Methods combining SAP thresholds and Structural data

Garway-Heath et al. (2002) looked at the relationship between the number of ganglion cells in the eye and the visual field sensitivity. As previously mentioned, visual field sensitivity is mea-

sured on the log scale in decibels. The decibel can also be expressed as 10×log(1/Lambert),

where Lambert measures the test spot intensity. Linear and quadratic regressions were used to investigate the relationships between differential light sensitivity (DLS) (as decibels and 1/Lambert) and both pattern electroretinogram (related to the number of functioning gan- glion cells), and neuroretinal rim area. Curvilinear relationships were found when variables were regressed with DLS, whilst linear relationships were found when pattern electroretino- gram and neuroretinal rim area were regressed against DLS as 1/Lambert. In the past it had been supposed that there was a set value of ganglion cells, or a functional reserve, at which one starts to lose visual field functionality. Largely this is due to structural damage being identified before functional damage. This is due to the nature of the logarithmic scale, as well

as the high test-retest variability in visual field testing. This work, however, supports the hypothesis of a continuous linear structure-function relationship between number of ganglion cells and 1/Lambert DLS. If a linear structure-function relationship with the log scale DLS is assumed, underestimation of early functional loss and over estimation of more severe func- tional loss will result, as the true relationship is curvilinear. Reus & Lemij (2005) also looked at the relationship between DLS and structural measurements. They concluded that due to the curvilinear relationship between DLS and the structural measurements, the structural tests were able to identify glaucomatous loss earlier than SAP. Because dB are measured on the logarithmic scale, a clinically relevant structural change measured on the linear scale may be associated with only small changes in DLS. Reus & Lemij (2005) conclude that confocal scanning laser ophthalmology and scanning laser polarimetry might be better at estimating early glaucomatous damage.

More recent studies have combined SAP data with structural datasets within a machine learning environment. Bowd et al. (2008) found that combining optical coherence tomogra- phy data with SAP did not significantly improve the performance of the model compared with the structural and functional models on their own. Bowd et al. (2012) found that rel- evance support vector machine classifiers, combining SAP total deviation and confocal laser scanning ophthalmoscope images, more accurately identified progression than either the SAP or onfocal laser scanning ophthalmoscope global indices. Li et al. (2013) combine a temporal bootstrap model with Hidden Markov Models in order to create a pseudo time-series model from cross-sectional data. Average values from the VF sectors as defined by Garway-Heath et al. (2000) from 160 eyes were combined with Heidelberg Retinal Tomography data. The authors found that their model was able to separate stable states showing rim narrowing and abnormal VF sensitivities, and transitory states with fields showing subtle rim narrowing and VF sensitivity loss. This agreed with the current understanding of progression where rim loss may precede VF sensitivity loss and vice versa.

Bayesian Analysis

Medeiros et al. (2011) used Bayesian hierarchical models to combine structural and functional data in order to better detect the progression of glaucoma. It is suggested that an improved assessment of progression may be achieved by combining the structural measurements of the retinal nerve fibre layer and the functional measurements of the SAP visual field index. This model requires an additional dataset containing retinal nerve fibre layer measurements which are obtained using scanning laser polarimetry.

A joint multivariate mixed effects model was used within a Bayesian framework in order to combine these longitudinal measures. Random effects allowed for both within and between patient variation. Eyes were nested within patient in order to account for the correlation between a subject’s two eyes. A multivariate skew t-distribution was used as a prior for the random effects as non-normality was suspected. MCMC sampling was carried out in Win- BUGS and a specific eye was judged as progressing if the upper bound of the 95% credible interval was less than 0. These results were compared to the more standard approach of ordinary least squared linear regression, which was carried out individually on each eye.

Medeiros et al. (2011) ran the model on 434 eyes from 257 participants. At the baseline visit 38% were glaucomatous, 55% were glaucoma suspects and 7% were normal eyes. Compared with linear regression, the Bayesian method identified a significantly higher proportion of progressing eyes. Of the 405 glaucomatous and glaucoma suspect eyes the Bayesian method identified 22.7% as progressing compared with 12.8% by the regression method. When using optic disk stereographs as a reference endpoint for progression, the Bayesian method again outperformed the regression method identifying 74% as progressing compared with 37%. Of note is that the Bayesian method was able to detect eyes with faster rates of change than the regression method which struggled to classify with slopes with larger standard errors. From a clinical point of view these cases are more important to identify as they are likely to require intervention. However combining structural and functional information requires the collection of two datasets. In addition, because the model uses visual field index rather than

the individual threshold values the model is limited. Information on spatial correlation cannot be incorporated into the model, and while the model can give an overall eye progression rate, it cannot provide rates by sector or hemifield.