Multivariate Longitudinal Modeling of Macular Ganglion Cell Complex: Spatiotemporal Correlations and Patterns of Longitudinal Change

Performance of Linear Mixed Models in Estimating Structural Rates of Glaucoma Progression Using Varied Random Effect Distributions

Purpose

To compare how linear mixed models (LMMs) using Gaussian, Student t, and log-gamma (LG) random effect distributions estimate rates of structural loss in a glaucomatous population using OCT and to compare model performance to ordinary least squares (OLS) regression.

Design

Retrospective cohort study.

Subjects

Patients in the Bascom Palmer Glaucoma Repository (BPGR).

Methods

Eyes with ≥ 5 reliable peripapillary retinal nerve fiber layer (RNFL) OCT tests over ≥ 2 years were identified from the BPGR. Retinal nerve fiber layer thickness values from each reliable test (signal strength ≥ 7/10) and associated time points were collected. Data were modeled using OLS regression as well as LMMs using different random effect distributions. Predictive modeling involved constructing LMMs with (n - 1) tests to predict the RNFL thickness of subsequent tests. A total of 1200 simulated eyes of different baseline RNFL thickness values and progression rates were developed to evaluate the likelihood of declared progression and predicted rates.

Main Outcome Measures

Model fit assessed by Watanabe-Akaike information criterion (WAIC) and mean absolute error (MAE) when predicting future RNFL thickness values; log-rank test and median time to progression with simulated eyes.

Results

A total of 35 862 OCT scans from 5766 eyes of 3491 subjects were included. The mean follow-up period was 7.0 ± 2.3 years, with an average of 6.2 ± 1.4 tests per eye. The Student t model produced the lowest WAIC. In predictive models, all LMMs demonstrated a significant reduction in MAE when estimating future RNFL thickness values compared with OLS (P < 0.001). Gaussian and Student t models were similar and significantly better than the LG model in estimating future RNFL thickness values (P < 0.001). Simulated eyes confirmed LMM performance in declaring progression sooner than OLS regression among moderate and fast progressors (P < 0.01).

Conclusions

LMMs outperformed conventional approaches for estimating rates of OCT RNFL thickness loss in a glaucomatous population. The Student t model provides the best model fit for estimating rates of change in RNFL thickness, although the use of the Gaussian or Student t distribution in models led to similar improvements in accurately estimating RNFL loss.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Detecting Fast Progressors: Comparing a Bayesian Longitudinal Model to Linear Regression for Detecting Structural Changes in Glaucoma

PURPOSE

Demonstrate that a novel Bayesian hierarchical spatial longitudinal (HSL) model identifies macular superpixels with rapidly deteriorating ganglion cell complex (GCC) thickness more efficiently than simple linear regression (SLR).

DESIGN

Prospective cohort study.

SETTING

Tertiary Glaucoma Center.

SUBJECTS

One hundred eleven eyes (111 patients) with moderate to severe glaucoma at baseline and ≥4 macular optical coherence tomography scans and ≥2 years of follow-up.

OBSERVATION PROCEDURE

Superpixel-patient-specific GCC slopes and their posterior variances in 49 superpixels were derived from our latest Bayesian HSL model and Bayesian SLR. A simulation cohort was created with known intercepts, slopes, and residual variances in individual superpixels.

MAIN OUTCOME MEASURES

We compared HSL and SLR in the fastest progressing deciles on (1) proportion of superpixels identified as significantly progressing in the simulation study and compared to SLR slopes in cohort data; (2) root mean square error (RMSE), and SLR/HSL RMSE ratios.

RESULTS

Cohort- In the fastest decile of slopes per SLR, 77% and 80% of superpixels progressed significantly according to SLR and HSL, respectively. The SLR/HSL posterior SD ratio had a median of 1.83, with 90% of ratios favoring HSL. Simulation- HSL identified 89% significant negative slopes in the fastest progressing decile vs 64% for SLR. SLR/HSL RMSE ratio was 1.36 for the fastest decile of slopes, with 83% of RMSE ratios favoring HSL.

CONCLUSION

The Bayesian HSL model improves the estimation efficiency of local GCC rates of change regardless of underlying true rates of change, particularly in fast progressors.

Visual Field Outcomes in the Primary Tube Versus Trabeculectomy Study

PURPOSE

To describe visual field outcomes in the Primary Tube Versus Trabeculectomy (PTVT) Study.

DESIGN

Cohort analysis of a prospective multicenter randomized clinical trial.

SUBJECTS

A total of 155 eyes from 155 subjects randomly assigned to treatment with tube shunt surgery (n=84) or trabeculectomy with mitomycin C (n=71).

METHODS

The PTVT Study was a multicenter randomized clinical trial comparing the safety and efficacy of trabeculectomy and tube shunt surgery in eyes without prior intraocular surgery. Subjects underwent standard automated perimetry (SAP) at baseline and annually for five years. SAP tests were deemed reliable if the false positive rate was ≤15%. Tests were excluded if visual acuity was ≤20/400 or loss of ≥2 Snellen lines from baseline were attributed to a non-glaucomatous etiology. Linear mixed-effects models were used to compare rates of change in SAP mean deviation (MD) between the two treatment groups. Intraocular pressure (IOP) control was assessed by percentage of visits with IOP <18 mmHg and mean IOP.

OUTCOME MEASURES

Rate of change in SAP MD during follow-up.

RESULTS

A total of 730 SAP tests were evaluated, with an average of 4.7 tests per eye. The average SAP MD at baseline was -12.8±8.3 dB in the tube group and -12.0±8.4 dB in the trabeculectomy group (p=0.57). The mean rate of change in SAP MD was -0.32±0.39 dB/year in the trabeculectomy group and -0.47±0.43 dB/year in the tube group (p=0.23). Eyes with mean IOP 14-17.5 mmHg had significantly faster rates of SAP MD loss compared to eyes with mean IOP <14 mmHg (-0.59±0.13 vs. -0.27±0.08 dB/year, p=0.012) and eyes with only 50-75% of visits with IOP <18 mmHg had faster rates than those with 100% of visits with IOP <18 mmHg (-0.90±0.16 vs. -0.29±0.08 dB/year, p<0.001). Multivariable analysis identified older age and worse IOP control as risk factors for faster progression in both treatment groups.

CONCLUSIONS

No statistically significant difference in mean rates of visual field change was observed between trabeculectomy and tube shunt surgery in the PTVT Study. Worse IOP control was significantly associated with faster rates of SAP MD loss during follow-up. Older patients were also at risk for faster progression.

Study of the ganglion cell complex of the macula by optical coherence tomography in the diagnosis of glaucoma progression

INTRODUCTION

The aim of this work is to evaluate the usefulness of the study of the ganglion cell complex of the macula using the OCT technique to estimate the progression of glaucoma according to its severity.

MATERIAL AND METHODS

This is a retrospective cross-sectional study. It includes 205 eyes of 131 patients with glaucoma or ocular hypertension followed for a mean of 5.7 years. The parameters and rates of three tests have been analyzed using the progression software of each instrument: visual field, optical coherence tomography (OCT) in the ganglion cell complex of the macula and in the nerve fiber layer of the optic nerve. The results of each test, the concordance between them and how they differ according to severity stage have been evaluated.

RESULTS

Visual field classifies more cases of progression in moderate-advanced glaucoma, while in mild glaucoma its capacity is limited. Optic nerve fiber layer OCT classifies more cases of progression in mild glaucoma than in moderate-advanced glaucoma, as it is artifacted by the floor effect. OCT of the macular ganglion cell complex is the test that classifies more cases of progression and has the highest agreement with visual field, regardless of severity.

CONCLUSION

In both mild and moderate-advanced glaucoma, OCT of the macula ganglion cell complex may be a better biomarker of progression than OCT of the macula ganglion cell complex.

Structure-function relationship of reading performance in patients with early to moderate glaucoma

PURPOSE

To assess reading performance in patients with mild to moderate primary open-angle glaucoma (POAG), and to determine the relationship between reading ability and visual field (VF), microperimetry, and optical coherence tomography (OCT) parameters.

METHODS

Reading performance of 30 POAG patients examined by the Minnesota Reading Acuity Chart (MNREAD) was compared to that of 21 age-matched controls collected from Ankara University in Turkey. Humphrey Field Analyzer (HFA) 24-2 SITA Standard and 10-2 patterns, and microperimetry were used for VF measurements. All subjects underwent OCT analysis for retinal nerve fiber layer thickness (RNFLT), optic nerve head (ONH) measurements, and ganglion cell inner plexiform layer thickness (GCIPLT). The linear relationship between reading parameters and VF, microperimetry, and OCT parameters was investigated. Univariate and multiple logistic regression models were used to identify the risk factors for glaucoma.

RESULTS

In POAG patients, maximum reading speed (MRS) had a significant association with average rim area, mean cup-to-disc ratio (CDR), and cup volume (p < 0.05, for all). Decreased MRS was associated with thinner average GCIPLT and inferotemporal, superior, and inferior GCIPLT quadrants (p < 0.05, for all). Global index values for the HFA 24-2/10-2 tests, microperimetry, and ONH/RNFLT parameters had no correlation with reading performance. After accounting for the better and worse eyes, gender, education, age, and visual acuity of the glaucoma patients, MRS score was 23 units lower in the worse eye (p = 0.009), critical print size (CPS) was 0.21 units larger in the better eye (p = 0.03) and 0.25 units larger in the worse eye (p < 0.001), reading accesibility index (ACC) was 0.11 units lower in the better eye (p = 0.02) and 0.13 units lower in the worse eye (p = 0.002), and RA was 0.13 units higher in the worse eye (p = 0.003) of POAG patients.

CONCLUSION

POAG had significantly lower reading performance when compared to healthy subjects. Reading speed was associated with decreased macular GCIPLT indicating that reading performance may be affected in the earlier stages of the disease.

A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in Glaucomatous Eyes

Purpose

Demonstrate that a novel Bayesian hierarchical spatial longitudinal (HSL) model improves estimation of local macular ganglion cell complex (GCC) rates of change compared to simple linear regression (SLR) and a conditional autoregressive (CAR) model.

Methods

We analyzed GCC thickness measurements within 49 macular superpixels in 111 eyes (111 patients) with four or more macular optical coherence tomography scans and two or more years of follow-up. We compared superpixel-patient-specific estimates and their posterior variances derived from the latest version of a recently developed Bayesian HSL model, CAR, and SLR. We performed a simulation study to compare the accuracy of intercept and slope estimates in individual superpixels.

Results

HSL identified a significantly higher proportion of significant negative slopes in 13/49 superpixels and a significantly lower proportion of significant positive slopes in 21/49 superpixels than SLR. In the simulation study, the median (tenth, ninetieth percentile) ratio of mean squared error of SLR [CAR] over HSL for intercepts and slopes were 1.91 (1.23, 2.75) [1.51 (1.05, 2.20)] and 3.25 (1.40, 10.14) [2.36 (1.17, 5.56)], respectively.

Conclusions

A novel Bayesian HSL model improves estimation accuracy of patient-specific local GCC rates of change. The proposed model is more than twice as efficient as SLR for estimating superpixel-patient slopes and identifies a higher proportion of deteriorating superpixels than SLR while minimizing false-positive detection rates.

Translational Relevance

The proposed HSL model can be used to model macular structural measurements to detect individual glaucoma progression earlier and more efficiently in clinical and research settings.

Association of Blood Pressure With Rates of Macular Ganglion Cell Complex Thinning in Patients With Glaucoma

Importance

There are scarce data on the association of blood pressure measures with subsequent macular structural rates of change in patients with glaucoma.

Objective

To investigate the association of baseline blood pressure measures with rates of change of the macular ganglion cell complex in patients with central or moderate to advanced glaucoma damage at baseline.

Design, Setting, and Participants

This prospective cohort study, conducted from August 2021 to August 2022, used data from patients in the Advanced Glaucoma Progression Study at the University of California, Los Angeles. Participants were between 39 and 80 years of age and had more than 4 macular imaging tests and 2 or more years of follow-up.

Exposures

A diagnosis of glaucoma with either central damage or a visual field mean deviation worse than -6 dB.

Main Outcomes and Measures

The main outcome was the association of blood pressure measures with ganglion cell complex rates of change. Macular ganglion cell complex thickness rates of change were estimated with a bayesian hierarchical model. This model included relevant demographic and clinical factors. Blood pressure measures, intraocular pressure, and their interactions were added to the model to assess the association of baseline blood pressure measures with global ganglion cell complex rates of change.

Results

The cohort included 105 eyes from 105 participants. The mean (SD) age, 10-2 visual field mean deviation, and follow-up time were 66.9 (8.5) years, -8.3 (5.3) dB, and 3.6 (0.4) years, respectively, and 67 patients (63.8%) were female. The racial and ethnic makeup of the cohort was 15 African American (14.3%), 23 Asian (21.9%), 12 Hispanic (11.4%), and 55 White (52.4%) individuals based on patient self-report. In multivariable analyses, female sex, history of taking blood pressure medications, higher intraocular pressure, thicker central corneal thickness, shorter axial length, higher contrast sensitivity at 12 cycles per degree, and higher baseline 10-2 visual field mean deviation were associated with faster ganglion cell complex thinning. Lower diastolic blood pressure was associated with faster rates of ganglion cell complex thinning at higher intraocular pressures. For intraocular pressures of 8 and of 16 mm Hg (10% and 90% quantiles, respectively), every 10 mm Hg-lower increment of diastolic blood pressure was associated with 0.011 μm/y slower and -0.130 μm/y faster rates of ganglion cell complex thinning, respectively.

Conclusions and Relevance

In this cohort study, a combination of lower diastolic blood pressure and higher intraocular pressure at baseline was associated with faster rates of ganglion cell complex thinning. These findings support consideration of evaluating and addressing diastolic blood pressure as a therapeutic measure in patients with glaucoma if supported by appropriate clinical trials.