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
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
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.