Studying hypertension in ocular fundus images using Hausdorff dispersion ordering

Retinal arterial and vein diameters are altered in individuals at risk of cardiovascular events mainly due to high blood pressure. The measurement of retinal vessel diameters has been proved to reflect individuals' vascular health. Dispersion of such measures which are obtained by means of ocular fundus images is a major factor not usually considered in clinical research. In this paper, a method to evaluate if different levels of clinically relevant covariables induce greater dispersion in retinal arterial and vein diameters is proposed. A multivariate dispersion ordering, the Hausdorff dispersion order, is used to compare the level of dispersion in such diameters for different groups of patients. Our statistical conclusions show that dispersion is higher in individuals with long-standing hypertension and in those who need two or more drugs to control hypertension. Hereby, dispersion is increased in the most severely ill persons. However, a greater level of smoking seems to be associated with a lesser dispersion. Dispersion of the vessel diameters must be taken into account in the image analysis of retinal vessel diameters because the comparison between homogeneous groups will produce highly accurate results in medical research.