A Growth Mixture Model for Progression of Glaucoma based on Visual Field

Abstract

Purpose : Developmental profiles of visual field (VF) parameters provide information on the progression of glaucoma. The purpose of this study was to develop a new statistical method based on a latent group trajectory model to categorize trajectory groups using longitudinal VF parameters.

Methods : A total of 170 eyes (99 glaucoma, 46 glaucoma suspect, 25 healthy) from 105 subjects with 5 qualified visits were included. A latent class regression (LCR) was performed using VF mean deviation (MD) pattern standard deviation (PSD) and visual field index (VFI) as responses. Length of follow-up (t_ij) was the single explanatory variable. Baseline age was concomitant variable. A growth mixture model with K latent groups can be described as combination of K growth curves, weighted by proportions p_ik:
y_ijm = Σ^k_k=1p_ik (α_km + β_km t_ij) + ε_ijm , m = MD PSD VFI
where y_ijm is the response (MD, PSD or VFI) of the i^th eye measured at follow-up time t_ij. α,β are intercepts and slopes. p_ik's are posterior probabilities of class membership of the i^th eye, which is based on the prior probabilities of class membership (which depends on baseline age in this model) and the time profiles for each of the responses for this eye. If one p_ik is much higher than others of the i^th eye, the classification is very clear cut and unambiguous. Otherwise it may have some uncertainty as to class.
The R statistical software and OpenMx package were used to describe the structural equation model (SEM) for the growth curve mixture model. Fig 1 shows the path diagram of the SEM model.

Results : Two class memberships were detected (K=2). Fig 2 shows the posterior probabilities of being Class 2. Most posterior probabilities are 0 (class 1) or 1 (class 2). Only 4 eyes had some uncertainty as to the class. Fig 3 shows the estimated intercepts and slopes of the 3 responses for the 2 classes. Class 1 had 103 eyes where MD and VFI tend to increase and PSD tends to drop. So eyes in Class 1 tend to get better; Class 2 had 67 eyes where the intercept was much lower than that of Class 1 and MD tends to slightly increase only by 25% of the rate of Class 1, VFI tends to drop and PSD tends to rise. So eyes in Class 2 tends to be bad and sort of getting worse.

Conclusions : Growth Mixture Model classified most eyes clearly and unambiguously as progressors or non-progressors based on the visual field parameters with only a small number of eyes having uncertainty as to class.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.