purpose. To determine the usefulness of confirmatory factor analysis in examination of morphometric, electrophysiological, and psychophysical quantitative methods that measure the extent of global glaucomatous damage without referring to a preselected gold standard.

methods. In a cross-sectional clinical study, 406 eyes of 203 glaucoma patients and 200 eyes of 100 normal control subjects 18 to 70 years old underwent optic disc morphometry, automated perimetry, measurement of temporal contrast sensitivity by a full-field flicker test, blue-on-yellow visually evoked potential (VEP), and black-and-white pattern-reversal electroretinogram (ERG). Diagnosis of glaucoma was based on a qualitative classification of the optic nerve head and retinal nerve fiber layer independent of intraocular pressure and visual field. Confirmatory factor analysis was performed in the patient group as a whole and in a subgroup showing moderate to advanced glaucomatous optic nerve head damage.

results. The confirmatory factor analysis models explained the data
satisfactorily (*P* > 0.18, all patients; *P* > 0.34, subgroup). Global glaucomatous damage
was quantified best by the mean defect of automated perimetry
(*r* = 0.81; *r* = 0.87), followed
by the area of the neuroretinal rim (*r* = 0.64; *r* = 0.73), the full-field flicker test
(*r* = 0.59; *r* = 0.65), the
pattern-reversal ERG amplitude (*r* = 0.54; *r* = 0.55), and the VEP peak time
(*r* = 0.55; *r* = 0.54).

conclusions. Confirmatory factor analysis allows quantification of the validity of established and new procedures that measure global glaucomatous damage using cross-sectional data. The results are not dependent on the preselection of a specific gold standard. Psychophysical testing and morphometry quantified glaucomatous damage best, compared with electrophysiological procedures.

^{ 1 }

^{ 2 }The use of correlation measures is criticized sharply by the investigators in the second study.

^{ 2 }However, if different measurement scales are compared, the use of correlation and regression analyses is characterized as at least of limited use.

^{ 2 }

^{ 3 }To our knowledge no really convincing alternatives have been proposed. Therefore, in studies concerning glaucoma, correlation analyses using accepted measures of glaucomatous damage as reference criteria are used frequently. These criteria—the gold standard—are, for example, the neuroretinal rim area (NRRA) and the mean visual field defect. This strategy, however, has several drawbacks. It is difficult to prove the validity of the gold standard (e.g., morphometry or perimetry) itself. Measures that are sensitive to the same type of glaucomatous damage (e.g., diffuse glaucomatous damage) show more similar results than measures that reflect a different pattern (e.g., localized glaucomatous damage) of the disease. Measures may be influenced by common factors independent of the disease: Different parameters derived from the same measurement or different psychophysical tests influenced by the compliance of the proband show more similar results than measures with independent errors. To cite an example, correlations among different psychophysical tests are expected to be higher than correlations between one psychophysical test and an electrophysiological or morphometric measure. If perimetry is set as the gold standard, agreement with electrophysiological measures may be underestimated, whereas agreement with psychophysical measures may be overestimated.

^{ 4 }that does not rely on the selection of a gold standard and that allows evaluation of how well diagnostic measures quantify global glaucomatous damage. We used this method to analyze five different procedures—one morphometric measurement and four tests of visual function—that have been proven

^{ 5 }

^{ 6 }

^{ 7 }to be useful in the diagnosis of the glaucomatous diseases. One particular reason for this study was the finding reported in earlier studies,

^{ 3 }that correlations between the NRRA and sensory measures, which have been observed in patients with moderate or advanced glaucomatous damage, are to a much smaller degree observed among patients in the early state of the disease.

^{ 6 }This fact may be subject to measurement errors or to the pathogenic mechanisms of the disease. We therefore investigated whether in those patients sensory measures provide

*any*information about glaucomatous damage. We restricted the analysis to measures that were sensitive to global damage, omitting measures exclusively sensitive to localized glaucomatous damage or to the variance of the damage (e.g., perimetric loss variance). We did not include methods that allow differentiation between diffuse and localized loss, such as the pattern deviation probability map.

^{ 8 }

^{ 5 }The ocular and camera magnifications were corrected according to Littmann’s method,

^{ 9 }taking into account the anterior corneal curvature and the refractive error. The standard protocol for grading of the optic disc photographs consisted of a check list including the following variables: size and shape of the optic disc, size and shape of the neuroretinal rim, shape of the optic cup, size of the optic cup in relation to the size of the optic disc, presence of disc hemorrhages, location and extent of alpha and beta zones of peripapillary atrophy, diameter of the retinal arterioles, and visibility of the retinal nerve fiber layer. This protocol was used for evaluation of all optic disc photographs. The photographs of the patients included in the study were mixed with photographs of other patients with glaucomatous or nonglaucomatous optic nerve damage and with photographs of normal subjects. The evaluations were performed in a masked fashion by two examiners who had had experience evaluating optic disc photographs of more than 2000 individuals. The coefficient of variation for the morphometric determination of the optic disc structures had been examined in a previous study.

^{ 10 }Intraobserver variation coefficients were 0.01 for the assessment of the optic disc area and 0.03 for the measurement of the optic cup area. Interobserver coefficients were 0.03. The neuroretinal rim was calculated as the difference of disc area minus cup area.

^{ 11 }(pathologic cumulative perimetric defect curves based on graphical display of ranked local defects compared with the 95th and 99th percentiles of normal curves with identification of localized, diffuse, and broadly distributed visual field losses).

^{ 6 }with a full-field bowl (58 cm in diameter) and a white flicker light was used. The test was performed under photopic conditions and required no fixation by the subject. The flicker threshold was determined at a constant frequency of 37.1 Hz at a time-average luminance of 10 candelas [cd]/m

^{2}. The mean luminance of the full-field bowl was corrected by taking into account the pupil diameter and the Stiles–Crawford effect. The contrast sensitivity was assessed using a staircase tracking procedure. The mean value of at least six threshold crossings entered the evaluation.

^{ 7 }one channel provided a high-contrast, 0.88-cyc/deg square-wave stripe pattern of blue light (460 nm, 3.3 × 10

^{2}trolands [td]), the other channel provided a homogeneous yellow adaptation light (570 nm, 1.3 × 10

^{4}td) that was superimposed on the stripe pattern. Stimulation was in the onset (200 msec)–offset (500 msec) mode. Recording was monopolar from the inion against the left ear lobe while the right ear lobe was grounded. After amplification (EMP 88 [Electronic Medicine Technique, Pölzl, Munich, Germany], filter: 0.5–70 Hz), 150 sweeps (400 msec in length) were averaged (500-Hz sampling rate). Peak time measurements of the onset responses were made from the moment of pattern onset to the peak of the main negative wave (N1). For amplitude of the black-and-white pattern-reversal electroretinogram (ERG), only one channel of the viewing system was used. The stimulus was a vertical, high-contrast (0.93), black-and-white square-wave stripe pattern with a spatial frequency of 0.88 cyc/deg. The pattern reversal was square wave and occurred at a frequency of 7.8 Hz. The mean luminance was 4263 photopic td. The responses were recorded with a carbon glide electrode hooked over the subject’s lower eye lid. After amplification (EMP 88, filter: 0.5 Hz-70 Hz, no notch filter) the responses were averaged and stored in a digital computer (IBM-AT, Armonk, NY; sampling rate 1000 Hz, 256 msec sweep,

*n*= 30). Four pattern-reversal responses, and therefore eight amplitudes, were analyzed within one sweep. A subsequent fast Fourier analysis evaluated the amplitude of the second harmonic component of a total of 240 pattern-reversal responses. In both procedures, ERG and VEP, two recordings were made to check for reproducibility.

^{ 5 }Visual field loss and intraocular pressure (IOP) were no inclusion criteria. The description of the sample, however, included visual field loss and tonometry. The definition of normal-pressure glaucoma (max IOP, ≤21 mm Hg) and open-angle glaucoma (max IOP, >21 mm Hg) was based on at least two IOP measurements before initial medical therapy.

^{2}(equivalent to the mean − 1 SD in the control group), and the other subgroup contained 297 eyes of 170 patients with NRRA of less than 1.35mm

^{2}. One hundred eighty-six of all 203 glaucoma patients had primary open-angle glaucoma, 17 had secondary open-angle glaucoma (9 primary melanin dispersion, 6 pseudoexfoliative syndrome, 1 anterior chamber angle recession after ocular contusion, 1 who developed glaucoma under systemic cortisone therapy). Three hundred fifteen of the 406 glaucomatous eyes were treated topically. On the day of examination, no subject had intraocular pressure more than 24 mm Hg.

*t*-test for independent samples. For significance testing of correlations and path coefficients (see later description) the SEs were determined by the bootstrap method and corrected according to the number of subjects, not the number of eyes. This means that, although both eyes of one patient were included, the precision of our results refers to the number of patients instead of the number of eyes. In the subgroup analyses of patients with NRRA of less than/at least 1.35 mm

^{2}, the Bonferroni correction with factor 2 was applied.

^{2}test was used. The level of significance was 0.05 (two-sided) in all statistical tests. With 203 patients, a true correlation coefficient

*r*= 0.20 was detectable with a power of 80%;

*r*= 0.25 was detectable with a power of 90%. For convenience of presentation, all procedures were rescaled so that higher values always indicated the pathologic domain. For graphical presentation of more than one procedure on the same axis of a figure, values were standardized by subtracting the mean value of the control group and dividing by the SD of this group. Nonlinear curve fitting was performed using the Lowess algorithm.

^{ 12 }All statistical analyses were conducted with commercially available software (SPSS for Windows, ver. 6.1.3; SPSS, Chicago, IL)

^{ 13 }with an integrated module (AMOS, ver. 3.6; SmallWaters; Chicago, IL).

^{ 14 }

^{ 15 }

^{ 16 }

^{ 17 }

^{ 18 }

^{ 19 }

^{ 20 }these or related approaches are rarely applied in ophthalmology, we provide a short description of how the method works.

*r*

_{1}and

*r*

_{2}. Then it can be shown by simple calculations that the correlation between the two measures, say

*r*

_{12}, would be at least equal to the product

*r*

_{1}·

*r*

_{2}. For example, if the first measure correlated to the gold standard with

*r*

_{1}equal to 0.8 and the second measure with

*r*

_{2}equal to 0.9, then the correlation

*r*

_{12}between both measures would be at least 0.72. However, under certain circumstances a correlation

*r*

_{12}would be considerably larger than

*r*

_{1}·

*r*

_{2}. This would be the case, if the two measures were also influenced by common factors different from the glaucoma disease. If both measures were psychophysical, such a common factor could be, for example, the concentration of the patient. The dependency of both measures on the concentration of the patient would increase the correlation coefficient. This, of course, would not increase the validity of both measures concerning the underlying disease. Procedures that do not share common factors different from glaucomatous damage and for which therefore

*r*

_{12}equals exactly

*r*

_{1}·

*r*

_{2}, are called conditionally independent.

*r*

_{12}between diagnostic measures can be determined. However, if at least three measures are conditionally independent, then it is possible to calculate from the pairwise correlations

*r*

_{12},

*r*

_{13},

*r*

_{23}the values of

*r*

_{1},

*r*

_{2}, and

*r*

_{3}in absence of any gold standard procedure. The system of equations

^{ 21 }

*r*

_{1},

*r*

_{2}, and

*r*

_{3}are usually called factor loadings or path coefficients. These path coefficients have values between 0 and 1. A path coefficient of 0 shows that the measurement does not contain any information about the underlying disease. A path coefficient of 1 corresponds to a measurement that perfectly quantifies the disease.

^{ 22 }This index comprises the best approximation of a gold standard by using the procedures under investigation.

^{ 23 }Second, for all pairs of measures we compared the correlations in the sample to the correlations predicted by the model. This answers the question of whether the smaller set of path coefficients is able to explain the larger set of pairwise correlations. Third, for all possible groups of three and four variables we computed the path coefficients and compared the different results. If the path coefficients differed in these analyses, this would contradict the assumptions of our model.

^{2}test.

^{ 14 }

*P*> 0.6) between patients and control subjects. Glaucoma patients were 6.5 years older than the control subjects (

*P*< 0.001). The visual acuity in the control group and the glaucoma groups was not significantly different (

*P*> 0.1). All diagnostic measurements were significantly different in the group with reduced NRRA compared with the control group (

*P*< 0.001). Significant differences between the control subjects and the subgroup with NRRA of at least 1.35 mm

^{2}were observed only for flicker sensitivity (

*P*< 0.01), but not for peak latency of the blue-on-yellow VEP (

*P*> 0.05), the NRRA, the perimetric mean defect (

*P*> 0.1 both), and the amplitude of the pattern reversal ERG (

*P*> 0.3).

*r*= 0.28,

*P*< 0.01). All correlations within the whole patient group were significant with a range of

*r*= 0.31 (amplitude of pattern-reversal ERG and peak latency of blue-on-yellow VEP) to

*r*= 0.66 (perimetric mean defect and flicker sensitivity). In the subsample of eyes with NRRA of less than 1.35 mm

^{2}the range was

*r*= 0.31 to

*r*= 0.68, with the same two pairs of measures showing the lowest and the highest correlation. In the group of glaucoma patients with rim area of at least 1.35 mm

^{2}, only the correlation between the perimetric mean defect and flicker sensitivity (

*r*= 0.53) reached statistical significance. The Spearman correlations are given for the complete glaucoma group only and are slightly reduced compared with the Pearson correlations with the exception of the amplitude of the pattern-reversal ERG for which the correlations are slightly increased (Table 2) . In Figures 3 and 4 the association of sensory measures with the NRRA is shown for the patient and control groups. The splitting of the glaucoma group into two subgroups is justified by the fact that the association of sensory measures with rim area disappears for areas of at least 1.35 mm

^{2}.

*P*> 0.18). Therefore, the hypotheses that all correlations were due to one factor, global glaucomatous loss, was acceptable, with the exception of the correlation between the perimetric mean defect and the flicker sensitivity. There was a significant additional correlation between both these measures but not between the two electrophysiological measures, peak latency of the blue-on-yellow VEP and amplitude of the pattern-reversal ERG. Inspection of the path coefficients showed a ranking of the measurements with the perimetric mean defect clearly representing best the damage of glaucomatous disease. The flicker test and the area of the neuroretinal rim followed, whereas the pattern-reversal ERG amplitude and blue-on-yellow VEP peak latency showed the lowest correlation to the common factor, global glaucomatous damage.

^{2}.

*P*= 0.34), but this was mainly due to the reduced sample size in analysis II compared with that in analysis I. When the sample size independent Holter criterion is used for reference (results not given), both models showed nearly identical fit. Again there was a significant additional correlation between perimetric mean defect and flicker sensitivity but not between the peak latency of the blue-on-yellow VEP and the amplitude of the pattern-reversal ERG. The path coefficients of the NRRA, the perimetric mean defect, and the flicker sensitivity were higher in analysis II than in analysis I, whereas for the electrophysiological procedures there were no differences between both models (Table 3) . All pairwise correlations between the five measures were predicted by the model with a deviation below 0.04 (Table 2) . The greatest difference again appeared for the correlation between the flicker sensitivity and the amplitude of the pattern-reversal ERG: The observed correlation was 0.392, and the predicted correlation was 0.356. The scatter of coefficients in 12 different subgroups of the five measurements (Table 4) was nearly identical in analysis I and analysis II. The index of global damage obtained from the reduced sample was (0.53 · MD) + (0.07 · FLI) + (0.26 · NRRA) + (0.13 · ERG) + (0.13 · VEP).

^{2}.

^{ 5 }

^{ 6 }

^{ 7 }However, it should be noted that some investigators have found that in many cases localized visual field loss would be an early indicator of beginning glaucoma.

^{ 24 }Whereas in other cross-sectional studies some procedures (e.g., perimetry and morphometry) are preselected as a gold standards, in the present analysis established methods and new experimental procedures were given identical chances to prove validity. Therefore, perimetrically detectable visual field loss was not an inclusion criterion in our sample. However, the grouping of our sample in patients and control subjects relied on the gold standard morphologic damage. The definition of glaucoma itself has been discussed widely. In the Rotterdam Eye Study,

^{ 25 }two different definitions were used to account for this problem. Therefore, in our analysis we also investigated to what degree a bias might have resulted from this design.

^{ 16 }a model with a priori hypotheses was performed to explain multistage mechanisms of activities of daily living after cataract surgery. To our knowledge in all other applications, exploratory factor analysis was used. In two studies

^{ 17 }

^{ 20 }the classic application of factor analysis, identification of underlying concepts in items of questionnaires, was performed. In one study

^{ 19 }factor analysis was used on a grouping of clinical history, preoperative findings, and operative problems to explore associations within these findings and with postoperative visual acuity. In two older studies

^{ 15 }the purely exploratory approach was also used. Principal component analysis, a method devoted to data reduction but not to exploration of correlational structures, was performed on normal visual field data

^{ 18 }in the Barbados Eye Study.

^{ 26 }

^{ 27 }In summary, to our knowledge factor analysis as a tool for avoidance of a gold standard has not been performed before in ophthalmic research.

^{2}(Table 1) . This result is in accordance with the literature.

^{ 28 }

^{ 29 }A growing number of histologic and clinical studies have convincingly shown that optic nerve damage in patients with glaucoma occurs and can be detected before conventional perimetry uncovers early visual field defects.

^{ 1 }Clinical investigations using morphologic techniques have shown that quite a number of optic nerve head variables, such as the neuroretinal rim as a whole and measured separately in various disc sectors, the shape of the neuroretinal rim, and the presence and size of peripapillary atrophy, were abnormal in some individuals with ocular hypertension but normal findings in conventional visual field examinations.

^{ 2 }In contrast, the flicker test showed a significant difference between the control group and the group with NRRA at least 1.35 mm

^{2}but was inferior to perimetry in quantifying global glaucomatous damage. Both results are not contradictory.

^{2}, we observed no correlation between the NRRA and sensory measures. Nevertheless, the analyses showed that within this subsample compared with the healthy control group the perimetric mean defect and the flicker sensitivity correlated with each other to a much higher degree, but not to the rim area. One explanation is that morphologic diagnosis of glaucoma is not based on the NRRA alone, but also on other morphologic criteria, such as the presence of localized retinal nerve fiber layer defects. We therefore conclude that also in this study group with rim area at least 1.35 mm

^{2}the psychophysical measures quantify global glaucomatous damage to a certain degree. Measures that reflect the status of disease to only a moderate degree may still be useful in early diagnosis. Also the amplitude of the ERG and the peak latency of the VEP did not show significant differences between the control subjects and the patients with NRRA of at least 1.35 mm

^{2}. Therefore, at least in patients with “normal” NRRA (but other morphologic signs that indicate glaucoma) both measures are not sensitive in early diagnosis of glaucoma.

Control Subjects | Chronic Open-Angle Glaucoma Patients | |||||
---|---|---|---|---|---|---|

NRRA ≥1.35 mm^{2} | NRRA <1.35 mm^{2} | Full Sample | ||||

Subjects (n) | 100 | 76^{*} | 170^{*} | 203^{*} | ||

Eyes (n) | 200 | 109 | 297 | 406 | ||

Gender (M/F) | 53/47 | 49/27 | 79/91 | 101/102 | ||

Age (y) | 44.7 ± 11.5 | 48.6 ± 10.9^{, †} | 51.2 ± 11.2^{, §} | 50.3 ± 11.1^{, §} | ||

Visual field loss (n yes/no) | (0/200) | (13/96) | (146/151) | (159/247) | ||

IOP (mm Hg; n elevated/normal) | 17.4 ± 2.1 (0/200) | 28.6 ± 9.6^{, §} (22/87) | 26.6 ± 7.7^{, §} (93/204) | 27.2 ± 8.3^{, §} (292/114) | ||

VA | 1.09 ± 0.12 | 1.09 ± 0.12 | 1.06 ± 0.14 | 1.07 ± 0.14 | ||

NRRA | 1.65 ± 0.3 (1.43, 1.82) | 1.61 ± 0.26 (1.43, 1.71) | 0.96 ± 0.27^{, §} (0.78, 1.18) | 1.14 ± 0.39^{, §} (0.89, 1.36) | ||

MD | 1.05 ± 1.25 (0.20, 1.79) | 1.75 ± 3.03 (0.18, 2.35) | 4.13 ± 4.81^{, §} (0.84, 5.74) | 3.49 ± 4.53^{, §} (0.60, 4.50) | ||

FLI | 1.46 ± 0.17 (1.35, 1.59) | 1.37 ± 0.22^{, ‡} (1.25, 1.51) | 1.29 ± 0.26^{, §} (1.16, 1.46) | 1.31 ± 0.25^{, §} (1.19, 1.48) | ||

VEP | 117.5 ± 8.4 (112.8, 122.3) | 120.9 ± 10.6 (113.8, 125.8) | 126.4 ± 14.0^{, §} (115.3, 134.5) | 124.9 ± 13.4^{, §} (114.6, 132.1) | ||

ERG | 3.78 ± 1.08 (3.01, 4.48) | 3.62 ± 1.01 (3.01, 4.12) | 3.09 ± 0.98^{, §} (2.35, 3.69) | 3.23 ± 1.02^{, §} (2.48, 3.86) |

**Figure 1.**

**Figure 1.**

Procedures | Control Subjects | Glaucoma Patients | ||||||
---|---|---|---|---|---|---|---|---|

NRRA ≥ 1.35 mm^{2} | NRRA < 1.35 mm^{2} | Full Sample | ||||||

Subjects (n) | 100 | 76^{*} | 170^{*} | 203^{*} | ||||

Eyes (n) | 200 | 109 | 297 | 406 | ||||

Method | Pearson | Pearson | Pearson | Pearson | Spearman | |||

NRRA–MD | −0.04 | 0.00 | 0.64^{, ‡} (0.64) | 0.53^{, ‡} (0.52) | 0.50^{, ‡} | |||

NRRA–FLI | 0.00 | 0.05 | 0.44^{, ‡} (0.48) | 0.34^{, ‡} (0.38) | 0.32^{, ‡} | |||

NRRA–VEP | −0.03 | −0.08 | 0.40^{, ‡} (0.40) | 0.33^{, ‡} (0.35) | 0.31^{, ‡} | |||

NRRA–ERG | −0.05 | −0.02 | 0.39^{, ‡} (0.40) | 0.36^{, ‡} (0.34) | 0.40^{, ‡} | |||

MD–FLI | 0.28^{, †} | 0.53^{, ‡} | 0.68^{, ‡} (0.68) | 0.66^{, ‡} (0.66) | 0.61^{, ‡} | |||

MD–VEP | 0.15 | 0.27 | 0.46^{, ‡} (0.47) | 0.45^{, ‡} (0.45) | 0.40^{, ‡} | |||

MD–ERG | 0.07 | 0.05 | 0.47^{, ‡} (0.48) | 0.42^{, ‡} (0.43) | 0.46^{, ‡} | |||

FLI–VEP | 0.00 | 0.06 | 0.38^{, ‡} (0.35) | 0.33^{, ‡} (0.32) | 0.33^{, ‡} | |||

FLI–ERG | 0.08 | 0.16 | 0.39^{, ‡} (0.36) | 0.35^{, ‡} (0.31) | 0.38^{, ‡} | |||

VEP–ERG | 0.12 | 0.17 | 0.31^{, ‡} (0.30) | 0.31^{, ‡} (0.29) | 0.33^{, ‡} |

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

NRRA | MD | FLI | VEP | ERG | |
---|---|---|---|---|---|

Full sample | |||||

Path coefficient^{*} | 0.64 ± 0.07 | 0.81 ± 0.08 | 0.59 ± 0.07 | 0.55 ± 0.07 | 0.54 ± 0.06 |

Subsample | |||||

Path coefficient^{*} | 0.73 ± 0.05 | 0.87 ± 0.05 | 0.65 ± 0.08 | 0.54 ± 0.07 | 0.55 ± 0.07 |

^{2}. Log transformation for MD and FLI; log–log transformation for VEP. The variables are rescaled so that higher values show presence of disease.

*P*> 0.18 (full sample),

*P*> 0.34 (subsample); additional correlations MD–FLI:

*r*= 0.39,

*P*< 0.05 (full sample);

*r*= 0.32,

*P*< 0.05 (subsample); ERG–VEP:

*r*= 0.03,

*P*> 0.5 (full sample);

*r*= 0.03,

*P*> 0.5 (subsample).

Path Coefficients of Selected Measurements | NRRA | MD | FLI | VEP | ERG |
---|---|---|---|---|---|

Full sample | |||||

NRRA, MD, VEP | 0.62 | 0.85 | — | 0.53 | — |

NRRA, MD, ERG | 0.67 | 0.79 | — | — | 0.53 |

NRRA, FLI, VEP | 0.58 | — | 0.58 | 0.57 | — |

NRRA, FLI, ERG | 0.58 | — | 0.58 | — | 0.61 |

NRRA, VEP, ERG | 0.62 | — | — | 0.54 | 0.58 |

MD, VEP, ERG | — | 0.78 | — | 0.58 | 0.54 |

FLI, VEP, ERG | — | — | 0.62 | 0.54 | 0.57 |

NRRA, MD, FLI, VEP^{*} | 0.62 | 0.85 | 0.58 | 0.53 | — |

NRRA, MD, FLI, ERG^{*} | 0.66 | 0.79 | 0.56 | — | 0.54 |

NRRA, MD, VEP, ERG | 0.65 | 0.81 | — | 0.55 | 0.53 |

NRRA, FLI, VEP, ERG | 0.59 | — | 0.59 | 0.55 | 0.59 |

MD, FLI, VEP, ERG^{*} | — | 0.78 | 0.62 | 0.57 | 0.54 |

Range of path coefficients | 0.59–0.67 | 0.78–0.85 | 0.56–0.62 | 0.53–0.57 | 0.53–0.61 |

Subsample | |||||

NRRA, MD, VEP | 0.75 | 0.85 | — | 0.53 | — |

NRRA, MD, ERG | 0.73 | 0.88 | — | — | 0.54 |

NRRA, FLI, VEP | 0.68 | — | 0.65 | 0.59 | — |

NRRA, FLI, ERG | 0.66 | — | 0.67 | — | 0.59 |

NRRA, VEP, ERG | 0.71 | — | — | 0.57 | 0.55 |

MD, VEP, ERG | — | 0.83 | — | 0.55 | 0.57 |

FLI, VEP, ERG | — | — | 0.69 | 0.55 | 0.57 |

NRRA, MD, FLI, VEP^{, †} | 0.75 | 0.86 | 0.62 | 0.54 | — |

NRRA, MD, FLI, ERG^{, †} | 0.72 | 0.89 | 0.65 | — | 0.54 |

NRRA, MD, VEP, ERG | 0.74 | 0.86 | — | 0.54 | 0.54 |

NRRA, FLI, VEP, ERG | 0.68 | — | 0.66 | 0.58 | 0.57 |

MD, FLI, VEP, ERG^{, †} | — | 0.83 | 0.69 | 0.55 | 0.57 |

Range of path coefficients | 0.66–0.75 | 0.83–0.89 | 0.62–0.69 | 0.53–0.59 | 0.54–0.59 |

^{2}. Log-transformation for MD and FLI; log–log transformation for VEP. The variables are rescaled so that higher values show presence of severe disease. The path coefficients measure the validity of each procedure in quantifying global glaucomatous damage. A value of 0 corresponds to a measure that contains no information about the underlying disease; a value of 1 corresponds to a measure that perfectly quantifies the disease. The rows correspond to twelve separate confirmatory factor analyses in twelve different subgroups of the five measurements. The moderate scatter of the path coefficients reflects the adequacy of confirmatory factor analysis modelling.

**Figure 5.**

**Figure 5.**

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