Nonlinear, multilevel mixed-effects approach for modeling longitudinal standard automated perimetry data in glaucoma

Area of Science:

• Ophthalmology
• Biostatistics
• Medical Data Analysis

Background:

• Ordinary least squares linear regression (OLSLR) is unsuitable for analyzing trends in longitudinal perimetry data.
• Multilevel modeling offers a more appropriate framework for such data.

Purpose of the Study:

• To evaluate multilevel linear mixed-effects (LME) and nonlinear mixed-effects (NLME) models for analyzing longitudinal perimetry data.
• To determine if NLME models offer significant advantages over LME and OLSLR methods.

Main Methods:

• Examined LME and NLME (exponential) models with two nesting levels (subject and eye within subject).
• Used analysis of variance, Akaike's information criterion, and Bayesian information criterion for model comparison.

Main Results:

• Nonlinear exponential models demonstrated significantly better fits than linear models (P < 0.0001).
• NLME models improved data validity, showing reduced autocorrelation and better residual distribution.
• Calculated an average glaucomatous progression rate of -0.07 dB/year at age 70, accelerating to -0.12 dB/year by age 80.

Conclusions:

• Multilevel mixed-effects models outperform OLSLR by accounting for group effects and within-group correlation.
• Fitted LME models inadequately track visual field changes over time.
• Exponential NLME models significantly enhance the accuracy of tracking visual field changes compared to linear models.