Hierarchical Censored Bayesian Analysis of Visual Field Progression.

Giovanni Montesano,David F Garway-Heath,Giovanni Ometto,David P Crabb

doi:10.1167/tvst.10.12.4

Giovanni Montesano, David F Garway-Heath + Show 2 more

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https://doi.org/10.1167/tvst.10.12.4

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PurposeTo develop a Bayesian model (BM) for visual field (VF) progression accounting for the hierarchical, censored and heteroskedastic nature of the data.MethodsThree versions of a hierarchical BM were developed: a simple linear (Hi-linear); censored at 0 dB (Hi-censored); heteroskedastic censored (Hi-HSK). For the latter, we modeled the test variability according to VF sensitivity using a large test-retest cohort (1396 VFs, 146 eyes with glaucoma). We analyzed a large cohort of 44,371 VF tests from 3352 eyes from five glaucoma clinics. We quantified the bias in the estimated rate-of-progression, the detection of progression (Hit-rate [HR]), the median time-to-progression and the prediction error of future observations (mean absolute error [MAE]). HR and time-to-progression were compared at matched false-positive-rate (FPR), quantified using permutations of a separate test-retest cohort (360 tests, 30 eyes with glaucoma). BMs were compared to simple linear regression and Permutation-Analyses-of Pointwise-Linear-Regression. Differences in time-to-progression were tested using survival analysis.ResultsCensored models showed the smallest bias in the rate-of-progression. The three BMs performed very similarly in terms of HR and time-to-progression and always better than the other methods. The average reduction in time-to-progression was 37% with the BMs (P < 0.001) at 5% FPR. MAE for prediction was very similar among methods.ConclusionsBayesian hierarchical models improved the detection of VF progression. Accounting for censoring improves the precision of the estimates, but minimal effect is provided by accounting for heteroskedasticity.Translational RelevanceThese results are relevant for quantification of VF progression in practice and for clinical trials.

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Glaucoma is a progressive optic neuropathy causing deterioration of the visual field (VF) as a consequence of the loss of retinal ganglion cells (RGCs) and their axons
Translational Relevance: These results are relevant for quantification of VF progression in practice and for clinical trials
The survival analysis and the formal comparisons mirrored the results seen for the HR curves (Fig. 4), in that all hierarchical models performed significantly better than the other methods and Permutation analyses of pointwise linear regression (PoPLR) performed better than simple linear regression (P < 0.001)

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Introduction

Glaucoma is a progressive optic neuropathy causing deterioration of the visual field (VF) as a consequence of the loss of retinal ganglion cells (RGCs) and their axons. Standard automated perimetry is repeated at successive visits to assess progression of VF damage both for the whole field (global metrics) and at individual locations (pointwise analysis). Made difficult by complex features in VF data that can compromise their effective use in glaucoma care. A commonly used method to assess progression is ordinary least squares (OLS) regression, either on global or pointwise data. Assumptions for such a method are, often violated. The variability of measured sensitivity is known to increase with the level of damage (heteroskedasticity), likely a consequence of the changes in response profile at damaged locations.[4,5]

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