Nonlinear, Multilevel Mixed-Effects Approach for Modeling Longitudinal Standard Automated Perimetry Data in Glaucoma

PURPOSE. Ordinary least squares linear regression (OLSLR) analyses are inappropriate for performing trend analysis on repeatedly measured longitudinal data. This study examines multilevel linear mixed-effects (LME) and nonlinear mixed-effects (NLME) methods to model longitudinally collected perimetry data and determines whether NLME methods provide significant improvements over LME methods and OLSLR. METHODS. Models of LME and NLME (exponential, whereby the rate of change in sensitivity worsens over time) were examined with two levels of nesting (subject and eye within subject) to predict the mean deviation. Models were compared using analysis of variance or Akaike's information criterion and Bayesian information criterion, as appropriate. RESULTS. Nonlinear (exponential) models provided significantly better fits than linear models (P < 0.0001). Nonlinear fits markedly improved the validity of the model, as evidenced by the lack of significant autocorrelation, residuals that are closer to being normally distributed, and improved homogeneity. From the fitted exponential model, the rate of glaucomatous progression for an average subject of age 70 years was -0.07 decibels (dB) per year. Ten years later, the same eye would be deteriorating at -0.12 dB/y. CONCLUSIONS. Multilevel mixed-effects models provide better fits to the test data than OLSLR by accounting for group effects and/or within-group correlation. However, the fitted LME model poorly tracks visual field (VF) change over time. An exponential model provides a significant improvement over linear models and more accurately tracks VF change over time in this cohort.