A Functional Regression Model of the Retinal Nerve Fiber Layer Thickness in Healthy Subjects

A new functional regression model is presented to explain the intersubject variability of the circumpapillary retinal nerve fiber layer (RNFL) thickness in healthy subjects.

To evaluate the functional regression approach we used data from 202 healthy volunteers, divided equally into training samples (TS) and validation samples (VS). Covariates included RNFL, fovea distance, fovea angle, optic disk ratio, orientation and area provided by Fourier-domain-optical coherence tomography, age, and refractive error. Root mean square errors (RMSE) were calculated for each of the 256 sectors and for the 12 clock-hour sectors in the TS and VS and were compared to the RMSE of the previous model and the standard deviation of the raw data.

With the functional regression approach, we were able to explain on average 27.4% of the variation in the TS and 25.1% of the variation in the VS. The new model performed better compared to a multivariate linear regression model. It performed best in the superior-temporal and inferior-temporal clock-hour sectors where the percentage of RMSE reduction ranged between 26.3% and 44.1% for the TS and between 20.6% and 35.4% for the VS.

The new functional regression approach improves on the multivariate linear regression model and allows an even larger reduction of the amount of intersubject variability, while at the same time using a substantially smaller number of parameters to be estimated.

The demonstrated reduction of interindividual variation is expected to translate into an improved diagnostic separation between healthy and glaucomatous subjects, but this remains to be demonstrated in further studies.