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Andrew Anderson; Influence of prior information on Bayesian estimators of visual field progression. Invest. Ophthalmol. Vis. Sci. 2013;54(15):3932.
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© ARVO (1962-2015); The Authors (2016-present)
Progression of visual field damage in glaucoma is often assessed by linear regression of the summary index mean deviation (MD). Bayesian estimators allow likely progression rates in the population (the prior distribution) to constrain rate estimates for individuals. We examined the benefits of having a prior distribution accounting for one of progression’s major risk factors - whether intraocular pressure (IOP) is treated - to gauge the maximum benefit expected from developing priors for other glaucoma risk factors.
Our prior distribution was derived from published clinical data from either treated (Canadian Glaucoma Study: matched-prior condition) or untreated (Early Manifest Glaucoma Trial; unmatched-prior condition) patients with primary open angle glaucoma, each fitted with a modified hyperbolic secant. We simulated series of MD values (2 fields per year for 6 years) with true underlying rates of progression (R) drawn from the same distribution as the prior for the matched-prior condition. The standard deviation of MD values was 1.0 dB. We estimated progression rates (r) for subsets of each series (2 through 11 visual field assessments) through linear regression, and determined the likelihood of obtaining this estimate as a function of a range of true underlying progression rates (the likelihood function for the conditional probability r|R). The maximum likelihood estimate of rate was calculated from the most likely value of the posterior distribution formed by the product of the prior distribution and the likelihood function.
For short (4) visual field series, the matched-prior condition, unmatched-prior condition and linear regression gave median errors (r minus R) of 0.02, 0.20 & 0.00 dB/year, respectively. Positive predictive values for determining rapidly progressing (= worse than -1 dB/year) rates in the simulated patient cohort were 0.46, 0.42 and 0.38, with negative predictive values of 0.93, 0.94 and 0.95. For more extended series (7 fields) the magnitude of the differences between techniques decreased, although the order was unchanged.
Performance shifts in Bayesian estimators of visual field progression are modest even when prior distributions do not adequately reflect large risk factors, such as IOP treatment.
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