Glaucoma Service, Dana Center for Preventive Ophthalmology, Wilmer Eye Institute, Johns Hopkins University, Baltimore, MD, USA

Health Sciences Informatics, Johns Hopkins University, Baltimore, MD, USA

Abstract

Background

The definitive diagnosis of glaucoma is currently based on congruent damage to both optic nerve structure and function. Given widespread quantitative assessment of both structure (imaging) and function (automated perimetry) in glaucoma, it should be possible to combine these quantitative data to diagnose disease. We have therefore defined and tested a new approach to glaucoma diagnosis by combining imaging and visual field data, using the anatomical organization of retinal ganglion cells.

Methods

Data from 1499 eyes of glaucoma suspects and 895 eyes with glaucoma were identified at a single glaucoma center. Each underwent Heidelberg Retinal Tomograph (HRT) imaging and standard automated perimetry. A new measure combining these two tests, the structure function index (SFI), was defined in 3 steps: 1) calculate the probability that each visual field point is abnormal, 2) calculate the probability of abnormality for each of the six HRT optic disc sectors, and 3) combine those probabilities with the probability that a field point and disc sector are linked by ganglion cell anatomy. The SFI was compared to the HRT and visual field using receiver operating characteristic (ROC) analysis.

Results

The SFI produced an area under the ROC curve (0.78) that was similar to that for both visual field mean deviation (0.78) and pattern standard deviation (0.80) and larger than that for a normalized measure of HRT rim area (0.66). The cases classified as glaucoma by the various tests were significantly non-overlapping. Based on the distribution of test values in the population with mild disease, the SFI may be better able to stratify this group while still clearly identifying those with severe disease.

Conclusions

The SFI reflects the traditional clinical diagnosis of glaucoma by combining optic nerve structure and function. In doing so, it identifies a different subset of patients than either visual field testing or optic nerve head imaging alone. Analysis of prospective data will allow us to determine whether the combined index of structure and function can provide an improved standard for glaucoma diagnosis.

Background

For decades, ophthalmologists have recognized a relationship between the structure of the optic nerve and its function in patients with glaucoma

Glaucomatous functional deficits similarly result from ganglion cell loss, with defects in visual sensitivity found in the receptive fields of the damaged neurons. This relationship between optic nerve head topography and visual function is so fundamental to our understanding of the disease that it is used clinically to differentiate damage due to glaucoma from other diseases of the optic nerve head. In fact, one or both of these measures have been used as inclusion criteria and primary outcome measures in the major clinical trials of glaucoma

It is logical that the two approaches, structural and functional, should give information that is highly correlated, since both depend on atrophy of retinal ganglion cells whose anatomical and physiological features are known. On the other hand, data from clinical trials have failed to confirm a strong concordance between changes in optic nerve and visual field criteria. In the Ocular Hypertension Treatment Study, for example, treated subjects met both field and optic nerve criteria for change only 8% of the time, while 42% reached the visual field end point alone and 50% reached the optic disc end point alone

Hence, the merging of the two sets of data could provide important corroboration that true abnormality had developed or was progressing. This has not been previously done in optimal fashion for a variety of reasons. First, there has been no attempt to combine quantitatively structural and functional deficits using continuous probabilities of abnormality for each measure. Rather, specific cut-off criteria at extreme probability levels are given in current imaging or field analysis. These values have been chosen to maximize the specificity of each test, though at the cost of sensitivity. Second, there has been no consensus regarding a map between the position of a field deficit and corresponding structural changes to the NFL thickness or optic nerve head topography. Some proposed models for matching structure and function used probabilistic approaches that produced findings inconsistent with known anatomic facts--linking superior visual field defects to superior optic disc abnormality, for instance

We believe a single measure combining these elements is an improvement for 4 reasons. First, quantitative measures of optic nerve structure and function are increasingly available and improving in quality. Second, the discordance between simultaneous progression suggests that both structure and function contain complementary information. Third, a reliable mapping of visual field points to the optic nerve head and nerve fiber layer is available. Finally, modulation of the variability of structural and functional tests by emphasizing those that are anatomically related will reduce the overall variability of the system. To test the hypothesis that a combined measure of optic nerve structure and function might be able to detect glaucoma, we designed the Structure Function Index (SFI) as a model unifying retinal ganglion cell structure and function. The link between the two was created using our knowledge of retinal nerve fiber layer anatomy. We then analyzed the characteristics of the model and compared it to tests of structure and function alone in terms of distinguishing eyes with glaucoma from eyes of glaucoma suspects.

Methods

This work was approved by the institutional review board of the Johns Hopkins University School of Medicine and adhered to the tenets of the Declaration of Helsinki.

Study Populations

Evaluation of the SFI required three groups of subjects: 1) A

We identified subjects for the

Similarly, glaucoma cases were identified as those subjects with a diagnosis of open angle glaucoma (ICD-9 365.11), a 'Reliable' visual field and at least 'Acceptable' quality HRT on the same day.

In cases where both eyes were available for a particular subject in the

To validate the diagnoses obtained using billing data, we randomly selected the clinical chart records of 100 subjects identified as glaucoma suspects and 103 subjects identified as having open angle glaucoma. Of the 100 records reviewed for glaucoma suspects, 97 supported the billing diagnosis based on the clinician's written assessment of the patient. Of the remaining three, one had angle closure glaucoma, one had no glaucoma diagnosis in the chart, and one had neurological disease. Of 103 records reviewed from those subjects with billing codes for open angle glaucoma, 99 had glaucoma (one angle closure), 3 were suspects and 1 had non-glaucomatous optic nerve disease. Based on this review, we can therefore estimate that only about 4% of billing codes do not accurately reflect the clinician's assessment. Furthermore, the number of misclassified individuals is similar in each group (suspect and glaucoma) so there should be no net bias of the classifier performance.

Defining the Structure Function Index

In brief, the SFI is calculated in three steps: 1) calculate a probability of abnormality for each point in the visual field, 2) calculate a probability of abnormality for each sector of the optic disc, and 3) combine those probabilities with the probability that a visual field point and optic disc sector are linked by retinal nerve fiber layer anatomy. As defined, the SFI produces one probability of structure-function abnormality for each point tested in the visual field. To allow the SFI to be compared to current diagnostic criteria, we analyzed these individual pointwise SFI values in a manner similar to the Glaucoma Hemifield Test

Definition of Reference Values

To calculate the probability of abnormality for each visual field point, we require reference data for each of those points. The probabilities of abnormality reported by the standard output of the HFA include only a small number of discrete cutoffs near the far end of the probability distribution function (p = 5%, 2%, 1%, 0.5%)

Second, we extracted HRT data for the 1000 reference eyes from our clinical database and generated empiric distributions for the difference between measured rim area and the rim area predicted by Moorfields regression analysis (MRA)

Example distributions of structural and functional data

**Example distributions of structural and functional data**. The distribution of HFA Total Deviation at the point 3 degrees to the right and 15 degrees above fixation (A), and the distribution of the difference between measured and predicted rim area for the inferior-temporal sector of right eyes in the reference group (B). The same values from the glaucoma group are plotted in C and D. The line in each figure represents the cumulative probability function (CPF) for each distribution and helps to demonstrate the probability of normality concept used in the SFI calculation. Values to the left have low probabilities of normality (low values of the CPF) and values to the right have high probabilities of normality (high values of CPF).

Linking Points in the Visual Field to Points on the Optic Disc

The third step in calculating the SFI links rim area to each field point based on a map developed using nerve fiber layer defects seen in red-free photographs

Probability of association between a visual field point and the optic disc

**Probability of association between a visual field point and the optic disc**. Probability of insertion around the optic nerve head for a visual field point 3 degrees to the right and 15 degrees above fixation in a right eye. The vertical lines indicate boundaries between the six standard sectors analyzed by the HRT. Calculating the area under the curve for each sector, the probability of this point being associated with the inferior-nasal sector is 26% and with the inferior-temporal sector is 74%.

Quantitative Combination of Structure and Function

Once the reference values are available for the tests of structure, function, and for the anatomical relationship between the two, the SFI is calculated for each of the 52 points outside the blind spot in the 24-2 pattern visual field by multiplying the three probabilities described above together and summing over all HRT sectors:

Where P(field) is the probability that the visual field point is abnormal (one minus the cumulative probability value defined above), P(sector) is the probability that an HRT sector is abnormal (using the cumulative probability function defined above), and P(anatomy) is the probability that the visual field point is linked to that sector of the nerve. Using this formula, the SFI will be close to 0 in cases where the probabilities of abnormality for the field and disc are small or when the two are unlikely to be linked by RNFL anatomy. It is also the case that when there is a modest probability of a defect in function and a modest probability of a defect in structure, the fact that the two are in linked by RNFL anatomy increases the value of the SFI compared to when they are not linked.

As an explicit example of how the SFI is calculated at each corresponding visual field point, assume we start with a visual field total deviation of -7 at the point 3°,15°. The probability that this value is "normal" can be obtained using the cumulative distribution shown in Figure ^{2 }and that the area predicted by Moorfields regression is 0.20 mm^{2}. The difference between these two measures (0.05) falls at the 98% point on the distribution shown in Figure

Distribution of Structure Function Index values

**Distribution of Structure Function Index values**. Distribution of values for the structure function index at the point 3 degrees to the right and 15 degrees above fixation in right eyes of the reference (A) and glaucoma (B) groups.

The SFI Hemifield Test

As defined above, the SFI produces values for an overall probability of abnormality corresponding to each point in the visual field. Since it is known that glaucoma often affects one hemifield (upper or lower) differentially, due to the presence of the horizontal raphe, we implemented an SFI Hemifield Test (SFI-HT) which is an algorithm similar to the Glaucoma Hemifield Test (GHT) used in the HFA

Regions for the Structure Function Index Hemifield Test (SFI-HT)

**Regions for the Structure Function Index Hemifield Test (SFI-HT)**. Regions defined for the Structure Function Index Hemifield Test (SFI-HT) in a visual field from a right eye.

As the SFI values within a region become closer to 1 (100% probability of abnormality), the value of the region score increases. The formula above is derived directly from that used for calculating region scores in the GHT. Because this value can reach very high levels as the SFI value becomes very small, we limited the score for any one point to a maximum of 100 (SFI value of 99.9%). The maximum score for a given region depends on the number of points included (3 to 6) and can therefore range from 300 for region 1 to 600 for region 4. The difference in the score between paired superior and inferior regions was then used to identify defects that might be due to glaucoma.

To define a reference distribution for the difference in hemifield score for each cluster pair, we again used the 1000 subjects in the reference population defined above. We calculated the SFI at each point in the visual field, calculated the region scores, and then calculated the differences between corresponding superior and inferior region pairs. Recognizing that upper to lower differences disappear when damage is severe in both hemifields, we also calculated the sum of all SFI-HT region scores. This value was included in the analysis to account for eyes with damage too diffuse to produce a significant superior-inferior difference in scores. Based on the 500 right and 500 left eyes, we were able to generate empiric distributions for the five differences in hemifield region scores and for the sum of region scores. When subsequently analyzing the glaucoma suspect and glaucoma subjects, we determined which of these six values was most statistically abnormal by comparing each to the corresponding empiric distribution from the reference population. To allow for receiver operating characteristic (ROC) analysis to be performed, each subject was summarized with the single largest probability of abnormality among its five regional score differences (Figure

Statistical Analysis

The demographics of the glaucoma and glaucoma suspect groups were compared using the t-test for age, Fisher's exact test for sex, and the chi-square test for racial background. The data for race are based on self-report as recorded in the Johns Hopkins Hospital patient registration system.

The SFI and the SFI-HT were calculated for each eye in the glaucoma group and for those eyes in the glaucoma suspect group that were not used as the reference population. Receiver operating characteristic analysis was then performed to characterize the ability of the SFI to distinguish eyes with glaucoma from eyes of glaucoma suspects. The probability of the most abnormal difference in SFI-HT region scores or of the sum of all SFI values was used as the summary statistic for the SFI with the clinical diagnosis serving as the "true" classification. To compare the SFI-HT to existing diagnostic criteria that rely on structure or function alone, we performed ROC analysis using the HFA mean deviation (MD) and the difference between actual and predicted rim area from the HRT. We also calculated the sensitivity and specificity of the HFA GHT and the categorical HRT Moorfields classification (MFC). The results of these two tests were considered positive for glaucoma when they were reported as "Outside Normal Limits". Areas under the ROC curves were compared using the method of Hanley and McNeil

Visual field and HRT data were analyzed using Matlab (version 7.11.0, The Mathworks, Inc., Natick, MA) and statistical analyses were performed using Matlab, and R version 2.11.1

Results

The test group of glaucoma suspects was significantly younger and contained a higher proportion of females than the glaucoma patients (Table

Characteristics of the glaucoma suspect and glaucoma patient groups.

**Glaucoma Suspects**

**(n = 499)**

**Glaucoma Patients**

**(n = 895)**

**p-value**

Age (years)

52(15)

65(13)

<0.001

Sex (% female)

65

52

<0.001

Race (%)

0.18

White

69

70

Black

17

17

Asian

3.4

3.2

Hispanic

1.8

0.5

Indian

0.8

0.1

Other

4.0

5.9

Unknown

3.5

3.3

HFA MD (dB)

-0.46(1.7)

-6.3(8.3)

<0.001

HFA PSD (dB)

1.8(1.0)

4.9(4.0)

<0.001

Distribution of visual field mean deviation

**Distribution of visual field mean deviation**. Frequency distribution of visual field mean deviation (MD) in 499 glaucoma suspects and 895 glaucoma patients.

As part of the review of clinical records for 100 of the glaucoma suspects, we determined that 48% were suspects based on the appearance of their optic nerve, 23% based on a history of elevated intraocular pressure, 11% based on family history, 6% based on the appearance of their anterior chamber angle, 4% based on their visual field, and 8% for other reasons. A cup-disc ratio was recorded for 189 eyes from these 100 suspects and the mean of these values was 0.49 with a standard deviation of 0.17. For comparison, a documented cup-disc ratio was found for 184 eyes of the 103 subjects reviewed in the glaucoma group and the mean was 0.76 with a standard deviation of 0.20.

SFI values were calculated for each member of both the suspect and glaucoma groups. The 52 SFI values for each subject were then summarized with a single value using the SFI-HT. As described above, the SFI-HT is a single probability value representing the most statistically abnormal difference between the upper and lower members of the 5 region pairs or the overall sum of region scores. To determine which hemifield regions are most likely to be abnormal in each group, the frequency with which each of these six values (five hemifield differences and sum of all regions) was most statistically abnormal is shown in Figure

Distribution of the most abnormal SFI-HT regions

**Distribution of the most abnormal SFI-HT regions**. Distribution of the statistically most abnormal difference between corresponding superior and inferior SFI-HT regions for 499 suspect and 895 glaucoma eyes. The SFI-HT region numbers correspond to the regions in Figure 3 and Sum refers to the sum of all region scores (to account for diffuse loss).

We assessed the ability of the SFI-HT to distinguish eyes with glaucoma from those that were suspicious for disease using ROC analysis (Figure

Receiver Operating Characteristic analysis

**Receiver Operating Characteristic analysis**. Receiver Operating Characteristic (ROC) analysis of the Structure Function Index Hemifield Test (SFI-HT), Humphrey Field Analyzer Mean Deviation (MD), pattern standard deviation (PSD) and difference between predicted and actual Heidelberg Retina Tomograph rim area. Each test was used to distinguish a group of 499 eyes from glaucoma suspects from a group of 895 eyes with glaucoma. The areas under the SFI-HT, MD, PSD, and HRT MRA curves are 0.78, 0.78, 0.80, and 0.66 respectively. The performance of the HFA Glaucoma Hemifield Test (GHT) and HRT Moorfields Classification (MFC) are also shown along with the performance of defining as abnormal any subject with either of these tests outside normal limits. Error bars represent 95% confidence intervals for sensitivity and specificity.

To further characterize the performance of the SFI and other diagnostic tests, we visualized the values of the tests pairwise for both the suspect and glaucoma groups. Examples include plots of visual field MD (Figure

Relationship between the SFI-HT and visual field mean deviation

**Relationship between the SFI-HT and visual field mean deviation**. Relationship between the Structure Function Index Hemifield Test (SFI-HT) and visual field mean deviation (MD) in the glaucoma suspect group (A) and the glaucoma group (B).

Relationship between the SFI-HT and values for difference from predicted HRT rim area

**Relationship between the SFI-HT and values for difference from predicted HRT rim area**. Relationship between the Structure Function Index Hemifield Test (SFI-HT) and HFA difference from predicted rim area in the glaucoma suspect group (A) and the glaucoma group (B).

Diagnosis of glaucoma by different methods

**Diagnosis of glaucoma by different methods**. Venn diagram of positive diagnostic tests in the 1058 members of the suspect and glaucoma groups with visual field mean deviation greater than -5dB. SFI = Structure Function Index Hemifield Test, GHT = Glaucoma Hemifield Test, MFC = Moorfields classification, OAG = clinical diagosis.

Discussion

These results characterize a potentially new approach to the diagnosis of glaucoma. Whereas the clinical diagnosis of glaucoma requires that defects in optic nerve structure and function should be found together, there is currently no test available to quantitatively combine measures of both structure and function. We propose the SFI as such a test. We have explicitly defined it to overcome some of the limitations of current testing. First of all, it utilizes continuous probabilities of abnormality rather than relying on the highly specific "abnormal" determinations of each device. The use of continuous probabilities has also been proposed for analysis of visual field data

The results presented above show some desirable characteristics of the SFI. We see that the values of the SFI in the reference population are heavily skewed toward the expected (lower) values (Figure

The ROC data also suggest that the SFI is a useful synthesis of structure and function. First of all, while the total area under the curve is not significantly different from those of MD and PSD, it does show higher sensitivity at the highest specificity values. The Venn diagram in Figure

The areas under our ROC curves are lower than some prior studies using other patient populations and other diagnostic tests. This is likely due to the fact that we purposefully studied a challenging classification problem by attempting to distinguish a group of glaucoma suspects from those classified as glaucoma. Studies that evaluate the ability to discriminate between eyes with glaucoma and normals would be expected to find more striking differences, though this comparison does not duplicate the problem encountered by clinicians. To that end, we chose to use glaucoma suspects to define our normal values since they are, in fact, the group that clinicians are most often forced to differentiate from patients with early glaucoma. It is seldom a dilemma in clinical practice to distinguish a patient with low glaucoma risk (no family history of glaucoma, normal optic nerve appearance, normal visual field, normal IOP) from someone with manifest disc or field change. On the other hand, it is a frequently encountered problem to determine which patients with clear risk factors (strong family history, "suspicious" discs, non-specific field changes, elevated IOP) have disease and which do not. By choosing to use suspects as our reference group, we are therefore making the classification problem more difficult, but also more applicable to clinical practice.

Previous research on combining measures of structure and function used regression models that included variables from various optic nerve analyses and from automated perimetry

Another area of investigation that has some relationship to what we present here is the modeling of structural and functional changes in glaucoma. Starting with the assumption that changes in sensitivity at a particular point in the visual field should correlate closely with changes in nerve fiber layer thickness or the number of ganglion cells, both Harwerth

Analysis of our study is clearly limited by the fact that it was carried out retrospectively. Specifically, the diagnostic criteria used by the clinicians as expressed in the billing code data were not standardized, so there is potential variability in diagnostic classification. We confirmed the validity of our diagnostic coding by reviewing a subset of charts, revealing a small error rate compared to the documented clinical impression and no evidence for bias in misdiagnosis favoring either group. Any study of glaucoma faces the difficulty that diagnostic criteria are either objective or subjective. When specific imaging and field criteria are chosen, there is the possibility that expert clinicians would differ on those criteria. When subjective expert judgment is the defining rule, one must be concerned that the result is not reproducible by some other group of experts. Clinician diagnostic biases may therefore be embedded in the characteristics of the two groups in this study and only through application of the method to other databases, collected prospectively, and with a variety of diagnostic criteria, will the ultimate value of the method be demonstrated.

A related issue with the glaucoma subjects used to test the SFI is that a significant portion of them has a visual field mean deviation with a value greater than 0 (Figure

Conclusions

Given the widespread availability of quantitative measures of optic nerve structure and function, clinicians now must combine those measures in a subjective manner. We believe there is a compelling need to develop computational models that unify visual field and optic nerve imaging data, based on known anatomy, to improve glaucoma diagnosis. The features of the SFI were intended to explicitly model our understanding of changes in optic nerve structure and function in glaucoma. Furthermore, the approach we have defined is not restricted to the testing modalities used here. The SFI could just as easily be calculated using other tests of visual function (frequency doubling perimetry, short wavelength perimetry, etc.) and other tests of optic nerve structure (optical coherence tomography, scanning laser polarimetry). Use of spectral domain OCT is particularly promising as it may be possible to image the nerve fiber layer in each retinal region corresponding to a visual field location. Relating structure and function in this way would avoid the use of the field-to-disc maps discussed above.

Based on the characteristics of the SFI in eyes with glaucoma and those merely suspected of having disease, we believe further work is warranted and that this approach, or one like it, might provide a new standard for diagnosing glaucoma.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

MB contributed to the design the SFI method and the study, analyzed the data, and drafted and approved the manuscript. HQ contributed to the design of the SFI method and the study, and drafted and approved the manuscript.

Acknowledgements

This work was supported by grants EY015025, and EY001765 from the National Eye Institute, Bethesda, MD, by William T. Forrester, and by a grant to the Wilmer Eye Institute from Research to Prevent Blindness, New York, NY.

Pre-publication history

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