Purpose. To extract unidimensional, well-separated latent scores that are anatomically and clinically valid from 52 standardized variables collected by Humphrey visual field (VF) perimetry (Carl Zeiss Meditec, Dublin, CA).

Methods. Visual field data of 437 patients were collected and classified by a glaucoma specialist into seven clinical groups: irregularities of VF (IVF), nasal step (NaS), arcuate scotoma (AC), paracentral scotoma (PCS), blind-spot enlargement (BSE), diffuse deficit (DD), and advanced deficit (AD). The number and content of constituent variable scores were identified by principal components analysis followed by Varimax Rotation and simple clustering, taking spatial distribution homogeneity and visual system anatomy into account. Unidimensionality was checked by a stepwise Cronbach α curve. Clinical predictability of the derived scores was checked by comparing clinical groups (ANOVA).

Results. Patients older than 60 years comprised 53.3% of the sample. The average mean deviation was −9.2 dB and pattern standard deviation was 6.5 dB. Six scores were identified: four peripheral scores (nasal superior, NS; nasal inferior, NI; temporal superior, TS; and temporal inferior, TI) and two paracentral scores (PCSs; superior, PCSS; and inferior, PCSI). Cronbach α was always >0.90. The six scores decreased sequentially from IVF to DD to AD. Scores of AC were lower in NS, NI, and TS; PCSS was less in PCS; BSE scores were less in TS and TI; NaS scores were less in NS and NI.

Conclusions. Six well-separated, optimal scores were obtained from the Humphrey perimetry matrix. Internal reliability was good. It was possible to discriminate between clinical subgroups. Further analyses, based on longitudinal data, must be performed to confirm these findings.

^{ 1 }

^{ 2 }

^{ 3 }

^{ 4 }It consists of approximately 100 quantitative threshold measures that permit evaluation of retinal sensitivity. Each measure is standardized in a population free of ocular disease, and two simple statistics are calculated: mean deviation (MD) and pattern standard deviation (PSD). These indices are widely used in glaucoma clinical trials and patient follow-up.

^{ 5 }is the average of all differences between measures and their normal values, weighted by the variance observed in the general population (where

*X*

_{ i }is the measured threshold,

*N*

_{ i }is the normal reference threshold at point

*i*,

*S*

^{2}

_{1i }is the variance of normal field measurement at point

*i*, and

*n*is the number of test points).

^{ 6 }

^{ 7 }used computerized neural networks with some success to identify patients with early glaucomatous visual field loss, yielding sensitivity and specificity both >70%. To achieve this, they had to include information on the automated visual field index and other structural data.

^{ 8 }identified 11 clusters by nearest-neighbor cluster analysis performed on Octopus visual fields (Haag-Streit, Köniz, Switzerland). A discriminant analysis was performed on the 11 scores used to classify patients with and without glaucoma. The sensitivity and specificity of this classification were very good (sensitivity and specificity >90%).

^{ 7 }and Mandava et al.

^{ 8 }shared a common objective to develop a classifying algorithm that would help clinicians to detect new VFDs. Brigatti et al.

^{ 7 }directly included global perimetry indicators that assume that MD, PSD, and short-term fluctuation are the optimal information that can be retrieved from this test. However, the model produces estimators that are completely disconnected from clinical reality, and clinicians still must be persuaded by the conclusions of neural network modeling. Mandava et al.

^{ 8 }used a cluster analysis with the sole purpose of optimizing information reduction before running a discriminant analysis. However, the clusters did not respect retinal anatomy very well, for example, they spanned the vertical meridian, and almost nothing was stated about either the construct validity or the internal consistency reliability of these clusters.

^{ 8 }we believe that the scores developed should be demonstrated to be clinically relevant before they are applied in the identification and monitoring of patients with glaucoma by using specific statistical techniques—for example, neural networks or discriminant function.

^{ 9 }

^{ 10 }

^{ 11 }was plotted to check the unidimensionality of the variables yielding the score. This calculation made it possible to verify that a group of items measured the same underlying unidimensional concept (construct validity). The curvature should increase monotonically when all items belong to the appropriate score. Otherwise, items should be allocated to another score. However, because it is influenced by sample fluctuations, it should be interpreted cautiously, especially when scores contain few items.

^{ 12 }The mean of each score was compared across all seven clinical groups by ANOVA.

*n*= 34: 7.8%); nasal steps (

*n*= 126: 28.8%); arcuate scotomas (

*n*= 154: 35.2%); paracentral scotomas (

*n*= 21: 4.8%); blind-spot enlargements (

*n*= 13: 3.0%); diffuse deficits (

*n*= 26: 5.9%); and advanced deficits (

*n*= 63: 14.5%).

^{ 1 }and so the min-eigen criterion also retained six factors.

^{ 13 }was always >0.90 (Fig. 3 , the maximum value reported in the curve), demonstrating good internal reliability. Cronbach α curves for peripheral scores increased monotonically, supporting the requirement that all items should contribute to the score. However, this was not the case for central scores, although Cronbach α curves were always >0.90. Last, the decrease of curvature was small and limited to a single item.

^{ 8 }because of the algorithm used. We believe that fewer scores for retinal anatomy would be easier both to apply and understand in daily practice. Because our scores demonstrated good construct and external validity, they should assist in patient follow-up, although additional longitudinal data are needed to confirm this. Comparison with the work of Brigatti et al.

^{ 6 }

^{ 7 }is not straightforward, since their main goal was to identify patients with glaucoma. Nonetheless, our scores could be used as entry parameters in a neural network to serve the same purpose.

^{ 14 }were not calculated for our sample of patients. Therefore, a head-to-head comparison with our six scores was not possible. The AGIS investigators decided that one single clinical score was appropriate to define the severity of glaucomatous VFDs. This assumption was somewhat contradicted by our findings. Our algorithm is also simpler than that used in AGIS and can be managed with a basic calculator. Finally, we demonstrated that our six scores brought additional information to the MD.

*X*

_{1},

*X*

_{2}, … ,

*X*

_{ k }, be a set of observed variables measuring the same underlying unidimensional latent (unobserved) variable. We define

*X*

_{ ij }as the measurement of patient

*i*, where

*i*= 1, … ,

*n*, given by a variable

*j*, where

*j*= 1, … ,

*k*. The model underlying Cronbach α is a simple, mixed, one-way model:

*X*

_{ ij }= μ

_{ j }+ α

_{ i }+ ε

_{ ij }, where μ

_{ j }is a variable fixed (nonrandom) effect and α

_{ i }is a random effect with zero mean and SE σ

_{α}corresponding to patient variability. It produces the variance of the true latent measure (τ

_{ ij }= μ

_{ j }+ α

_{ i }); and ε

_{ ij }is a random effect with zero mean and SE σ corresponding to the additional measurement error. The true measure and the error are uncorrelated: cov(α

_{ i }, ε

_{ ij }) = 0.

*X*

_{ ij }, the true score τ

_{ ij }, and the error ε

_{ ij }.

*X*

_{ j }(as an instrument to measure the true value) is given by

*k*variables equals

^{ 15 }:

^{ 16 }The PCA is usually based on an analysis of the latent roots of the correlation matrix of

*k*variables

*R*, which, under the parallel model, looks as follows:

_{1}= (

*k*− 1) ρ + 1, and the other multiple roots are λ

_{2}= λ

_{3}= λ

_{4}= … = 1 − ρ = (

*k*− λ

_{1})/(

*k*− 1). Thus, using the Spearman-Brown formula, we can express the reliability of the sum of variables as:

_{1}, which in practice is estimated by the corresponding value of the observed correlation matrix and thus the percentage of variance of the first principal component in a PCA. So, CAC is also considered as a measure of unidimensionality.

^{ 11 }

^{ 16 }The first step uses all variables to compute CAC. Then, at every successive step, one variable is removed from the scale. The removed variable is that which leaves the scale with its maximum CAC value. This procedure is repeated until only two variables remain. If the parallel model is true, increasing the number of variables increases the reliability of the total score, which is estimated by Cronbach α. Thus, a decrease of such a curve after adding a variable would cause us to suspect strongly that the added variable did not constitute a unidimensional set with the other variables.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

Cluster | Nasal Superior | Nasal Inferior | Temporal Superior | Temporal Inferior | Paracentral Superior | Paracentral Inferior |
---|---|---|---|---|---|---|

Nasal superior | 1.00 | |||||

Nasal inferior | 0.58 | 1.00 | ||||

Temporal superior | 0.80 | 0.53 | 1.00 | |||

Temporal inferior | 0.53 | 0.79 | 0.65 | 1.00 | ||

Paracentral superior | 0.45 | 0.76 | 0.52 | 0.77 | 1.00 | |

Paracentral inferior | 0.80 | 0.51 | 0.78 | 0.53 | 0.56 | 1.00 |

Clinical Group | Irregularities of Visual Field n = 34 | Nasal Step n = 126 | Arcuate Scotoma n = 154 | Para-Central Scotoma n = 21 | Blind Spot Enlargement n = 13 | Diffuse Deficit n = 26 | Advanced Deficit n = 63 |
---|---|---|---|---|---|---|---|

Nasal superior | −3.50 (0.34) | −6.46 (0.45) | −13.30 (0.68) | −6.96 (1.14) | −3.42 (0.98) | −7.87 (0.98) | −23.98 (0.85) |

Nasal inferior | −3.16 (0.33) | −6.10 (0.51) | −10.16 (0.62) | −6.47 (0.92) | −3.60 (0.87) | −6.52 (0.65) | −23.48 (0.92) |

Temporal superior | −4.71 (0.46) | −4.00 (0.39) | −12.42 (0.62) | −4.68 (0.77) | −6.80 (1.77) | −7.94 (0.62) | −20.70 (0.85) |

Temporal inferior | −3.25 (0.31) | −3.16 (0.34) | −8.56 (0.51) | −3.92 (0.71) | −6.39 (1.37) | −7.96 (0.79) | −19.88 (1.13) |

Paracentral inferior | −2.42 (0.26) | −2.44 (0.29) | −5.80 (0.45) | −6.91 (1.40) | −5.65 (1.37) | −7.36 (0.71) | −18.58 (1.07) |

Paracentral superior | −2.99 (0.34) | −3.13 (0.31) | −9.60 (0.63) | −10.61 (1.25) | −4.43 (0.91) | −6.75 (0.89) | −22.00 (1.01) |

Humphrey MD (dB) | −3.19 (0.23) | −4.67 (0.31) | −10.04 (0.41) | −6.72 (0.65) | −4.49 (0.94) | −7.19 (0.61) | −22.17 (0.61) |

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**