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R. A. Bilonick, K. Sung, G. Wollstein, H. Ishikawa, K. A. Townsend, L. Kagemann, R. J. Noecker, J. S. Schuman; Evaluating Glaucoma Progression Using a Latent Class Model for MD, PSD, AGIS, and VFI With RNFL as Covariate. Invest. Ophthalmol. Vis. Sci. 2008;49(13):3610. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
This study predicts glaucoma progression using a longitudinal latent class regression (LCR) model of visual field global parameters: mean deviation (MD), pattern standard deviation (PSD), advanced glaucoma intervention study (AGIS) score, and visual field index (VFI). Baseline optical coherence tomography retinal nerve fiber layer (RNFL) average thickness was included as an exogenous covariate and longitudinal RNFL as an endogenous covariate.
LCR model isf(yi|zi, θ) = Σk πk|zi Πj fk(yij|zi, θjk) where yi = responses, zi = covariates, θ = model parameters, πk|zi = prior probability for class k given exogenous covariates z, f = response joint density, and fk = univariate response densities for each class. Posterior probabilities for class (progressor, nonprogressor) were computed. Models with 2 classes were fitted to MD, PSD, AGIS, and VFI measured 5 times over a 5 year period for 61 glaucoma subjects and glaucoma suspects (106 eyes). Model 1 included RNFL as an exogenous covariate with time as an endogenous covariate. Model 2 added RNFL and RNFL × time as endogenous covariates. Response variables were standardized. Maximum likelihood was used to estimate the model parameters using R and the mmlcr package.
Baseline RNFL was highly statistically significant in both models. Profiles for progressors and nonprogressors were substantially different (see table). In Model 1, slopes were flat for nonprogressors. MD and VFI slopes for progressors were strongly negative and for PSD and AGIS strongly positive. Slope magnitude was highest for VFI. AICs indicated Model 2 as the better model. There were no interactions for nonprogressors but there were substantial interactions for progressors. For high RNFL, PSD tends to increase over time while for low RNFL, PSD remains flat for progressors.
LCR provided a very flexible method for classifying subjects and describing the relationships among response variables adjusting for covariates.
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