**Purpose: **:
We have shown previously that a nonlinear exponential model fits longitudinal series of mean deviation (MD) better than a linear model. This study extends that work to investigate the mode (linear versus nonlinear) of change for pointwise sensitivities.

**Methods: **:
Data from 475 eyes of 244 clinically managed participants were analyzed. Sensitivity estimates at each test location were fitted using two-level linear and nonlinear mixed effects models. Sensitivity on the last test date was forecast using a model fit from the earlier test dates in the series. The means of the absolute prediction errors were compared to assess accuracy, and the root means square (RMS) of the prediction errors were compared to assess precision.

**Results: **:
Overall, the exponential model provided a significantly better fit (*P* < 0.05) to the data at the majority of test locations (69%). The exponential model fitted the data significantly better at 85% of locations in the upper hemifield and 58% of locations in the lower hemifield. The rate of visual field (VF) deterioration in the upper hemifield was more rapid (mean, −0.21 dB/y; range, −0.28 to −0.13) than in the lower hemifield (mean, −0.14 dB/y; range, −0.2 to −0.09).

**Conclusions: **:
An exponential model may more accurately track pointwise VF change, at locations damaged by glaucoma. This was more noticeable in the upper hemifield where the VF changed more rapidly. However, linear and exponential models were similar in their ability to forecast future VF status.

**Translational Relevance: **:
The VF progression appears to accelerate in early glaucoma patients.

^{1,2}In clinical practice and research, attempts have been made to measure and predict the rate of VF change and various techniques have been developed to measure such change over time.

^{3–5}Studies done in the past have examined various statistical techniques to identify models that can describe VF decay and predict future VF test results. McNaught et al.

^{2}analyzed data using curve fitting software. They showed that complex polynomial models provided the best fit to VF data, but were less accurate when used for forecasting. They recommended less complex linear models for fitting and prediction, and argued against using curvilinear models. Caprioli et al.

^{6}explored VF progression in glaucoma using linear, quadratic, and nonlinear exponential models. They concluded that glaucomatous VFs progressed nonlinearly and an exponential decay model provided the best fit and better prediction for VF data. Kummet et al.

^{7}systematically evaluated criteria that can be applied to pointwise regression to assist in deciding if clinically useful progression has occurred. Most recently, Bryan et al.

^{8}examined fit and predictive ability of various linear and nonlinear models. None of the models they examined were found to be superior for fitting and prediction. However, they recommended using an uncensored linear model as the best compromise between fitting and forecasting.

*P*values for assessing the significance of change in VF series.

^{6}which assumes that the rate slows over time. This is an important issue, not only because it can inform us about the glaucomatous disease process, but also because the two models produce very different predictions of the likely VF status several years in to the future, as can be seen from Figure 1.

^{9}an analysis of VF MD demonstrated that a nonlinear model fit seemed better for MD. The overall goal of the current study is to validate and extend those findings, assessing whether pointwise VF sensitivity data are better described by a linear or nonlinear (exponential) model by examining sensitivity data at each of the 52 nonblind spot test locations in the 24-2 VF. In addition, we quantify and compare the ability of the linear and exponential models for predicting future VF results.

^{9}Data from 475 eyes of 244 clinically managed participants with early glaucoma or with high-risk ocular hypertension from the ongoing Portland Progression Project at Devers Eye Institute in Portland, OR, USA were used. The study protocol was approved by the Legacy Health Institutional Review Board. This study complies with the provisions of the Declaration of Helsinki. Consent was obtained from all participants after they were informed about the risks and benefits of participation.

^{10,11}systemic hypertension,

^{12}peripheral vasospasm,

^{13}migraine,

^{14}self-reported family history of glaucoma,

^{15}and/or previously documented glaucomatous optic neuropathy or suspicious optic nerve head appearance (cup-disc ratio asymmetry >0.2, neuroretinal rim notching or narrowing, disc hemorrhage

^{16,17}), African ancestry,

^{11}and diet-controlled diabetes.

^{18}Participants having visual acuity worse than 20/40 in either eye or who had worse than mild cataract or media change at baseline were excluded. Other exclusion criteria included any other disease or use of any medications likely to affect the VF, or having undergone intraocular surgery (except for uncomplicated cataract surgery).

^{20}The 24-2 test pattern and the Swedish Interactive Threshold Algorithm (SITA) were used to collect all VF data.

^{21}An optimal lens correction was placed before the tested eye and an eye patch was used to occlude the fellow eye. All participants had previous experience with VF testing before entering the study and most had performed multiple previous tests. The VF tests with >33% fixation losses or false negatives, or >15% false positives, were considered unreliable and excluded. Eyes with baseline MD ≤ −6 dB also were excluded from the analyses. Participants with six or more observations per eye meeting the reliability criteria were included in the analyses. Distributions of the sensitivity estimates (left) and MDs (right) at baseline are illustrated in Figure 2. Likewise, the average of baseline sensitivity data and corresponding standard errors are shown in Figure 3.

_{1}.age + β

_{2}.t + ε) and nonlinear (exponential, Sens = μ − e

^{(β}

_{1}

^{+ β}

_{2}

^{.age) t}+ ε) models with two levels of grouping (participant, eye within participant) were fitted to the sensitivity data. Within group errors (ε) of the fitted models were assessed using the continuous autoregressive (CAR1 [Φ]) method to determine whether serial correlation was present in the data. The CAR1 (Φ) mode serial correlation suggests that the correlation between error terms of longitudinal data decreases exponentially with the duration between them. Follow-up time (year) and the age at time of testing (a risk factor for glaucomatous progression

^{11}) were used as covariates. The following four mixed effects models were constructed and compared at each VF location, as detailed in our previous study

^{9}; M1, linear change over time, uncorrelated residuals; M2, linear change over time, auto-correlated residuals; M3, nonlinear (exponential) change over time, uncorrelated residuals; and M4, nonlinear change over time, auto-correlated residuals.

*P*< 0.05) than model M2 at two VF locations, and model M2 fitted the data significantly better (

*P*< 0.05) than model M1 at four VF locations. Models M1 and M2 were statistically equivalent (

*P*> 0.05) at 46 (88%) VF locations. Similarly, between the two exponential models (M3 and M4), model M3 performed significantly better (

*P*< 0.05) than model M4 at six VF locations (

*P*< 0.05), and model M4 was significantly better (

*P*< 0.05) than model M3 at three VF locations. In addition, models M3 and M4 were not significantly different (

*P*> 0.05) at 43 (83%) VF locations.

*P*< 0.05) than the linear model. In the lower hemifield, the exponential model provided a significantly better (

*P*< 0.05) fit to the data than the linear model at 15 (58%) of the VF locations.

*P*= 0.26).

^{6}The model we describe has individualized offsets (baseline value) and rate of change. Moreover, when extrapolated back in time, the proposed exponential model used here asymptotes to a flat region that can be thought of as representing the predisease state.

^{9}

^{22,23}An exponential decline in dB sensitivity, according to our model, corresponds to a constant rate of change on a linear scale. Therefore, if we assume that change in dB is linear, we are implicitly assuming that the proportion of remaining retinal ganglion cells that die per year is approximately constant throughout the series (e.g., 10% of the remaining cells per year). By contrast, the exponential model used in this study implicitly assumes that the number of retinal ganglion cells that die per year remains approximately constant. Distinguishing between these two possibilities may provide important information about the glaucomatous disease process.

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