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Nonlinear Mixed-Effects Modeling of MNREAD Data

¹From the Department of Psychology, The University of Hong Kong, Hong Kong SAR, China; and the ²Department of Psychology, University of Minnesota, Minneapolis, Minnesota.

PURPOSE. It is often difficult to estimate parameters from individual clinical data because of noisy or incomplete measurements. Nonlinear mixed-effects (NLME) modeling provides a statistical framework for analyzing population parameters and the associated variations, even when individual data sets are incomplete. The authors demonstrate the application of NLME by analyzing data from the MNREAD, a continuous-text reading-acuity chart.

METHODS. The authors analyzed MNREAD data (measurements of reading speed vs. print size) for two groups: 42 adult observers with normal vision and 14 patients with age-related macular degeneration (AMD). Truncated sets of MNREAD data were generated from the individual observers with normal vision. The MNREAD data were fitted with a two-limb function and an exponential-decay function using an individual curve-fitting approach and an NLME modeling approach.

RESULTS. The exponential-decay function provided slightly better fits than the two-limb function. When the parameter estimates from the truncated data sets were used to predict the missing data, NLME modeling gave better predictions than individual fitting. NLME modeling gave reasonable parameter estimates for AMD patients even when individual fitting returned unrealistic estimates.

CONCLUSIONS. These analyses showed that (1) an exponential-decay function fits MNREAD data very well, (2) NLME modeling provides a statistical framework for analyzing MNREAD data, and (3) NLME analysis provides a way of estimating MNREAD parameters even for incomplete data sets. The present results demonstrate the potential value of NLME modeling for clinical vision data.