Royston-Parmar flexible parametric survival model to predict the probability of keratoconus progression to corneal...

To assess a Royston-Parmar flexible parametric survival model to generate a personalised risk profile for keratoconus progression.

We re-analysed a historic database of 2723 individuals with keratoconus. A Royston-Parmar survival model was fitted to predict the likelihood of the worse eye progressing to corneal transplantation. We used a backwards selection multivariable fractional polynomial procedure to assist with selection of covariates and identify appropriate transformation(s) to retain in the final model. Time-dependent receiver operating characteristic (ROC) curves from censored survival data using the Kaplan-Meier (KM) method were computed to visually assess how well the model identified eyes likely to progress.

In all, 5020 eyes from 2581 patients were available for model development. This included 2378 worst affected eyes, and 313 eyes that progressed to transplantation. The best fitting model [df = 1: Bayes information criterion (BIC) = 1573] included three variables, keratometry [hazard ratio (HR) 0.36: 95% confidence limits (CI) 0.32-0.42], age at baseline [HR 0.97: CI 0.95-0.99] and ethnicity [HR 3.92: CI 2.58-5.95]. Specificity at 1 year was 92.8% (CI 90.4-95.2%) with a corresponding sensitivity of 64.6% (CI 58.9-60.0%). These three prognostic factors account for 41.3% (CI 33.6 - 48.2%) of the variation among the survival curves.

Researchers should consider the Royston-Parmar model as an alternative to the Cox model. We illustrate the concepts and our results may lead to better tools that identify individuals at high risk of keratoconus progression.