Auditing service delivery in glaucoma clinics using visual field records: a feasibility study

Estimating the Distribution of True Rates of Visual Field Progression in Glaucoma

Purpose

The purpose of this study was to estimate the distribution of the true rates of progression (RoP) of visual field (VF) loss.

Methods

We analyzed the progression of mean deviation over time in series of ≥ 10 tests from 3352 eyes (one per patient) from 5 glaucoma clinics, using a novel Bayesian hierarchical Linear Mixed Model (LMM); this modeled the random-effect distribution of RoPs as the sum of 2 independent processes following, respectively, a negative exponential distribution (the "true" distribution of RoPs) and a Gaussian distribution (the "noise"), resulting in a skewed exGaussian distribution. The exGaussian-LMM was compared to a standard Gaussian-LMM using the Watanabe-Akaike Information Criterion (WAIC). The random-effect distributions were compared to the empirical cumulative distribution function (eCDF) of linear regression RoPs using a Kolmogorov-Smirnov test.

Results

The WAIC indicated a better fit with the exGaussian-LMM (estimate [standard error]: 192174.4 [721.2]) than with the Gaussian-LMM (192595 [697.4], with a difference of 157.2 [22.6]). There was a significant difference between the eCDF and the Gaussian-LMM distribution (P < 0.0001), but not with the exGaussian-LMM distribution (P = 0.108). The estimated mean (95% credible intervals, CIs) "true" RoP (-0.377, 95% CI = -0.396 to -0.359 dB/year) was more negative than the observed mean RoP (-0.283, 95% CI = -0.299 to -0.268 dB/year), indicating a bias likely due to learning in standard LMMs.

Conclusions

The distribution of "true" RoPs can be estimated with an exGaussian-LMM, improving model accuracy.

Translational Relevance

We used these results to develop a fast and accurate analytical approximation for sample-size calculations in clinical trials using standard LMMs, which was integrated in a freely available web application.

Measures of multiple deprivation and visual field loss in glaucoma clinics in England: lessons from big data

BACKGROUND/OBJECTIVES

To examine the association between multiple deprivation with late diagnosis and rapid worsening of glaucoma in patients in English hospital eye services (HES).

METHODS

602,439 visual fields (VFs) were extracted from five regionally different glaucoma clinics in England. Mean Deviation (MD) worse than -12 dB was used as a surrogate definition for advanced VF loss at diagnosis in patients with ≥2 reliable VF records. MD loss worse than -1 dB per year was used to define rapid VF progression in patients with ≥6 VFs. Patient data were stratified into deciles of the Index of Multiple Deprivation (IMD) from residential postcodes.

RESULTS

There was an association between IMD and advanced VF loss at diagnosis in 44,956 patients with 18% (293/1608) and 11% (771/6929) in the most and least deprived IMD decile, respectively. Age-corrected odds ratio (OR) for having advanced VF loss at entry into HES was 1.42 (95% confidence interval [CI] 1.21-1.67) and 0.75 (95% CI: 0.66-0.85) in the most and least deprived IMD decile respectively (reference = fifth decile). In 15,094 patients with follow up data (median [interquartile range] of 6.9 [4.5, 10.0] years), the proportion having rapid VF progression did not differ across the IMD spectrum.

CONCLUSION

Large-scale VF data from clinics indicates that glaucoma severity at presentation to English HES is associated with levels of multiple deprivation. We found no evidence to suggest likelihood of having rapid VF progression during follow-up is associated with IMD; this hints at equity of glaucoma care and outcomes once patients are in English HES.

Validating Trend-Based End Points for Neuroprotection Trials in Glaucoma

Purpose

The purpose of this study was to evaluate the power of trend-based visual field (VF) progression end points against long-term development of event-based end points accepted by the US Food and Drug Administration (FDA).

Methods

One eye from 3352 patients with ≥10 24-2 VFs (median = 11 years) follow-up were analyzed. Two FDA-compatible criteria were applied to these series to label "true-progressed" eyes: ≥5 locations changing from baseline by more than 7 dB (FDA-7) or by more than the expected test-retest variability (GPA-like) in 2 consecutive tests. Observed rates of progression (RoP) were used to simulate trial-like series (2 years) randomly assigned (1000 times) to a "placebo" or a "treatment" arm. We simulated neuroprotective "treatment" effects by changing the proportion of "true progressed" eyes in the two arms. Two trend-based methods for mean deviation (MD) were assessed: (1) linear mixed model (LMM), testing average difference in RoP between the two arms, and (2) time-to-progression (TTP), calculated by linear regression as time needed for MD to decline by predefined cutoffs from baseline. Power curves with 95% confidence intervals were calculated for trend and event-based methods on the simulated series.

Results

The FDA-7 and GPA-like progression was achieved by 45% and 55% of the eyes in the clinical database. LMM and TTP had similar power, significantly superior to the event-based methods, none of which reached 80% power. All methods had a 5% false-positive rate.

Conclusions

The trend-based methods can efficiently detect treatment effects defined by long-term FDA-compatible progression.

Translational Relevance

The assessment of the power of trend-based methods to detect clinically relevant progression end points.

Rates of Visual Field Change in Patients With Glaucoma and Healthy Individuals: Findings From a Median 25-Year Follow-up

Importance

Estimating the rate of glaucomatous visual field change provides practical assessment of disease progression and has implications for management decisions.

Objective

To assess the rates of visual field change in patients receiving treatment for glaucoma compared with healthy individuals over an extensive follow-up period and to quantify the impact of important covariates for these rates.

Design, Setting, and Participants

This prospective longitudinal cohort study was conducted in a hospital-based setting from January 1991 to February 2020. The study included 40 patients receiving treatment for open-angle glaucoma and 29 healthy participants. One eye of each participant was randomly selected as the study eye.

Exposures

Patients with glaucoma and healthy participants received testing with standard automated perimetry every 6 months. Individual rates of mean sensitivity change were computed using ordinary least-squares regression analysis, and linear mixed-effects modeling was used to estimate the mean rates of mean sensitivity change in the 2 groups and the impact of baseline mean sensitivity, baseline age, and follow-up intraocular pressure for rate estimates.

Main Outcomes and Measures

Rate of mean sensitivity change in patients with glaucoma and healthy participants.

Results

A total of 40 patients with glaucoma (median age, 53.07 years [IQR, 48.34-57.97 years]; 21 men [52%]) and 29 healthy participants (median age, 48.80 years [IQR, 40.40-59.07 years], 17 women [59%]) were followed up for a median of 25.65 years (IQR, 22.49-27.02 years) and 19.56 years (IQR, 16.19-26.21 years), respectively. Most participants (65 individuals [94%]) self-identified as White, with the exception of 2 patients with glaucoma (1 self-identified as Black and 1 as South Asian) and 2 healthy participants (both self-identified as South Asian). The mean follow-up intraocular pressure of patients with glaucoma (median, 15.83 mm Hg [IQR, 13.05-17.33 mm Hg]) was similar to that of healthy participants (median, 14.94 mm Hg [IQR, 13.28-16.01 mm Hg]; P = .25). In an ordinary least-squares regression analysis, 31 patients (78%) with glaucoma had rates of mean sensitivity change within the range of healthy participants (ie, between -0.20 dB/y and 0.15 dB/y). Linear mixed-effects modeling revealed that the mean (SE) rate of mean sensitivity change in healthy participants was 0.003 (0.033) dB/y (95% CI, -0.062 to 0.068; P = .93). In comparison, patients with glaucoma had a mean (SE) rate of mean sensitivity change that was -0.032 (0.052) dB/y faster, but this difference was not statistically significant (95% CI, -0.134 to 0.070; P = .53). Among covariates, only baseline mean sensitivity was associated with the rate of mean sensitivity change (mean [SE], 0.021 [0.010] dB/y/dB; 95% CI, 0.002-0.041; P = .03).

Conclusions and Relevance

The results of this cohort study suggest that over a median follow-up of more than 25 years, the rate of visual field change in patients receiving treatment for glaucoma was comparable to that of healthy individuals. These findings could guide practitioners in making management decisions.

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.