In ophthalmology, there is a need to explore the relationships between clinical parameters of the cornea and the corneal shape. This study explores the paradigm of machine learning with nonlinear regression methods to verify whether corneal shapes can effectively be predicted from clinical data only, in an attempt to better assess and visualize their effects on the corneal shape.

The dimensionality of a database of normal anterior corneal surfaces was first reduced by Zernike modeling into short vectors of 12 to 20 coefficients used as targets. The associated structural, refractive and demographic corneal parameters were used as predictors. The nonlinear regression methods were borrowed from the scikit-learn library. All possible regression models (method + predictors + targets) were pre-tested in an exploratory step and those that performed better than linear regression were fully tested with 10-fold validation. The best model was selected based on mean RMSE scores measuring the distance between the predicted corneal surfaces of a model and the raw (non-modeled) true surfaces. The quality of the best model's predictions was visually assessed thanks to atlases of average elevation maps that displayed the centroids of the predicted and true surfaces on a number of clinical variables.

The best model identified was gradient boosting regression using all available clinical parameters to predict 16 Zernike coefficients. The predicted and true corneal surfaces represented in average elevation maps were remarkably similar. The most explicative predictor was the radius of the best-fit sphere, and departures from that sphere were mostly explained by the eye side and by refractive parameters (axis and cylinder).

It is possible to make a reasonably good prediction of the normal corneal shape solely from a set of clinical parameters. In so doing, one can visualize their effects on the corneal shape and identify its most important contributors.