Regression Modeling for Pointwise Visual Field Perimetry Data for Patients with Glaucoma

Abstract

 

Purpose:

 

To re-examine the conventional use of pointwise linear regression (PLR) to track visual field (VF) perimetry data with statistical models that may be more structurally appropriate for VF trend analysis.

 

Methods:

 

We obtain visual field perimetry data (Humphrey, 24-2) from patients (minimum follow-up time of 6 years) with glaucoma from the UCLA and Advanced Glaucoma Intervention Study (AGIS) databases and perform four pointwise regressions for each test point location for each eye using the entire VF time series. Candidate regression models are:1^st order linear model (PLR)1^st-order Tobit normal model (censored for dB less than 0, nonlinear, max-likelihood)1^st order linear-exponential power model, a+be^x1^st order nonlinear-exponential decay model, e^a+bxWe perform post-regression diagnostics with the Akaike information criteria (AIC) to compare the non-nested linear/nonlinear models for "goodness-of-fit" calculations. The model with the lowest AIC value is considered the optimal model for that eye/location.

 

Results:

 

The relative proportions of the optimal regression models for the combined AGIS and UCLA visual field data series (n=798 eyes with mean follow up = 9.4 years, mean number of visual field exams per eye = 15.2, and total number of VF data series = 43,092) based on the AIC are: nonlinear-exponential 88.1%, Tobit 8.5%. linear-exponential 3.1% and linear 0.2%. A ternary plot (with the linear and linear-exponential subtotals combined) shows the % distribution of the optimal models per eye (Figure below).

 

Conclusions:

 

The nonlinear models (exponential, left- censored) using maximum-likelihood are the optimal structure models to track the visual field (VF) progression in patients with glaucoma. The nonlinear-exponential model provided the best-fit for the majority of the pointwise regressions. The Tobit (left-censored, nonlinear) regression model would be an appropriate candidate model to track VF perimetry for test locations that approach 0 dB.  

 

Keywords: perimetry • visual fields • detection