A mathematical model to predict the probability of keratoconus progression

Abstract

Purpose : Due to potential sight-threatening complications following corneal cross-linking (CXL) treatment is normally reserved for patients with demonstrable keratoconus progression. To improve our ability to assess the risk of progression we have developed a mathematical model to provide a personalised risk profile for each eye of individuals with keratoconus.

Methods : We retrospectively analysed data from 2,723 keratoconics. A Royston-Parmar flexible parametric survival model was fitted to predict the likelihood of the worse eye progressing to a corneal graft. Data were randomly split into a model building set (75%) and a validation set (25%). A backwards selection multivariable fractional polynomial procedure was used to assist with selection of covariates and identify appropriate transformation(s) to retain in the final fully adjusted model. The selection of the final model and selection scales and number of degrees of freedom (df) for the baseline function were guided by the Bayes information criterion (BIC) statistic. Royston and Sauerbrei’s D statistic was used as a measure of discrimination, and R²_D as a measure of explained variation on the natural scale of the model. Finally, a Kaplan Meier plot was constructed by applying the model to the internal validation set and this was compared with the observed Kaplan Meier plot to allow visual inspection of the model

Results : 4,756 eyes were available for data analysis (2,378 worse; 2,378 best) with full covariate data available for 1,778 (75%) worse eyes. The best fitting model (df = 1; BIC = 1573) included 3 variables (keratometry HR = 0.36; 95% CI = (0.32, 0.42), age at baseline 0.97; 95% CI = (0.95, 0.99) and race 3.92; 95% CI = (2.58, 5.95)). Prognostic factors account for 39% (95% CI = (33, 45) of the variation among the survival curves. Harrel’s C discrimination index was 0.78 in the model building set and 0.79 in the validation set indicating good model discrimination.

Conclusions : Internal validation suggests the model reliably predicts patient outcome. External validation is required to support its use in counselling patients on their risk of keratoconus progression and need for CXL.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.

 

Predicted and observed survival curves from the internal validation approach. At 5 years, Kaplan-Meier curves show the likelihood of requiring a corneal graft is 8% (lowest risk profile) to 37% (highest risk profile)