purpose. To evaluate the structure/function relationship between visual field sensitivity and retinal nerve fiber layer (RNFL) thickness measured by StratusOCT (Carl Zeiss Meditec, Inc., Dublin, CA) and GDx VCC (Laser Diagnostic Technologies, Inc., San Diego, CA).

methods. Eighty-nine subjects (27 who had healthy eyes, 21 who were glaucoma suspect, 41 who had glaucoma) were enrolled in this cross-sectional study. RNFL thickness was measured using the StratusOCT and the GDx VCC, and visual field (VF) was examined using the Humphrey VF analyzer. The relationship between RNFL thickness and VF sensitivity—expressed in terms of mean deviation (MD) in decibel (dB) scale, unlogged 1/lambert (L), and Advanced Glaucoma Intervention Study (AGIS) and Collaborative Initial Glaucoma Treatment Study (CIGTS) VF scores—were evaluated with linear and nonlinear regression models. Coefficient of determination (*R* ^{2}) was calculated, and regression models were compared using the Akaike information criterion and the F test.

results. In plotting MD against RNFL thickness, curvilinear regression models demonstrated the best fit, whereas linear regression attained the best associations when VF sensitivity was expressed in 1/L. However, when healthy subjects were excluded from the analyses, the second-order polynomial was better than linear regression in describing the relation between 1/L and GDx VCC–measured RNFL thickness. Regression profiles between AGIS/CIGTS VF scores and RNFL thickness were best described in the linear and the first-order inverse models for GDx VCC and StratusOCT RNFL measurements, respectively. In general, StratusOCT RNFL measurements achieved higher associations with visual function in all the respective regression analyses than did GDx VCC.

conclusions. Description of structure/function relationships in glaucoma depends on the choice of perimetry scale, the type of RNFL measuring device, and the characteristics of the studied groups. The higher association with visual function in StratusOCT RNFL measurements compared with that in GDx VCC suggested optical coherence tomography might be a better approach for evaluating structure/function relationships. Curvilinear regression profiles found between StratusOCT RNFL thickness and MD/VF scores provide an explanation for those longitudinal observations, showing that VFs with higher AGIS/CIGTS VF scores or worse MD at baseline are at higher risk for deterioration. Regression analysis of the structure/function profile could provide important information in the assessment of the trend and pattern of glaucoma progression.

^{ 1 }

^{ 2 }

^{ 3 }

^{ 4 }StratusOCT (Carl Zeiss Meditec, Inc., Dublin, CA) and GDx VCC (Laser Diagnostic Technologies, Inc., San Diego, CA) are the two latest commercially available imaging modalities designed to measure RNFL thickness. A number of recent studies have reported high correlations between VF sensitivity and RNFL thickness in glaucoma with the use of these nerve fiber analyzers. In the study by Reus and Lemij,

^{ 1 }the relationship between VF sensitivity (in decibel [dB]) and GDx VCC RNFL measurements in patients with glaucoma was found with coefficients of correlation of 0.77, 0.52, 0.46, 0.51, and 0.38 at the supratemporal, supranasal, nasal, infranasal, and infratemporal sectors, respectively. With the use of StratusOCT (Carl Zeiss Meditec), Leung et al.

^{ 4 }showed that the coefficient of correlation between VF mean deviation (MD) and average RNFL thickness was 0.79. Although statistically significant correlations were found in these studies, the structure/function relationship was primarily investigated with linear regression analysis, which may not be an adequate model to describe and fit the nonlinear portion of the relationship. In fact, a curvilinear relationship has been reported between GDx VCC (Laser Diagnostic Technologies)–measured RNFL thickness and VF sensitivity.

^{ 5 }Therefore, comparisons with linear and nonlinear regression models are essential to identify and confirm the precise nature of the structure/function relationship. The regression function would then be useful for understanding the trend and pattern of disease progression and for selecting an appropriate monitoring strategy to detect the changes.

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }

^{ 10 }

^{ 11 }

^{ 12 }To avoid the confounding effect of variability, a number of analytical procedures were suggested to determine the true progression. The Humphrey visual field analyzer (Humphrey Field Analyzer II; Humphrey Instruments, Dublin, CA) has a built-in “change analysis” option that performs linear regression analysis of the VF MD. Major clinical trials such as the Advanced Glaucoma Intervention Study (AGIS) and the Collaborative Initial Glaucoma Treatment Study (CIGTS) use defect classification scoring systems to provide a discrete score, between 0 and 20, for each VF result.

^{ 13 }

^{ 14 }The AGIS and the CIGTS define progression as an increase in VF score of 4 and 3, respectively. However, the scoring systems can be arbitrary, and the scale may not be linear. A change in score from 1 to 5 may not be equal to a change from 16 to 20. Analyzing the structure/function profiles in terms of VF scores may reveal the nature of the scaling of these scoring systems and may provide better understanding regarding the trend of disease progression observed in these trials. Using different nonlinear and linear regression models, we investigated and compared the relationship between VF sensitivity—expressed in terms of decibel unit (MD), unlogged (1/Lambert [1/L]), and AGIS/CIGTS VF scores—and RNFL thickness, measured with StratusOCT and GDx VCC, in subjects with glaucoma.

*P*< 0.05) non–edge-contiguous points, with at least one at the

*P*< 0.01 level on the same side of the horizontal meridian in the pattern deviation plot and classified outside normal limits in the glaucoma hemifield test. Any detected field defect had to be confirmed in at least one other attempt to be classified as abnormal. Average visual sensitivity was expressed in 3 different forms: MD, unlogged 1/L scale, and AGIS and CIGTS VF scores. MD represents an age-matched average visual sensitivity index expressed in decibels. It is calculated based on the total deviation plot in the Humphrey VF analysis. Differential light sensitivity at each tested location is measured in decibels, where the differential light sensitivity (dB) = 10 × log

_{10}(

*L*

_{max}/(

*L*

_{t}–

*L*

_{b}), with

*L*

_{max}is the maximal stimulus luminance,

*L*

_{t}is the stimulus luminance at threshold, and

*L*

_{b}is the background luminance. For simplicity, this relationship can be written as 10 × log

_{10}(1/L). The unlogged 1/L at each tested location was calculated by dividing the decibel unit by 10 and then unlogging it. The average value was then evaluated. Each VF in the glaucoma group was also analyzed to determine the AGIS/CIGTS VF scores. Both scoring systems use 20-interval scales, with 0 representing no defect and 20 representing severe damage. The scorings of the VFs were computed according to the original descriptions in the respective trials.

^{ 13 }

^{ 14 }

^{ 15 }The RNFL (3.4) scan (with 512 scan points) was selected for RNFL measurement. RNFL thickness was measured by averaging the results of 3 sequential circular scans with 3.4-mm diameters centered at the optic nerve head. The parameter, average RNFL thickness, is obtained in the analysis printout. A good-quality scan was defined as one with a signal-to-noise ratio of >35, 100% accepted A-scans, and well-delineated anatomic boundaries. A subject would be excluded from the study if the OCT image was not of good quality after 3 attempts. All OCT scans were of good quality, and no subject was excluded.

^{ 16 }The parameter TSINT average, equivalent to the average RNFL thickness, in the analysis printout was used in the study. Nine eyes were excluded in this study because of suboptimal scanning quality secondary to poor fixation, motion artifacts, or overilluminated images.

*P*< 0.05 was considered statistically significant.

*y*=

*ax*+

*b*) was compared with four common nonlinear models, including the second-order polynomial (

*y*=

*ax*

^{2}+

*bx*+

*c*), the third-order polynomial (

*y*=

*ax*

^{3}+

*bx*

^{2}+

*cx*+

*d*), the first-order inverse (

*y*=

*a*ln(

*x*) +

*b*), and the logarithmic regressions (

*y*=

*a*log(

*x*) +

*b*). In regression analysis, the goodness-of-fit of any particular regression model is expressed as the coefficient of determination,

*R*

^{2}, which indicates how much of the total variation in the dependent variable can be accounted for by the regression function. However, it is not possible to determine whether model A is more correct than model B in describing the relationship profile based on the value of

*R*

^{2}because the model with more parameters often has a higher

*R*

^{2}than the model with fewer parameters. The extra-sum-of-square F test and the Akaike information criterion (AIC) are two mathematical approaches that take model complexity (the number of data points and the number of parameters) into account in calculating the F ratio and the AIC difference, respectively, to determine which regression model to accept.

_{A}and SS

_{B}are the sum-of-squares and DF

_{A}and DF

_{B}are the degrees of freedom of models A and B, respectively. Probability is then computed based on the F ratio. The hypothesis is to test whether the alternative nonlinear model is better than the linear model. If

*P*< 0.05, one can conclude that the alternative nonlinear model fits better than the linear model. If

*P*> 0.05, the null hypothesis would stipulate accepting the linear model. The major drawback in using the F ratio is that it only applies to nested models when one model has more parameters (i.e., is more complex) than the other. In the current analysis, the F test was used when comparing the linear, second-order, and third-order polynomials.

^{ 17 }Because the logic behind AIC is not hypothesis testing, there is no

*P*value in the calculation. The model with the lowest AIC is more likely to be correct, and the difference in corrected AIC (AICc) between model A and model B is defined as:

*N*is the number of data points, SS is the sum-of-square of the vertical distances of the points from the regression equations, and

*K*is the number of parameters in the model plus 1. As in the F test, the difference in AICc is calculated with reference to the sum-of-squares and the number of parameters of the models compared. The probability that a particular model is correct in a comparison is given as:

*P*value of the F test (in nested models only) were computed. All these parameters, though expressed in different forms, are in agreement with each other to determine which one is the best-fit regression model.

*P*= 0.004) and the StratusOCT RNFL measurements, respectively (F test;

*P*< 0.001) and demonstrated the largest difference in AICc (7.37 and 26.42 for GDx VCC and StratusOCT RNFL measurements, respectively) with respect to the linear regression models (Fig. 1) . However, when VF sensitivity was expressed in the unlogged 1/L scale, simple linear fit had the best association with GDx VCC and StratusOCT RNFL measurements (Fig. 2) .

*P*= 0.048; difference in AICc, 1.85) when the RNFL thickness was measured by GDx VCC (Fig. 4A) . This is in contrast to the analysis in which a linear fit was better than a nonlinear fit when healthy subjects were included (Fig. 2A) . However, linear regression remained the best-fit model when RNFL thickness was measured using StratusOCT (Fig. 4B) .

*n*= 41) were analyzed and translated to the AGIS and the CIGTS VF scores according to the methods described in the respective studies.

^{ 13 }

^{ 14 }Characteristics of the VF scores are illustrated in Table 2 . The mean CIGTS VF score was higher than the mean AGIS VF score (10.57 versus 8.05;

*P*< 0.001; paired

*t*-test). AGIS and the CIGTS VF scores were highly correlated with each other and with the VF MD. Although the linear regression model best described the relationship between AGIS/CIGTS VF scores and GDx VCC–measured RNFL thickness (Figs. 5A and 6A) , nonlinear first-order inverse regression was better fit than linear regression when plotting the AGIS/CIGTS VF scores against StratusOCT-measured RNFL thickness (differences in AICc were 2.81 and 3.49 for the AGIS VF score and the CIGTS VF score, respectively; Figs. 5B 6B ). In all the respective regression analyses, StratusOCT-measured RNFL thickness attained higher

*R*

^{2}in association with different visual sensitivity measures (MD, 1/L, VF scores) than did the GDx VCC RNFL measurement.

^{ 18 }

^{ 19 }

^{ 20 }

^{ 21 }). To eliminate this factor, therefore, we excluded healthy persons in the second analysis (Fig. 3) . It was confirmed that the nonlinear models were better than the linear model (best fit with the logarithmic and the second-order polynomials for the GDx VCC and the StratusOCT RNFL measurements, respectively) in analyzing the relationship between RNFL thickness and VF MD. These regression models describe a curvilinear structure/function relationship, suggesting that the progression of visual field loss, when it is expressed in MD (dB), increases during the course of the disease. This observation is also consistent with postmortem histologic measurement in patients with glaucoma, indicating that at least 25% to 35% of retinal ganglion cells were lost before abnormalities were statistically detected through automated visual field testing.

^{ 22 }

^{ 23 }Heidelberg retina tomography (HRT)–measured neuroretinal rim area,

^{ 23 }and GDx VCC–measured RNFL thickness.

^{ 5 }It was proposed that the structure/function change is linear and that it was the decibel scaling in the VF sensitivity that gave the impression of a functional reserve in the curvilinear relationship. In these clinical studies, however, only subjects with glaucoma with mild to moderate defect were included (the mean visual field MD ± SD in the glaucoma group was –4.15 ± 3.05 dB in the study by Garway-Heath et al.

^{ 23 }and –6.9 ± 5.6 dB in that by Schlottmann et al.

^{ 5 }). Examining a full spectrum of glaucomatous optic neuropathy, from glaucoma suspect to end-stage glaucoma, would be essential to reveal the complete profile of the structure/function relationship. (In the present study, the mean visual field MD ± SD in the glaucoma group was –11.1 ± 7.74 dB; the range was –2.36 to –30.00 dB). The better fitting with a quadratic model in GDx VCC RNFL measurement among the glaucoma and glaucoma-suspect groups (Fig. 4A)suggested this relationship may vary with the composition of the study group. On the other hand, though first-order inverse regression best described the relationship between StratusOCT-measured RNFL and AGIS/CIGTS VF scores, it was the linear model that best fit in the relationships when RNFL thickness was measured by GDx VCC (Figs. 5 6) . Taking all these results into consideration, we concluded that the pattern of the structure/function relationship in glaucoma not only varied with the scale/method of expression in visual sensitivity, it depended on the choice of the RNFL imaging devices and the composition of the study groups.

^{ 24 }Yet it was recently reported that the birefringence retardation detected by SLP actually varied with the position around the optic nerve head.

^{ 25 }As a result, using a constant proportion for calculation of RNFL thickness may not reflect the true thickness in some sectors around the optic nerve head. Furthermore, changes in the SLP measurements could result from the changes in either RNFL thickness or RNFL birefringence. Morphologic alteration like gliosis, partial loss of organelles, or shrinkage of ganglion cells might lead to changes in the birefringence pattern before the irreversible loss of axons.

^{ 26 }

^{ 27 }Therefore, variations in the regression profiles of the structure/function relationship may signify the difference in the inherent measuring capacity between OCT and SLP. In the present study, the OCT RNFL measurements attained higher associations with visual function in all the respective regression analyses compared with the GDx VCC RNFL measurements. In addition, plotting of the OCT RNFL measurements against MD (dB) and the unlogged 1/L scale demonstrated consistent curvilinear and linear relationships, respectively (Figs. 1B 2B 3B 4B) , which is in greater agreement with the results from the histologic study in experimental glaucoma investigating the association between ganglion cell loss and decrease in VF sensitivity.

^{ 28 }

^{ 29 }It was reported that the relationship between sensitivity loss (in decibels) and ganglion cell loss (in percentages) was curvilinear and that it changed to a linear function when both VF sensitivity and ganglion cell loss were expressed in decibels.

^{ 28 }

^{ 29 }Collectively, we believe the use of StratusOCT may provide a better approach to understanding the structure/function relationship in glaucoma than the use of GDx VCC.

^{ 30 }This was repeated by the results in the Early Manifest Glaucoma Trial (EMGT), which reported an increased risk for progression in patients with MD worse than –4 dB.

^{ 9 }Conversely, the AGIS found that lesser VF defect increased the risk for additional VF loss.

^{ 31 }Interestingly, using the same AGIS VF scoring system, Chen and Park

^{ 10 }showed that an increased initial AGIS score was associated with progression. Although most studies supported the finding that increased severity of initial visual field was associated with further visual field worsening,

^{ 9 }

^{ 10 }

^{ 11 }

^{ 12 }

^{ 30 }

^{ 32 }others showed no association,

^{ 6 }

^{ 7 }

^{ 8 }and a few arrived at the same conclusions reported in the AGIS.

^{ 33 }

^{ 34 }In the present study, regression analysis revealed that first-order inverse regression best described the relationship between the AGIS/CIGTS VF scores and StratusOCT-measured RNFL thickness (Figs. 5B 6B) . Assuming the rate of loss of the retinal ganglion cell and its nerve fiber in glaucoma is constant during progression, our results provide an explanation for the findings in those longitudinal studies showing that increased severity of VF defect (documented by the AGIS/CIGTS VF scores or MD) at baseline indicates higher risk for progression. For the same degree of structural damage (reduction in RNFL thickness), the decrease in VF score or decibel is more dramatic in the advanced stages of the disease than in the early stages. For example, based on the regression functions in the study (Figs. 5B 6B) , a reduction in RNFL thickness from 80 to 70 μm (in the early stage) would lead to a corresponding increase in the AGIS score of 2.0 and in the CIGTS score of 2.1. When the RNFL thickness is reduced from 50 to 40 μm (in the advanced stage), the corresponding increase in the AGIS and the CIGTS scores would be 5.7 and 5.9, respectively. Therefore, it is easier to detect the change in VF progression in VF scores during the moderate/advanced stages of disease, leaving the impression of increased risk for progression when the baseline VF scores are high. Therefore, the current AGIS and CIGTS scoring systems are considered less sensitive for detecting progression in the early stages of glaucoma because the steps for progression (an increase in score of 4 in the AGIS and 3 in the CIGTS) is defined independently of the disease stage. Consistent with earlier investigations, we demonstrated the CIGTS VF scores were systematically higher than the AGIS VF scores, and both scorings were highly correlated with each other and with the VF MD.

^{ 35 }

^{ 36 }Our results are also consistent with the findings of longitudinal studies showing that the CIGTS scoring method leads to higher rates of detection of disease progression than the AGIS scoring system.

^{ 35 }

^{ 37 }

Normal | Suspect | Glaucoma | P ^{*} | |
---|---|---|---|---|

No. of subjects | 27 | 21 | 41 | — |

Age (yrs) mean ± SD | 47.9 ± 13.8 | 55.9 ± 16.6 | 59.1 ± 11.7 | 0.005^{, †} |

Refraction (D) mean ± SD | −0.37 ± 2.17 | −1.35 ± 3.34 | 0.05 ± 2.28 | 0.124 |

Visual field MD (dB) ± SD | −1.47 ± 1.03 | −1.42 ± 1.47 | −11.1 ± 7.74 | <0.001^{, ‡} |

TSNIT Average (μm) (GDx VCC) | 55.26 ± 4.32 | 52.94 ± 5.47 | 38.66 ± 7.64 | <0.001^{, ‡} |

Average RNFLT (μm) (StratusOCT) | 101.38 ± 7.73 | 96.91 ± 12.16 | 65.34 ± 14.08 | <0.001^{, ‡} |

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