Hierarchical Censored Bayesian Analysis of Visual Field Progression

Purpose: To develop a Bayesian model (BM) for visual field (VF) progression accounting for the hierarchical, censored and heteroskedastic nature of the data. Methods: Three 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. Results: Censored 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. Conclusions: Bayesian 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 Relevance: These results are relevant for quantification of VF progression in practice and for clinical trials.

Automated summary

Developed hierarchical Bayesian models to account for the nature of visual field progression data, with censored models showing the smallest bias in rate-of-progression. Results indicate that Bayesian models performed better in terms of Hit-rate and time-to-progression compared to other methods. Account for censoring improved precision of estimates, with minimal effect from accounting for heteroskedasticity.