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 , 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 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 ( < 0.001). Gaussian and Student models were similar and significantly better than the LG model in estimating future RNFL thickness values ( < 0.001). Simulated eyes confirmed LMM performance in declaring progression sooner than OLS regression among moderate and fast progressors ( < 0.01).

Conclusions: LMMs outperformed conventional approaches for estimating rates of OCT RNFL thickness loss in a glaucomatous population. The Student model provides the best model fit for estimating rates of change in RNFL thickness, although the use of the Gaussian or Student 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.