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Colleen Kummet, Gideon Zamba, Trudy Burns, Paul Romitti, Paul Artes, Carrie Doyle, Chris Johnson, Michael Wall; Linear, Tobit and Nonlinear Exponential Regression Modeling of Visual Field Data. Invest. Ophthalmol. Vis. Sci. 2013;54(15):3942.
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© ARVO (1962-2015); The Authors (2016-present)
This glaucoma progression statistical modeling study compared the goodness-of-fit of linear, nonlinear exponential, and tobit regression models of longitudinal visual field series data to determine an appropriate model for analysis of these data.
Visual field data for 52 locations (blind spot locations excluded) in each of 96 glaucomatous eyes, one/subject, were collected using the Humphrey Field Analyzer II 24-2. The Goldmann size III stimuli were used with 24-2 SITA Standard. The dataset included visual field exams at 9 time points taken every 6 months over 4 years. Locations with ≥8 floor (0dB) sensitivity values were excluded. Maximum likelihood was used for the estimation of model parameters and the Akaike information criterion (AIC) was computed. Models with the lowest AIC were determined to be the best fitting for that location. The Wilcoxon Signed Rank test was used to determine if the pairwise differences in AIC values between the normal linear, nonlinear exponential, and the tobit regression models were significant within each subject. The R statistical software package was used.
Of the 4740 visual field locations, the tobit regression model fit the data as well or better than the normal model in 99.98% of locations (88.5% the AICs were the same, 11.5% the tobit AIC was lower). Across all subjects, the difference in AIC generated by the normal model and the tobit model was significantly, positively correlated with the number of floor observations (Spearman r=0.99, p<0.0001) indicating that as more 0dB values are present, the advantage of fitting the tobit model increases. Examination of intra-subject differences in AIC, showed that the tobit regression model fit significantly better in 41.7% of subjects. These subjects had significantly lower mean defect (MD) at baseline (p<0.0001); with a MD=-10.3 on average for those in which the tobit model fit better, and MD=-4.3 on average in those with no significant difference between the normal linear and tobit models.
Our results show that these visual field location data were best fit by the tobit model when floor observations are recorded. The tobit model is particularly useful for subjects with advanced disease such as seen in progressive glaucoma. Increased precision in modeling may contribute to accurate and early detection of visual field change and consequently early treatment to preserve visual function.
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