Applied statistical modelling and inference in ophthalmology : analysis of visual field and video data for glaucoma patients : a thesis presented in total fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Manawatu, New Zealand

Abstract

Eyesight is arguably the most important of our senses with the eye absorbing 80% of external information from our surroundings. The field of ophthalmology studying the anatomy, physiology and diseases of the eye, is of extreme importance. Many methods exist to measure vision and the eye, creating a large range of interesting datasets. We developed methods to analyse three datasets from subjects with glaucoma, the second leading cause of blindness worldwide. Visual field testing using standard automated perimetry, is the most common method for monitoring glaucoma progression. A numerical matrix representing the dimmest intensity seen by a particular locus on the eye is outputted. This can be thought of as a map, and disease mapping techniques applied. We employed conditional autoregressive priors to account for the spatial correlation structure in the visual field results, in a way that respects the physiological and optical properties of the eye. Model diagnostics showed our model superior to the currently used point-wise linear regression methods. Visual field mean deviation, the mean light intensity across all loci adjusted for age matched controls, provides a global estimate of glaucoma progression. We investigated the shape of the relationship between mean deviation and time over long series of visual fields using splines. We considered imposing a monotonic non-increasing constraint. When a curve deviated from being linear or monotonic non-increasing, this was an indication of physiological or treatment change in the eye. We developed methods to extract and analyse data from video sequences of retinal venous pulsation, observed as change in blood flow, varying with the cardiac cycle. Video sequences were divided into individual frames, and the mean pixel intensity was calculated separately for three vessel segments representing the artery, lower vein and upper vein. Simple harmonic terms modelled the periodic component of the trend. The non-periodic trend, caused by patient movement, was modelled by linear splines. An autoregressive process modelled error correlation. Retinal blood flow has been linked to many diseases, so the characteristics of these curves have clinical importance.