has been reported to indicate higher rotation risk, and thicker lenses in older patients have been linked to a greater tendency for rotation in some cohorts.9 IOL-related factors have also been emphasized. Haptic design can alter friction and fixation within the capsular bag, and material properties that increase capsule adhesion have been associated with improved stability.6
Current precautions, such as removal of ophthalmic viscosurgical device (OVD) and strict early activity restrictions, can reduce—but do not eliminate—the risk of rotation.10,11 In our large-scale study based on a Chinese population, the incidence of rotation in plate-haptic toric IOLs was approximately 7%, with about 2% of patients requiring secondary surgical repositioning.12 The first 1 to 3 days postoperatively seemed to be a critical period for IOL rotation.8 Although patients were instructed to avoid strenuous activities and decrease frequent head movements to enhance stability, postoperative rotation could not be completely prevented. These findings underscore the urgent need for a reliable, patient-specific tool to identify individuals at high risk of substantial postoperative rotation associated with plate-haptic toric IOL-facilitating tailored preoperative counseling, intraoperative strategies, and postoperative management. Yet, no such predictive model is currently available.
This study aimed to identify independent preoperative predictors of clinically significant rotation (≥10 degrees) in plate-haptic toric IOLs and to develop and validate a predictive nomogram, which could help surgeons estimate the risk of postoperative rotation, optimize perioperative strategies, and ultimately enhance visual quality for patients undergoing toric IOL implantation.
METHODS
Study Participants
This prospective observational study enrolled patients with cataracts and preexisting regular corneal AST (≥0.75 D) who underwent phacoemulsification and implantation of a plate-haptic toric IOLs (AT TORBI 709M, Carl Zeiss Meditec AG) at the Eye and ENT Hospital of Fudan University and Shanghai Heping Eye Hospital between August 2021 and December 2024. Patients with the following conditions were excluded from the study: a history of corneal or intraocular surgery, a history of ocular trauma, intraoperative anterior capsular tear or posterior capsular rupture, poor pupillary dilation during or after surgery, severe intraocular infection after surgery, and evidence of zonular weakness or dialysis detected preoperatively or intraoperatively. Eligible patients who underwent surgery at Eye and ENT Hospital of Fudan University were included in the training cohort, whereas those who underwent surgery at Shanghai Heping Eye Hospital were included in the validation cohort (external validation). This study was conducted in accordance with the tenets of the Declaration of Helsinki and was approved by the Institutional Review Board. Written informed consent was obtained from the participants (NCT05797298). All data relevant to the study are included in the article.
Preoperative Examinations
All patients underwent a complete ophthalmic examination, including the measurement of uncorrected and corrected visual acuity, refraction examination, slitlamp examination, fundoscopy, B-scan ultrasonography, and corneal topography (Pentacam HR, Oculus Optikgeräte GmbH). IOLMaster 700 (Carl Zeiss Meditec AG) was used to measure the biometric parameters, such as axial length (AL), anterior chamber depth (ACD), lens thickness (LT), WTW, flat keratometry (K1), steep keratometry (K2), and corneal AST. The type of corneal AST was categorized as with-the-rule (WTR), against-the-rule (ATR), or oblique (OB) based on the steep meridian: WTR was defined as 60 to 120 degrees, ATR as 0 to 30 degrees or 150 to 180 degrees, and OB as all other meridians. The online calculator recommended by the manufacturer of the IOLs was used to calculate the spherical power, cylinder power, and target axis of the toric IOLs (https://zcalc.meditec.zeiss.com/).
Surgery
The surgery was performed by 2 experienced ophthalmologists using the Callisto Eye system (Carl Zeiss Meditec AG) under local anesthesia. The surgical incision was placed at 140 degrees. A 2.3 mm clear corneal incision was made, followed by continuous curvilinear capsulorhexis (CCC), hydrodissection, phacoemulsification, and capsular polishing. Using the navigation system, the capsulorhexis was precisely centered and sized 5.4 mm in diameter to ensure complete optic coverage. The toric IOL was implanted subsequently and aligned at the target position. The incisions were hydrated after thoroughly removing the OVD from behind the IOLs and verifying the toric IOL axis. The eyelid speculum was removed subsequently, and the IOL axis was reverified to ensure correct alignment. The surgical procedures performed by the 2 surgeons were identical in all operative steps.
All patients underwent day surgery. Postoperatively, patients were instructed to remain sedentary for the first hour and to avoid vigorous movements and eye rubbing for 1 month. Topical medications included 1% prednisolone acetate and 0.5% levofloxacin eyedrops, both administered 4 times daily for 2 weeks. In addition, 0.1% pranoprofen was prescribed 4 times daily for 4 weeks to control inflammation (additional postoperative instructions are provided in the Supplementary Material, available at http://links.lww.com/JRS/B573).
Postoperative Examination
Patients were followed up on postoperative day 1, day 3, week 1, week 2, and at 1 month. The 2-week timepoint was chosen for rotation assessment. Postoperative examinations included the measurement of uncorrected and corrected visual acuity, refraction examination, slitlamp microscopy, and the measurement of the intraocular pressure. Given the high degree of similarity between bilateral eyes in the same individual, this study included only the right eye for analysis.13 Postoperative IOL rotation was quantified using a previously described, validated photographic method.14 Rotation grading was performed independently by 2 masked observers. Intraoperative videos were recorded, and iris or scleral landmarks and the IOL axis at the end of surgery were identified from captured video frames. At each postoperative visit, high-resolution slitlamp digital retroillumination photographs were obtained. To mitigate the effects of head tilt, ocular cyclotorsion, and other alignment artifacts, each postoperative image was registered to the end-of-surgery baseline frame using iris or scleral landmarks. The rotation angle was defined as the difference between the IOL axis at the end of surgery and that at each postoperative visit. When the 2 observers differed by > 3 degrees in signed rotation, both observers repeated the assessment.
Model Construction
Least absolute shrinkage and selection operator (LASSO) regression was performed on variables derived from the training cohort.10 The penalty parameter (λ) was optimized through tenfold cross-validation. Features with nonzero coefficients were retained. Variables identified by LASSO were subsequently evaluated using stepwise multivariate logistic regression to determine the final set of independent predictors included in the model. A nomogram was constructed to visualize the model and facilitate clinical interpretation. The binary outcome variable was defined as whether significant toric IOL rotation occurred at 2 weeks postoperatively.
Model Validation
Model performance was assessed using receiver operating characteristic (ROC) curves, with the area under the curve (AUC) used to assess the model's discriminative ability. Calibration curve was assessed by plotting predicted probabilities against observed outcomes using calibration plots, providing a visual measure of model fit. Clinical utility was evaluated through decision curve analysis (DCA), which assessed the net clinical benefit across a range of threshold probabilities.
Statistical Analyses
All statistical analyses were performed using SPSS Statistics for Windows (v. 22.0, IBM Corp.) and R statistical software (v. 4.3.3). Normality was assessed using the Shapiro-Wilk test. Continuous variables are presented as the mean ± SD or median and interquartile range and were compared using the unpaired t test or Mann-Whitney U test. Categorical variables are expressed as n (%) and were compared using the chi-squared test. Two-sided P values of less than 0.05 were considered statistically significant.
RESULTS
Baseline Characteristics of the Study Population
The training and validation cohorts comprised 563 eyes of 563 patients and 242 eyes of 242 patients, respectively (Figure 1). Table 1 presents the baseline characteristics of the training and validation cohorts. All parameters were similar in both cohorts (P > .05). In the overall cohorts, the median absolute rotation was 4 degrees (2 to 8) in the training cohort and 5 degrees (2 to 8) in the validation cohort. Significant IOL rotation (≥10 degrees) occurred in 65 of 563 eyes (11.6%) in the training cohort and 30 of 242 eyes (12.4%) in the validation cohort. Among eyes with significant rotation, the median absolute rotation was 13.0 degrees (11.0 to 15.0) and 13.0 degrees (11.0 to 15.8), respectively, and when excluding nonrotated IOLs (absolute rotation = 0 degree), the absolute rotation was 5.0 degrees (3.0 to 9.0) and 5.0 degrees (2.0 to 9.0), respectively.
Figure 1.
Flowchart of training and validation cohorts.
Table 1.
Demographics and baseline characteristics
| Characteristic | P value | ||
| Training cohort (N = 563) | Validating cohort (N = 242) | ||
| Age (y) (Q1, Q3) | 67 (57, 75) | 67 (58, 74) | .802 |
| Sex, n (%) | |||
| Male | 348 (61.8) | 150 (62.0) | .963 |
| Female | 215 (38.2) | 92 (38.0) | |
| AL (Q1, Q3) | 25.56 (23.38, 27.75) | 25.26 (23.41, 27.40) | .540 |
| ACD (Q1, Q3) | 3.30 (2.96, 3.57) | 3.26 (2.90, 3.60) | .594 |
| LT (Q1, Q3) | 4.48 (4.24, 4.85) | 4.50 (4.20, 4.87) | .444 |
| WTW (Q1, Q3) | 11.80 (11.40, 12.18) | 11.83 (11.50, 12.10) | .714 |
| K1 (Q1, Q3) | 42.90 (41.98, 44.02) | 42.88 (41.89, 43.94) | .797 |
| K2 (Q1, Q3) | 44.58 (43.79, 45.66) | 44.54 (43.83, 45.69) | .869 |
| AST (Q1, Q3) | −1.60 (−2.11, −1.29) | −1.71 (−2.23, −1.32) | .163 |
| AST type, n (%) | |||
| ATR | 212 (37.7) | 96 (39.7) | .558 |
| OB | 41 (7.3) | 20 (8.3) | |
| WTR | 310 (55.1) | 126 (52.1) | |
| Absolute rotation (Q1, Q3) | 4 (2, 8) | 5 (2, 8) | .558 |
ACD = anterior chamber depth; AL = axial length; AST = astigmatism; CTR = capsular tension ring; LT = lens thickness; OB = oblique; WTW = white-to-white
Predicting Significant Toric IOL Rotation
A total of 11 preoperative variables were included in the LASSO regression analysis: sex, age, laterality, AL, ACD, LT, WTW, K1, K2, AST, and AST type (WTR, ATR, and OB). A total of 4 features were selected after applying LASSO regression with tenfold cross-validation, including age, ACD, LT, and WTW (Figure 2). These selected features were subsequently entered into a multivariate logistic regression model. All 4 variables were retained and used to construct the final prediction model: age (odds ratio [OR] = 1.04, P = .002), ACD (OR = 7.71, P < .001), LT (OR = 5.13, P < .001), and WTW (OR = 2.36, P = .002). The detailed regression results are summarized in Table 2, and the resulting nomogram is presented in Figure 3 (prediction equation: ln(P/[1 − P]) = 0.037 × age + 2.042 × ACD + 1.636 × LT + 0.858 × WTW − 28.407). For instance, a 70-year-old patient with an ACD of 3.50 mm, an LT of 5.00 mm, and a WTW of 11.8 mm, indicating that the risk of significant IOL rotation is approximately 41%.
Figure 2.
LASSO regression. A: Cross-validation plot, (B) coefficient path plot, and (C) coefficient plot of selected variables. LASSO = least absolute shrinkage and selection operator
Table 2.
Results of multivariate logistic regression based on LASSO
| Factors | OR | 95% CI | P value |
| Age | 1.04 | 1.01, 1.06 | .002 |
| ACD | 7.71 | 4.01, 15.46 | < .001 |
| LT | 5.13 | 2.83, 9.54 | < .001 |
| WTW | 2.36 | 1.36, 4.16 | .002 |
ACD = anterior chamber depth; CTR = capsular tension ring; LASSO = least absolute shrinkage and selection operator; LT = lens thickness; OR = odds ratio; WTW = white-to-white
Figure 3.
Nomogram for the significant plate-haptic toric IOL rotation. Risk indicates the predicted probability of significant postoperative IOL rotation as defined in the Methods. How to use (1) for each predictor (age, ACD, LT, and WTW), locate the patient's value on the corresponding axis and draw a vertical line upward to the “Points” scale to obtain the score. (2) Sum the scores to obtain “Total Points.” (3) Locate the total on the “Total Points” axis and draw a vertical line downward to the “Risk” axis to read the corresponding probability. The nomogram is intended for rapid, approximate estimation; for precise risk calculation, use the regression formula provided in the text. ACD = anterior chamber depth; LT = lens thickness; WTW = white-to-white
Validation of the Prediction Model
The AUCs of the model in different cohorts are illustrated in the following figures. ROC curve analysis demonstrated that the predictive model achieved an AUC of 0.809 (95% CI 0.759-0.860) in the training cohort, reflecting good discriminatory power for classifying significant IOL rotation (Figure 4, A). The model exhibited stable performance in the validation cohort, with an AUC of 0.848 (95% CI 0.785-0.911) (Figure 4, B).
Figure 4.
Validation of the nomogram. A: ROC curve of training cohort, (B) ROC curve of validation cohort, (C) calibration curve of training cohort, (D) calibration curve of validation cohort, (E) decision curve analysis of training cohort, and (F) decision curve analysis of validation cohort. AUC = area under the curve; ROC = receiver operating characteristic
The calibration performance of the nomogram was assessed in both the training and validation cohorts. In the training cohort, the calibration curve demonstrated good agreement between predicted and observed probabilities, with a C-index of 0.810 and a Brier score of 0.106, indicating satisfactory discrimination and overall accuracy. The calibration slope was 1.000, and the intercept was 0.000, suggesting that predicted risks were well-calibrated (Figure 4, C). In the validation cohort, the model maintained excellent discriminative power with a C-index of 0.848 and a Brier score of 0.103. The calibration slope was 1.209, and the intercept was 0.415, indicating a slight overestimation in predicted probabilities. The average calibration error (Eavg) was 0.042 in the training cohort and 0.022 in the test cohort. The Hosmer-Lemeshow test showed no significant lack of fit in the validation set (P = .815) (Figure 4, D). Overall, the nomogram exhibited good calibration and generalizability across both cohorts.
DCA further confirmed the clinical utility of the model (Figure 4, E and F). This research shows that the nomogram offers substantial net benefits for clinical application through its DCA curve.
DISCUSSION
The rotational stability of plate haptic toric IOLs is a critical determinant of postoperative visual outcomes.15 Although previous investigations have predominantly focused on identifying isolated risk factors or describing general rotational patterns of toric IOLs, they have not established predictive frameworks capable of quantifying individualized risk.7,16,17 In this prospective study, we investigated the associations between demographic, biometric, and operative variables and clinically significant toric IOL rotation using LASSO regression followed by multivariate logistic analysis. Age, ACD, LT, and WTW were identified as independent predictors of postoperative rotation. Based on these variables, we developed and externally validated a nomogram capable of reliably estimating the probability of significant toric IOL rotation. To the authors' knowledge, this is the first study to establish and validate a predictive model specifically for significant rotation after plate-haptic toric IOL implantation.
This study identified LT as a significant predictor of toric IOL rotation, consistent with previous findings in a cohort of 252 eyes, which also reported LT as a critical risk factor.10 This association is biologically plausible because increased LT may reflect a larger capsular bag, providing more intrabag space for IOL movement and reducing friction between the haptics and the capsule.18 Appropriately sized capsular bag provides sufficient support to the toric IOL and aids in its stabilization. Interestingly, Schartmüller et al. reported no such correlation, despite a similar mean LT in their European cohort.11 This discrepancy may reflect anatomical differences between ethnic groups because biometric parameters and capsular bag elasticity can vary across populations. It may also be attributed to the different proportions of high myopic patients between the 2 studies. This discrepancy underscores the importance of considering individual biometric characteristics when evaluating predictors of toric IOL rotation.
In addition to the above factors, WTW distance was also identified as an independent predictor of toric IOL rotation in our study. Previous studies have emphasized the role of capsular bag dimensions in predicting toric IOL rotation, although no tool allows direct measurement. It is clinically recommended to subtract 1 mm from the WTW when estimating capsular bag size.6 Our findings suggest that eyes with WTW >11.6 mm were at increased risk of rotation, likely due to a looser fit between the IOL and the capsular bag, which reduces rotational friction and stability.10 Similarly, Zhu et al. reported that plate-haptic toric IOLs exhibited greater rotational instability in eyes with larger WTW measurements and recommended considering additional stabilization strategies such as capsular tension rings in such cases.17 These results support the clinical utility of WTW as a practical and noninvasive predictor of postoperative rotational risk.
Moreover, some studies have shown that LT shows a positive correlation with age within a specific age range, which is consistent with our clinical observation that elderly patients may have thicker lenses.19 These findings may account for the positive correlation observed between age and significant IOL rotation in this study. Although LT and age are positively correlated within certain age ranges, both variables were independently retained in the multivariate model, indicating that each contributes unique predictive information regarding rotational instability. This suggests that age may influence rotation risk not only through anatomical changes such as increasing LT but also through other age-related factors such as capsule biomechanics or zonular laxity.
Although previous studies have primarily focused on AL as a key factor influencing postoperative rotation of toric IOLs, to our knowledge, this study is the first to report ACD as an independent predictor of significant rotation in plate-haptic toric IOLs. Although AL has traditionally served as a surrogate for capsular bag size, this association becomes unreliable in highly myopic eyes, where axial elongation primarily involves the posterior segment.20 By contrast, ACD more accurately reflects anterior segment anatomy and may better represent the biomechanical environment that influences IOL rotational stability.16,21
Given that most toric IOL rotation occurs in the early postoperative period, our study selected the 2-week postoperative timepoint to assess rotational stability.8 This interval captures most of the early rotational events and aligns with evidence suggesting that toric IOL rotation tends to stabilize around 2 weeks postoperatively. Moreover, previous studies support that the optimal timing for repositioning surgery is within 2 to 3 weeks after implantation.12
Although our study suggested that strict early activity restriction may help reduce IOL rotation, a recent randomized trial by Jandewerth et al. reported no difference in IOL rotation between patients walking or lying down in the first postoperative hour.22 The discrepancy likely arises from the use of nontoric C-loop IOLs in their study vs plate-haptic toric IOLs in ours, which differ in capsular bag interaction and rotational mechanics. In addition, their small sample size (38 eyes) limits the statistical power to detect subtle effects that may be more evident in large-scale datasets.
Recent evidence has highlighted the potential influence of capsulorhexis size on IOL stability, including toric IOL rotation.6,23 A protocol for a systematic review and individual participant data meta-analysis by Wang et al. emphasized that both excessively small and overly large capsulorhexis diameters may affect postoperative outcomes by altering anterior capsule behavior, increasing the risk of fibrotic contraction, or insufficient optic overlap.24 In our study, to minimize these risks, the CCC was standardized intraoperatively using a digital navigation system, ensuring a diameter sized 5.4mm. This range was selected to achieve complete optic coverage while preventing excessive anterior capsule shrinkage, thereby promoting rotational stability of the toric IOL.
The incidence of significant rotation (≥10 degrees) in this study was higher than the 7.61% previously reported.12 This may be attributed to earlier assessment (2 weeks), inclusion of high-myopia eyes, and the use of high-precision anterior segment optical coherence tomography measurements, which are more sensitive than slitlamp estimation and detect smaller but clinically relevant rotations.
This study has several limitations. First, although the sample size was relatively large and included an external validation cohort, the data were derived from 2 institutions within a single geographic region, which may limit the generalizability of the findings to broader populations or other ethnic groups. Second, the model was specifically developed for a single IOL design, and its applicability to other types remains to be determined. Further large-scale, multicenter studies with various types of toric IOLs must be conducted to identify additional potential risk factors for the incidence of significant IOL rotation.
In conclusion, leveraging a large, prospectively collected dataset from 2 independent eye centers, we established and externally validated the first nomogram specifically designed to predict significant rotation after plate-haptic toric IOL implantation in a Chinese population. By incorporating 4 easily accessible preoperative biometric parameters, the model offers an individualized, evidence-based risk estimation tool. This facilitates enhanced surgical planning, tailored patient counseling, and early postoperative intervention strategies. Given the growing demand for toric IOL implantation in refractive cataract surgery, this predictive tool represents a valuable advancement toward precision medicine and improved visual outcomes in routine clinical practice.
WHAT WAS KNOWN
The rotational stability of toric IOLs is crucial for successful visual outcomes, and a rotation of ≥10 degrees often requires secondary surgery.
Various factors, including ocular biometry, IOL design, and surgical technique, have been studied as potential influencers of toric IOL rotation.
No reliable, patient-specific predictive model was previously available to quantify the individualized risk of clinically significant postoperative rotation of plate-haptic toric IOLs.
WHAT THIS PAPER ADDS
To the authors' knowledge, this study is the first to establish and externally validate a predictive nomogram specifically for significant rotation after plate-haptic toric IOL implantation.
The nomogram is based on 4 easily accessible preoperative biometric parameters: age, anterior chamber depth, lens thickness, and white-to-white distance, with anterior chamber depth being a newly reported independent predictor in this context.
The validated nomogram provides surgeons with an individualized, evidence-based risk estimation tool that can facilitate tailored preoperative counseling, optimize perioperative strategies, and potentially reduce the need for secondary repositioning surgery.
Footnotes
This study was funded by the National Natural Science Foundation of China (grant 82171039).
X. Lin and Z. Hua contributed equally to this work.
Disclosures: None of the authors have any financial or proprietary interest in any material or method mentioned.
First author:
Xuanqiao Lin, MD
Department of Ophthalmology, Eye and ENT Hospital of Fudan University, Shanghai, China
Contributor Information
Xuanqiao Lin, Email: 1532483480@qq.com.
Zhixiang Hua, Email: 1036888182@qq.com.
Wenqian Shen, Email: shenwenqian2023@163.com.
Baoxian Zhuo, Email: baoxian1313@163.com.
Jiying Shen, Email: susu22yoyo@163.com.
Limei Zhang, Email: miaimejou@163.com.
Lifang Bai, Email: bai_lifang2021@163.com.
Lei Cai, Email: clyc0318@126.com.
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