Participants and Examination
This is a retrospective study involving five ophthalmic centers, including Guangzhou Aier Eye Hospital (GZ), Shenyang Aier Eye Hospital (SY), Chengdu Aier Eye Hospital (CD), Wuhan Aier Eye Hospital (WH), and Hankou Aier Eye Hospital (HK)5,16. Study participants were candidates of refractive surgery having preoperative assessment between 2017 and 2019. A total of 17538 eyes of 10448 subjects were included in the study. Inclusion criteria were eyes with good quality Scheimpflug scans. Exclusion criteria included coexisting corneal diseases, keratoconus, forme fruste keratoconus, severe dry eye, previous ocular trauma or surgery, uveitis, glaucoma, wearing contact lenses within the previous 2 weeks, age younger than 18 years (unstable refraction) or older than 40 years (unstable astigmatism)5,16. The study was approved by the Institutional Review Board (IRB) of GZ, IRB of SY, IRB of CD, IRB of WH and IRB of HK, and was in agreement with the Declaration of Helsinki. Since only review of medical records was conducted and no individual patient could be identified from the data, informed consent was waived by the IRBs5,16. The flowchart of this study was shown in Figure 1.
All the eyes underwent routine preoperative examination including best-corrected visual acuity (BCVA), intraocular pressure (IOP), cycloplegic and manifest refraction, anterior segment examination by slit-lamp, corneal topography and Pentacam examination. Anterior and posterior corneal radius within the central 3 mm area, and pachy apex (PA) were measured by Pentacam. Calculation of KA and PCA was previously described17,18. Procedures of Pentacam measurements, image quality control and data retrieving were described previously5,16,19. Other clinical data of the eyes were retrieved from the electronic medical record database.
RR models construction and validation
Data from GZ (4617 eyes of 2684 subjects) and SY (5871 eyes of 2684 subjects) were used for RR models construction and internal validation, and data from CD (3329 eyes of 2080 subjects), WH (2983 eyes of 1606 subjects) and HK (738 eyes of 387 subjects) were used for external validation.
There were four prediction tasks, including PCA magnitude in all eyes, PCA flat axis in all eyes, PCA magnitude in eyes with a PCA≥0.50D, and PCA flat axis in eyes with a PCA≥0.50D. Using pooled data of GZ and SY, one RR model was constructed for each prediction task. Data of PCA flat axis were found to follow skewed distribution, and they were processed to be normally distributed using piecewise function (if PCA flat axis <90°, the value was added with 180°). Firstly, homogenous test was performed for all the parameters including age (year), sex (male=1, female=2), eye laterality (right=1, left=2), anterior corneal radius (millimeter) on the steep (RS), flat (RF), vertical (RV) and horizontal (RH) axis, KA magnitude (KM, D), KA flat axis (KF, degree), and PA (micrometer). Significant collinearity was detected among RF, RS, RH and RV. Secondly, ridge regression was applied to address the collinearity. A series of increased penalty values were added to the RR (one penalty for one regression). Variables with a P≥0.05 were excluded from model equations. Ridge paths for the prediction of PCA magnitude and flat axis are shown in Figure 2. Thirdly, 10-fold cross validation was applied for each penalty. The penalty with the largest mean R2 and best generalization ability was selected to construct the model equation which was used for internal and external validations.
RR was also applied to the binary prediction of eyes with a PCA≥0.50D20. The predicted output of PCA magnitude was set to be 1 (≥0.50D) or 0 (<0.50D). The penalty was chosen based on the ridge path of the optimal RR model according to 10-fold cross-validation (Supplementary file 1). Accuracy of the binary classification of eyes with a PCA≥0.50D was evaluated by area under the receiver operating characteristic (ROC) curve (AUC).
Statistical analysis
Statistical analysis was performed using STATA sofware (version 15.0, stata, Inc.) Distribution of the demographics was evaluated by Kolmogorov-Smirnov test. Kruskal-Wallis test was used for comparison of demographics among the five ophthalmic centers. P<0.05 was considered to be statistically significant. The 95% limit of agreement (LoA) of Bland-Altman plots, mean absolute error (MAE) and root mean square error (RMSE) were used to evaluate the prediction accuracy of the RR models.