Research on Establishing Corneal Edema after Phacoemulsification Prediction Model Based on Variable Selection with Copula Entropy

Abstract

Background: Corneal edema (CE) affects the outcome of phacoemulsification. Effective ways to predict the CE after phacoemulsification are needed.

Methods: On the basis of data from patients conforming to the protocol of the AGSPC trial, 17 variables were selected to predict CE after phacoemulsification by constructing a CE nomogram through multivariate logistic regression, which was improved via variable selection with copula entropy. The prediction models were evaluated using predictive accuracy, the area under the receiver operating characteristic curve (AUC), and decision curve analysis (DCA).

Results: Data from 178 patients were used to construct prediction models. After copula entropy variable selection, which shifted the variables used for prediction in the CE nomogram from diabetes, best corrected visual acuity (BCVA), lens thickness and cumulative dissipated energy (CDE) to CDE and BCVA in the Copula nomogram, there was no significant change in predictive accuracy (0.9039 vs. 0.9098). There was also no significant difference in AUCs between the CE nomogram and the Copula nomogram (0.9637, 95% CI 0.9329-0.9946 vs. 0.9512, 95% CI 0.9075-0.9949; p = 0.2221). DCA suggested that the Copula nomogram has clinical application.

Conclusions: This study obtained a nomogram with good performance to predict CE after phacoemulsification, and showed the improvement of copula entropy for nomogram models.

Keywords: copula entropy; corneal edema; nomogram; phacoemulsification; prediction model.

Figure 1

Copula entropies of 17 selected potential predictors. The red line represents the median of all copula entropies. ACD: anterior chamber depth; AL: axial length; BCVA: best corrected visual acuity; CCT: central corneal thickness; CDE: cumulative dissipated energy; Dia: diabetes; ECD: endothelial cell density; EFU: estimated fluid used; HBP: hypertension; LT: lens thickness; NH: nuclear hardness; Pre IOP: preoperative intraocular pressure; TAT: total aspiration time, U/S time: ultrasound time.

Figure 2

(A): Multivariate logistic regression model for predicting CE after phacoemulsification with the variables selected via copula entropy. (B) Copula nomogram in patients with CE after phacoemulsification. *: The p value is less than 0.05. BCVA: best corrected visual acuity; CDE: cumulative dissipated energy; EFU: estimated fluid used; LT: lens thickness; NH: nuclear hardness; TAT: total aspiration time, U/S time: ultrasound time.

Figure 3

The predictive accuracy and out-of-bag error rate of each random forest model generated after selecting variables on the basis of copula entropy. ACD: anterior chamber depth; AL: axial length; BCVA: best corrected visual acuity; CCT: central corneal thickness; CDE: cumulative dissipated energy; Dia: diabetes; ECD: endothelial cell density; EFU: estimated fluid used; HBP: hypertension; LT: lens thickness; NH: nuclear hardness; Pre IOP: preoperative intraocular pressure; TAT: total aspiration time, U/S time: ultrasound time.

Figure 4

The calibration curves for the CE and copula nomograms.

Figure 5

(A): ROC curves and AUCs for all prediction models. (B): DCA for all prediction models. ROC: receiver operating characteristic; AUC: area under ROC curve; DCA: decision curve analysis; *: AUCs were significantly different from the CE nomogram; **: AUCs were significantly different from the Copula nomogram.