Spatio-temporal modeling of perimetric test data

This work describes the application of a spatio-temporal modeling to the study of glaucoma, a very serious ocular illness. The aim of this modeling is to solve various significant medical problems, namely the forecasting of future observations, the classification of observations as normal or defective, and the simulation of new longitudinal data sets. In order to ascertain whether a patient suffers from glaucoma, a perimetry is performed. The output of a perimetry is called a visual field and consists of a map with 52 numerical values plotted on a regular grid. In this work, a data set of healthy patients' visual fields is used. The work begins with an exploratory spatial data analysis. A semi-parametric approach is used to model the mean, and the variogram is fitted using a Matérn function. Once the spatial structure has been analysed, the spatial mean is subtracted from all the observations in the data set and the spatio-temporal correlation of the residuals is explored. All this information is used to build a space-time model, the parameters of which are estimated by maximum likelihood. Different methods are used to check the goodness of fit.