Competing/conflicts of interest: No stated conflict of interest.
Examination of the performance of different pointwise linear regression progression criteria to detect glaucomatous visual field change
Article first published online: 4 NOV 2011
© 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists
Clinical & Experimental Ophthalmology
Volume 40, Issue 4, pages e190–e196, May/June 2012
How to Cite
De Moraes, C. G., Liebmann, C. A., Susanna Jr, R., Ritch, R. and Liebmann, J. M. (2012), Examination of the performance of different pointwise linear regression progression criteria to detect glaucomatous visual field change. Clinical & Experimental Ophthalmology, 40: e190–e196. doi: 10.1111/j.1442-9071.2011.02680.x
Funding sources: Supported by the Prince Khalid bin Abdullah al-Saud Research Fund of the New York Glaucoma Research Institute, New York, NY, USA.
- Issue published online: 14 JUN 2012
- Article first published online: 4 NOV 2011
- Accepted manuscript online: 8 SEP 2011 12:17PM EST
- Received 28 February 2011; accepted 12 August 2011.
- trend analysis;
- visual field
Background: We aimed to investigate the performance of five different trend analysis criteria for the detection of glaucomatous progression and to determine the most frequently and rapidly progressing locations of the visual field.
Design: Retrospective cohort.
Participants or Samples: Treated glaucoma patients with ≥8 Swedish Interactive Thresholding Algorithm (SITA)-standard 24-2 visual field tests.
Methods: Progression was determined using trend analysis. Five different criteria were used: (A) ≥1 significantly progressing point; (B) ≥2 significantly progressing points; (C) ≥2 progressing points located in the same hemifield; (D) at least two adjacent progressing points located in the same hemifield; (E) ≥2 progressing points in the same Garway-Heath map sector.
Main Outcome Measures: Number of progressing eyes and false-positive results.
Results: We included 587 patients. The number of eyes reaching a progression end–point using each criterion was: A = 300 (51%); B = 212 (36%); C = 194 (33%); D = 170 (29%); and E = 186 (31%) (P ≤ 0.03). The numbers of eyes with positive slopes were: A = 13 (4.3%); B = 3 (1.4%); C = 3 (1.5%); D = 2 (1.1%); and E = 3 (1.6%) (P = 0.06). The global slopes for progressing eyes were more negative in Groups B, C and D than in Group A (P = 0.004). The visual field locations that progressed more often were those in the nasal field adjacent to the horizontal midline.
Conclusions: Pointwise linear regression criteria that take into account the retinal nerve fibre layer anatomy enhances the specificity of trend analysis for the detection glaucomatous visual field progression.
Glaucomatous visual field (VF) progression can be determined using event- or trend-based analyses. In event-based techniques, each subsequent VF test is compared with a set of baseline tests, with progressive loss defined using a binary outcome (progression vs. no progression).1–3 Trend-based analysis, on the other hand, uses all available VF data and plots the values of global VF indices or the sensitivity of tested points into a linear regression, which ultimately provides a slope (rate of VF change) and its significance (P-value).3–6
The major randomized clinical trials used different methods of event-based analysis.7–11 Recent reports have shown that this yields different progression results, as sensitivities and specificities for each analysis differ.2,3 These differences, along with the use of different study populations, may help explain the different risk factors for progression and the relative role of intraocular pressure reduction on the prevention of VF progression in each of the trials. Similarly, because of the growing interest in applying trend analysis to different populations as a means to determine progression outcomes and objective values of rates of VF change, it is important to investigate the sensitivity and specificity of different progression criteria using this approach. The purpose of the current study is twofold: (i) to map the most frequently and most rapidly progressive VF locations using trend analysis; and (ii) to investigate the performance of five different progression criteria of trend-based analysis in detecting VF progression in a population with treated, established glaucoma.
The study was approved by the New York Eye and Ear Infirmary Institutional Review Board and followed the tenets of the Declaration of Helsinki. This is a retrospective cohort and includes glaucoma patients seen in a referral practice within a 10-year period (New York Glaucoma Progression Study). Details of the selected population have been described elsewhere.12,13 All eyes had glaucomatous optic neuropathy based on clinical examination of the optic nerve complex (diffuse or localized neuroretinal rim thinning or retinal nerve fibre layer loss, cup-to-disc ratio >0.6 or inter-eye asymmetry >0.2, in the absence of other retinal or neurological abnormality that could explain these findings) and associated VF loss. Abnormal VF results were defined as a glaucoma hemifield test outside normal limits or the pattern standard deviation at P < 0.05 on at two consecutive baseline VF tests. The two baseline tests required reliability indices better than 25% in order to be included.
We used pointwise linear regression (PLR) analysis, in which linear regression is performed not only for each VF test point (pointwise progression), but also by averaging the sensitivities of all points in the VF (global progression). We performed automated PLR using commercially available software (PROGRESSOR, Version 3.3, Medisoft, Ltd., Leeds, UK). Details of the software have been described elsewhere.4 In brief, PROGRESSOR automatically calculates global and pointwise rates of VF change in decibels (dB) per year as well as the level of significance of the slopes (P-values). We used the steepness of the slopes generated by PLR as a measure of the velocity of VF progression in each case.
We used the default definition for a significantly progressing point provided by the manufacturer, which has also been used by other investigators,14,15 that is, a VF test point was flagged as statistically significantly progressing if the slope of sensitivity over time was <−1.0 dB loss/year, with P < 0.01. For edge points when using the 24-2 strategy (the two nasal-most points), we used a stricter slope criterion of <−2.0 dB loss/year (also with P < 0.01) because of their greater variability.16
We tested five criteria for VF progression.
- • Criterion A: An eye was considered to be progressing if any VF test point on the entire VF map (54 points) met the aforementioned criteria.
- • Criterion B: An eye was considered to be progressing if at least two points on the entire VF map met the above criteria, regardless of their location.
- • Criterion C: An eye was considered to be progressing if at least two points in the same hemifield met the above criteria.
- • Criterion D: An eye was considered to be progressing if at least two adjacent points in the same hemifield met the above criteria.
We compared the number of eyes reaching a progression end–point using each of the different criteria. Even though there is currently no gold-standard method to define VF progression (either using event- or trend-based analysis), we based our analyses on the assumption that glaucomatous eyes often have progressive VF loss over time, resulting, therefore, in negative slopes, which would differ based on the steepness (velocity of progression). Because of the lack of an external method that would allow differentiating false-positive from true-positive progression, we applied the same model defined by Strouthidis et al.18 in which eyes presenting positive slopes were unlikely to be presenting VF change because of glaucoma – and more likely related to variability of threshold sensitivities, for instance. Therefore, the number of eyes reaching a progression end–point that presented pointwise positive slopes (>+1.0 dB/year with P < 0.01) was used to estimate false-positive results, or the specificity of each criterion.18 We also compared the global and pointwise rates of VF change of those eyes reaching each progression criterion to determine whether they could influence on the steepness of the slopes.
Analysis of variance (anova) with Student–Newman–Keuls post hoc correction was used to compare global and pointwise rates of VF change among progressing eyes of each group. McNemar's test was used to compare the number of eyes reaching progression end–points among groups. Statistical significance was defined at P < 0.05. Computerized analyses were performed using MedCalc software (MedCalc, Inc., Mariakerke, Belgium).
Five hundred eighty-seven eyes (587 patients) were selected. The mean number of VF tests analysed per patient was 11.1 ± 3.0, spanning 6.4 ± 1.7 years. The mean baseline MD and pattern standard deviation values were −7.1 ± 5.1 and 6.6 ± 3.7 dB. Forty-eight per cent of patients had a baseline MD ≥−6.0 dB, 36% between −6.0 and −12.0 dB, and 16% ≤−12.0 dB.
Table 1 shows the number of progressing eyes, as well as the number of eyes presenting positive slopes based on each criterion. Criterion A, as expected, yielded the greatest number of eyes progressing (300 eyes), but also demonstrated the highest proportion of progressing eyes with positive slopes (13/300 = 4.3%). Criterion D, on the other hand, showed the smallest number of progressing eyes (170 eyes) and also the smallest proportion of false-positive results (2/170 = 1.1%). McNemar's test showed a significant difference in progression detection rates among all groups (Table 2).
|Population Parameters||Criterion A||Criterion B||Criterion C||Criterion D||Criterion E|
|Number of progressing eyes (%)||300 (51)||212 (36)||194 (33)||170 (29)||186 (32)|
|Number of progressing eyes with positive slopes (%)†||13 (4.3)||3 (1.4)||3 (1.5)||2 (1.1)||3 (1.6)|
|Progression Criteria||Criterion A||Criterion B||Criterion C||Criterion D||Criterion E|
Figure 2 shows the mean global and pointwise rates of VF change of progressing eyes based on each criterion, respectively. Groups B, C, D and E had more negative global slopes than the standard group (Group A, anova, P = 0.004), even though there was no significant difference among Groups B, C, D, and E. For pointwise rates of change, there was no statistically significant difference among all groups (anova, P = 0.77).
To investigate whether follow-up time and the number of VF tests influenced on the detection rates of each criterion, we plotted the absolute and relative progression rates at different time points, as shown in Figure 3. However, the standard criterion (Criterion A) was more sensitive to progression among patients with a shorter follow-up period (3 to 5 years), followed by criteria B and D. This trend was also more evident among eyes with longer follow-up periods.
Because Criterion D yielded the highest specificity, we further investigated the 170 eyes that progressed based on that criterion to determine the test points most frequently reaching a progression end–point, as well as their respective velocities of change (dB/year). Each point of the 24-2 strategy (54 points) was given a code and data from left eyes were adjusted so that the summed data could be presented as right eyes only. We excluded the two points above and below the blind spot, leaving 52 analysed points. As the edge points required a stricter slope of −2.0 dB/year, which could falsely result in greater velocities for these locations on our map, we considered the same slope of >−1.0 dB for all 52 points for the purpose of determining the median velocity for each point in this study.
Finally, two maps were created using the data from the 170 progressing eyes. Because continuous variables (rates of VF change) were not distributed normally, median values were calculated for each test point.
The 170 eyes (170 patients, mean age 67.0 ± 12.8 years, 56% women, 90% Caucasians) underwent an average of 12.3 ± 3.5 VF tests spanning 6.7 ± 1.7 years. Figure 4 shows the VF map with the most frequently progressing test points of the entire cohort. Points in the superior and nasal fields progressed most frequently (20–25% of all progressing eyes). Figure 5 shows the median and 10th percentile of the velocities (dB/year) of VF change for each test point. Similarly, test locations in the nasal field showed the most rapid rates of change (median −2.5 to −3.0 dB/year).
We investigated the performance of different PLR criteria to determine glaucomatous VF progression and found that the number of progressing points in the field and their spatial relationship significantly affected the rates of detection of VF progression using trend analysis. We obtained better results when we applied methods that required at least two points corresponding to the same retinal nerve fibre layer bundle (Groups D and E).
Similar to what has been reported for event-analysis,2,3 it is important to investigate which trend analysis progression criteria most accurately identify eyes with VF progression, while minimizing the number of false-positives. This study aimed to compare different progression criteria in a population with treated glaucoma using commercially available software to perform PLR. With growing interest in trend analysis to identify risk factors associated with VF progression,14,19,20 as well as the need to compare structural and functional tests using trend analysis,21,22 it may become useful to have common and standard methods to detect progression with better sensitivity and specificity. It is also important to define criteria that minimize the risk of falsely identifying patients as progressing, as progression determination increases the risks and costs to the patient associated with advancing treatment.
Other investigators have also attempted to develop more specific methods to define progression using PLR. Gardiner and Crabb23 compared different PLR methods and similarly found that the PLR criterion set as default by PROGRESSOR (Criterion A) was the most sensitive, but at the expense of high false-positive rates. The authors proposed the new ‘Two-Omitting’ and ‘Three-Omitting’ method, using two confirmation fields in a novel fashion, which significantly increased the specificity of PLR. Their methods differ from ours as they do not take into account spatial relationships between points, but rather confirm or deny the standard PLR method by adding or removing final VF data. The authors also used a Virtual Eye simulation, that is, a computerized system that simulated ‘stable’ and ‘progressing’ eyes based on the variability (‘noise’) between a series of tests. Our study used a real-world treated glaucoma population where mathematical assumptions may not apply. Moreover, our approach does not remove or add VF data to the analysis, but rather uses all available VF information from the patient to determine the slopes and their significance (P-value). We also believe our proposed criteria are easier to be applied clinically.
In 1995, Fitzke et al.24 also proposed a model of spatial filtering using Gaussian and median image processing filters and showed that these techniques may improve the reliable detection of VF loss using computerized perimetry. However, Spry et al.25 suggested that Gaussian spatial filtering reduces PLR discriminatory ability with reduced true progression rates or small progressive defect sizes and, therefore, would be of limited use for detection of VF progression. Additional factors that affect the sensitivity and specificity of PLR are the criteria used to define the slope of the regression and its significance. Using flatter slopes (e.g. <−0.5 dB/year) and less stringent P-values (e.g. P < 0.05) as opposed to the values used in this study (<−1.0 dB/year, P < 0.01) would have resulted in a more sensitive method to detect progression at the expense of lower specificity. Therefore, our findings can only be interpreted based on the specific PLR criteria applied to our sample.
Strouthidis et al.26 compared a novel spatial filter27 (which takes into account the physiologic orientation of nerve fibres) with the ‘Three-Omitting’ PLR method and found a similar specificity with a higher sensitivity to detect progressing eyes when the spatial filter was used. The main advantages of using filtering methods that take into consideration the pattern of the RNFL are reduced time and reduced dependence on confirmatory testing. In addition to that, the method with best clinical performance in our study (two adjacent points in the same hemifield) requires no sophisticated computerized analysis, but rather the mere visual inspection of the operator/investigator, similar to what is done using current criteria of glaucomatous VF abnormality.28
It should be emphasized that there is currently no gold-standard method to define glaucomatous progression. Therefore, our definitions of sensitivity and specificity were based on a method previously reported in the literature that assumes that eyes presenting pointwise positive slopes are unlikely to present true glaucoma progression, therefore treated here as false-positive results. Future studies capable of describing a gold-standard method to define progression should test the validity of this assumption.
New information provided by our study is how fast, on average, a particular point and its neighboring points may progress if treatment is not modified. Our study provides indirect evidence of where to search for VF progression in eyes with established glaucoma, as well as to estimate the future sensitivity loss of specific test points. For instance, the two superior paracentral points of the 24-2 VF in our study progressed in more than 20% of progressing eyes with a median rate of progressive loss of −2.5 to −3.0 dB/year once the eye was flagged as progressing based on the most specific criterion. This information could be used to target treatment and could be potentially used by automated perimetric algorithms to search more intently within areas at increased risk of progression. In 1987, Heijl et al.16 reported the first map describing the normal variability of static perimetric threshold sensitivity in a normal population, as well as the normal age-related slope of sensitivity over time. Even though the normal rate of VF change for each test point is very slow among normal subjects (ranging from −0.36 to −0.82 dB per decade), their pattern resembles the one described in the present study. This supports the hypothesis that glaucoma corresponds to an accelerated ageing process in which retinal ganglion cell death occurs at a much faster rate than would be expected compared with normal subjects because of various reported risk factors (intraocular pressure, ageing, central corneal thickness, blood pressure).7–11 A similar conclusion has been suggested using a structural test comparing normal subjects with glaucoma patients followed longitudinally.29 As opposed to that hypothesis, if sensitivity loss seen in normal subjects with ageing was due solely to lens opacification, one would not expect the specific pattern of functional16 and structural29 changes that have been previously described. Using trend analysis, the pattern of progressive VF loss in glaucoma resembles the sensitivity loss seen in normal, ageing subjects, even though the rate of sensitivity change is substantially more rapid in glaucoma. One should be reminded, however, that our study assumes linearity of VF progression using a trend-based approach, even though it remains unclear whether this assumption is appropriate for all patients and VF test locations.30–32
In summary, we confirmed that the current standard PLR progression criterion (Criterion A) is very sensitive and may have applicability in studies in which a greater sensitivity to detect progressing points in the VF is warranted. However, this method may result in high rates of false-positives, which may limit its clinical usefulness or its applicability in assessing risk factors for progression. Rather, methods requiring at least two progressing points following the physiologic pattern of progressive VF loss significantly improve the specificity of PLR in a rapid and easy fashion. Also, this is the first study to use trend analysis to describe the location and velocity of points within the VF that progress most frequently in a population with established and treated glaucoma undergoing documented functional progression in clinical practice. This information may be useful in focusing VF testing strategies in areas of the VF at greatest risk for progression.
- 28Automated Static Perimetry, 2nd edn. St. Louis: Mosby, Inc., 1999., .