Defining 10-2 Visual Field Progression Criteria Exploratory and Confirmatory Factor Analysis Using Pointwise Linear Regression Carlos Gustavo de Moraes, MD,1,2 Christian Song, MD,1 Jeffrey M. Liebmann, MD,1,2 Joseph L. Simonson, BA,2 Rafael L. Furlanetto, MD,2 Robert Ritch, MD2,3 Purpose: To test different visual field progression criteria using trend analysis in a glaucoma population followed with long sequences of 10-2 tests as a first attempt to understand and document rates of progression in the central field. Design: Retrospective cohort study. Participants: We included 146 eyes of 146 patients with established glaucoma. Methods: Pointwise linear regression analysis using the methods of ordinary least squares was performed on the 68 test locations of the 10-2 visual field sequences. Threshold sensitivities at each test location were plotted as the dependent variable against follow-up time as the independent variable. Statistically significant progression or improvement of a visual field test point was defined if its regression slope measured 1.0 dB/year or þ1.0 dB/year, respectively, at P < 0.01. We explored sets of criteria to define visual field progression, generating a hypothetical sensitivity (progression), specificity (improvement), and progression-to-improvement ratio (PIR) for each criterion. The criterion with the highest PIR was deemed the one with best performance. Latent class analysis (LCA) was used to determine visual field sectors with highest inter-correlation. Main Outcome Measures: The performance of different visual field progression criteria to detect fast rates of mean deviation (MD) change. Results: Median baseline 10-2 MD value was 12.0 dB (interquartile range [IQR], 6.7 to 17.8 dB), and the median rate of 10-2 MD change over time was 0.38 dB/year (IQR, 0.07 to 0.77 dB/year). The highest PIR was obtained with the progression criterion requiring at least 3 test points located in the same LCA-derived 10-2 visual field sector progressing faster than 1.0 dB/year at P < 0.01. This criterion was further validated for content and convergence. Conclusions: This is the first study to investigate progression criteria for 10-2 visual fields using rates of change and to test their performance and validity. These findings may be useful to improve the monitoring of patients with glaucoma at different levels of functional loss and to develop new perimetric algorithms that scrutinize specific visual field locations for a more accurate detection of progression. Ophthalmology 2014;121:741-749 ª 2014 by the American Academy of Ophthalmology. Supplemental material is available at www.aaojournal.org.
Standard automated perimetry (SAP) is a widely accepted reference standard for the assessment of visual function in glaucoma.1e3 Data provided by SAP enable ophthalmologists to detect stage and monitor and manage disease onset and progression to produce more favorable functional outcomes. The most commonly used SAP testing methods use static strategies and test locations spaced by 6 degrees, with the innermost test locations 3 degrees away from the horizontal and vertical meridians. Statistical packages aid in data interpretation.4 Increasing attention in the medical literature is being given to the importance of evaluating the macular region and central field in glaucoma not only to diagnose 2014 by the American Academy of Ophthalmology Published by Elsevier Inc.
disease5e9 but also to monitor progression.10e12 Despite the lack of consensus, the macular area can be defined as the region within 8 degrees from the foveal center.5 This region has the highest retinal ganglion cell (RGC) density and is vital for everyday visual function. Although this area represents less than 2% of the retinal area, it contains more than 30% of the RGCs.13 In addition, 10 degrees of the central field correspond to more than 60% of the primary visual cortex in humans as a function of cortical scaling.14,15 However, the central 8 is tested with a 24-2 SAP strategy using only 4 (7%) of its 54 test points. Thus, it is not surprising that eyes with glaucomatous damage can have an abnormal 10-2 test result but a normal 24-2 test
ISSN 0161-6420/14/$ - see front matter http://dx.doi.org/10.1016/j.ophtha.2013.10.018
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Ophthalmology Volume 121, Number 3, March 2014 result.5,16 For longitudinal analysis and detection of progression, this matter becomes even more dramatic given the lack of objective methods, such as inbuilt statistical packages, to define 10-2 progression using event- or trend-based approaches. In part, this is due to a lack of a reference database showing the inter-test variability of 10-2 fields for statistical analysis. From a patient perspective, loss of vision in the central visual field may have a large impact on quality of life, including loss of contrast sensitivity, driving ability, mobility, and reading.17e20 Although no consensus yet exists on the best method of detecting glaucoma progression, trend-based analysis with pointwise linear regression (PLR) has emerged as a useful way of evaluating longitudinal visual field data with less dependence on baseline and normative reference data than event-based analyses.21e27 The PLR and other trend-based methods of visual field progression analysis have been shown to have sensitivity and specificity comparable to event-based methods used in randomized controlled trials25e27 and can be more sensitive than those methods in eyes followed with longer sequences of visual field tests.25 Global visual field indices (e.g., mean deviation [MD] and pattern standard deviation) and threshold sensitivities of individual test points can be analyzed to obtain a slope (rate of change, decibels [dB]/year) and its statistical significance indicated by a P value. By assuming visual field progression to be linear,28 this information is used to predict future visual field outcomes and visual disability, thereby facilitating clinical determination of the appropriate level of treatment. Prior studies have investigated and compared the performance of different progression criteria using 24-2 or 30-2 SAP tests, including event- and trend-based methods.21e27 However, to the best of our knowledge, there are no studies investigating the performance of 10-2 progression criteria despite the importance of central field evaluation. As a first attempt to understand and document rates of progression in the central field, we tested different visual field progression criteria using trend analysis in a glaucoma population followed with 10-2 tests.
Methods The study was approved by the New York Eye and Ear Infirmary Institutional Review Board and followed the tenets of the Declaration of Helsinki. In this retrospective cohort study, we reviewed the charts of consecutive patients who were seen in a glaucoma referral practice during a 2-month period and who had at least 5 prior 10-2 visual field tests (SITA-standard, Humphrey Field Analyzer; Carl Zeiss Meditec, Inc., Dublin, CA) during their course of disease management. All selected patients had established glaucoma. Glaucoma was defined as the presence of glaucomatous optic neuropathy and repeatable glaucomatous visual field loss on 24-2 examinations. Glaucomatous optic neuropathy was defined by the presence of diffuse or localized neuroretinal rim thinning of the optic nerve, diffuse or localized retinal nerve fiber layer (RNFL) loss, or cup-todisc ratio >0.6 with an inter-eye asymmetry >0.2 (not explained by differences in optic disc size). Repeatable glaucomatous visual field loss was determined if the eye had at least 2 consecutive 24-2 SITA tests with a glaucoma hemifield test outside normal limits
742
and a pattern standard deviation worse than 95% of the normative values. We only analyzed 10-2 visual field tests with less than 25% fixation losses and false-positive and false-negative results. Eyes with baseline best-corrected visual acuity 50% of the total variance. The Kaiser method defines the number of sectors by including only the factors with eigenvalues >1. Once the number of sectors is defined, one needs to determine what group of visual field test points belongs to each sector. This is often done by looking at the factor loadings of a confirmatory factor analysis. It is commonly accepted that factor loadings >0.40 indicate a good relationship.30 Fitting statistics used in LCA are measures of how well the model correlation matrix reproduces the observed correlation matrix. We used a combination of methods, the Comparative Fit Index, Tucker Lewis Index, chisquare, standardized root mean square residual, Akaike Information Criterion, Bayesian Information Criterion, and root mean square error of approximation, to determine the goodness of the fit of our model based on the number of visual field sectors and what test points belong to each sector.39 Similar statistical principles applied in LCA have been used in perimetry studies that aimed to develop spatial filters for progression using 24-2/30-2 perimetry.40,41 In brief, both methods use the covariances or
correlations between sensitivities at each pair of points in the eye to define the clusters with the strongest relationship with another. Given the lack of an objective method to evaluate 10-2 visual field progression, 2 glaucoma specialists masked to all clinical data graded each visual field sequence of our sample and defined progression on the basis of their visual inspection and a modified version of the ParrisheHodappeAnderson criteria for progression. To be deemed as progressing, the visual field results were required to have 1 or a combination of the following patterns: (1) development of a new defect in a previously normal area of the field (defined as pattern deviation [PD] probability at P > 0.05) with a decrease of sensitivity 5 dB in the PD graph; (2) expansion of a previously abnormal area (defined as any cluster with PD probability at P < 0.05 in the PD graph); and (3) deepening in sensitivity of a previously abnormal area by 10 dB in the PD graph. Either of the patterns described had to be repeatable on the last 2 examinations when compared with the 2 baseline ones. Consensus was required to define progression versus stable. In cases where no consensus was reached, a third glaucoma expert adjudicated. For convergence validation purposes, we tested the performance of the progression criterion with the highest PIR in our final analysis in 2 ways: (1) We calculated the area under the curve (AUC) of the receiver operating characteristic (ROC) using the 102 visual field progression criteria results (progression vs. stable) as the binary classification variable and the 10-2 MD slope (dB/year) as the continuous variable. For comparison purposes, the same method was performed using the clinicians’ grading as the classification variable. The AUC-ROC is a statistical method that has long been used in medicine and other fields to test the performance of diagnostic tests and diagnostic criteria based on a reference binary classification system.42 It is based on the fact that any gain in sensitivity always happens at the cost of a decrease in specificity and vice versa. In an ROC curve, the true positive rate (sensitivity) is plotted in function of the false-positive rate (1-specificity) for different cutoff points of a parameter, which was the 10-2 MD rate of change in our study. Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular rate of 10-2 visual field change. The AUC-ROC is a measure of how well a parameter can distinguish between 2 diagnostic groups (progressing vs. stable). The “x” axis represents false-positive rates (1-specificity), and the “y” axis represents the sensitivity for the test. The values can range from 0.0 to 1.0, the latter meaning perfect performance, which would theoretically happen if a test had 100% sensitivity and 100% specificity (or 0% false-positives). The area below the diagonal line represents an AUC-ROC of 0.5, meaning the test has a 50% chance of providing the correct result, which is equivalent to guessing or flipping a coin. The goal is to have a curve above the diagonal line within the entire range of false-positive results (1-specificity, “x” axis). Values >0.7 (70%) are considered moderate to good; a value of 0.8, for instance, means that the test has an average sensitivity of 80% for all possible values of specificity.42 (2) Because the macular sensitivity correlates with the best-corrected visual acuity,19,43,44 we compared the number of Snellen chart lines lost during follow-up between progressing and stable groups on the basis of optimized PIR (OPIR). Statistical analyses were performed using STATA software (version 12.0; StataCorp LP, College Station, TX) and Mplus software (version 6.12; Muthen & Muthen Inc., Los Angeles, CA). The alpha level used to define statistical significance was set at 5%. Adjustments for multiple comparisons (e.g., Bonferroni, Tukey’s, and least significant difference) were not performed because these corrections may not be needed when the comparisons are complementary and only a few planned observations are performed.45
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Ophthalmology Volume 121, Number 3, March 2014
Results A total of 146 eyes of 146 patients were included in the study. Each eye underwent a median of 8 visual field tests (interquartile range [IQR], 6e13; range, 5e65) spanning a median of 7.5 years (IQR, 4.7e11.8; range, 1.5e21.1 years). Mean baseline 10-2 MD value was 12.0 dB (IQR, 6.7 to 17.8; range, 1.09 to 32.3 dB). Seventy-five eyes (51.3%) had a baseline MD
Standard automated perimetry (SAP) is a widely accepted reference standard for the assessment of visual function in glaucoma.1e3 Data provided by SAP enable ophthalmologists to detect stage and monitor and manage disease onset and progression to produce more favorable functional outcomes. The most commonly used SAP testing methods use static strategies and test locations spaced by 6 degrees, with the innermost test locations 3 degrees away from the horizontal and vertical meridians. Statistical packages aid in data interpretation.4 Increasing attention in the medical literature is being given to the importance of evaluating the macular region and central field in glaucoma not only to diagnose 2014 by the American Academy of Ophthalmology Published by Elsevier Inc.
disease5e9 but also to monitor progression.10e12 Despite the lack of consensus, the macular area can be defined as the region within 8 degrees from the foveal center.5 This region has the highest retinal ganglion cell (RGC) density and is vital for everyday visual function. Although this area represents less than 2% of the retinal area, it contains more than 30% of the RGCs.13 In addition, 10 degrees of the central field correspond to more than 60% of the primary visual cortex in humans as a function of cortical scaling.14,15 However, the central 8 is tested with a 24-2 SAP strategy using only 4 (7%) of its 54 test points. Thus, it is not surprising that eyes with glaucomatous damage can have an abnormal 10-2 test result but a normal 24-2 test
ISSN 0161-6420/14/$ - see front matter http://dx.doi.org/10.1016/j.ophtha.2013.10.018
741
Ophthalmology Volume 121, Number 3, March 2014 result.5,16 For longitudinal analysis and detection of progression, this matter becomes even more dramatic given the lack of objective methods, such as inbuilt statistical packages, to define 10-2 progression using event- or trend-based approaches. In part, this is due to a lack of a reference database showing the inter-test variability of 10-2 fields for statistical analysis. From a patient perspective, loss of vision in the central visual field may have a large impact on quality of life, including loss of contrast sensitivity, driving ability, mobility, and reading.17e20 Although no consensus yet exists on the best method of detecting glaucoma progression, trend-based analysis with pointwise linear regression (PLR) has emerged as a useful way of evaluating longitudinal visual field data with less dependence on baseline and normative reference data than event-based analyses.21e27 The PLR and other trend-based methods of visual field progression analysis have been shown to have sensitivity and specificity comparable to event-based methods used in randomized controlled trials25e27 and can be more sensitive than those methods in eyes followed with longer sequences of visual field tests.25 Global visual field indices (e.g., mean deviation [MD] and pattern standard deviation) and threshold sensitivities of individual test points can be analyzed to obtain a slope (rate of change, decibels [dB]/year) and its statistical significance indicated by a P value. By assuming visual field progression to be linear,28 this information is used to predict future visual field outcomes and visual disability, thereby facilitating clinical determination of the appropriate level of treatment. Prior studies have investigated and compared the performance of different progression criteria using 24-2 or 30-2 SAP tests, including event- and trend-based methods.21e27 However, to the best of our knowledge, there are no studies investigating the performance of 10-2 progression criteria despite the importance of central field evaluation. As a first attempt to understand and document rates of progression in the central field, we tested different visual field progression criteria using trend analysis in a glaucoma population followed with 10-2 tests.
Methods The study was approved by the New York Eye and Ear Infirmary Institutional Review Board and followed the tenets of the Declaration of Helsinki. In this retrospective cohort study, we reviewed the charts of consecutive patients who were seen in a glaucoma referral practice during a 2-month period and who had at least 5 prior 10-2 visual field tests (SITA-standard, Humphrey Field Analyzer; Carl Zeiss Meditec, Inc., Dublin, CA) during their course of disease management. All selected patients had established glaucoma. Glaucoma was defined as the presence of glaucomatous optic neuropathy and repeatable glaucomatous visual field loss on 24-2 examinations. Glaucomatous optic neuropathy was defined by the presence of diffuse or localized neuroretinal rim thinning of the optic nerve, diffuse or localized retinal nerve fiber layer (RNFL) loss, or cup-todisc ratio >0.6 with an inter-eye asymmetry >0.2 (not explained by differences in optic disc size). Repeatable glaucomatous visual field loss was determined if the eye had at least 2 consecutive 24-2 SITA tests with a glaucoma hemifield test outside normal limits
742
and a pattern standard deviation worse than 95% of the normative values. We only analyzed 10-2 visual field tests with less than 25% fixation losses and false-positive and false-negative results. Eyes with baseline best-corrected visual acuity 50% of the total variance. The Kaiser method defines the number of sectors by including only the factors with eigenvalues >1. Once the number of sectors is defined, one needs to determine what group of visual field test points belongs to each sector. This is often done by looking at the factor loadings of a confirmatory factor analysis. It is commonly accepted that factor loadings >0.40 indicate a good relationship.30 Fitting statistics used in LCA are measures of how well the model correlation matrix reproduces the observed correlation matrix. We used a combination of methods, the Comparative Fit Index, Tucker Lewis Index, chisquare, standardized root mean square residual, Akaike Information Criterion, Bayesian Information Criterion, and root mean square error of approximation, to determine the goodness of the fit of our model based on the number of visual field sectors and what test points belong to each sector.39 Similar statistical principles applied in LCA have been used in perimetry studies that aimed to develop spatial filters for progression using 24-2/30-2 perimetry.40,41 In brief, both methods use the covariances or
correlations between sensitivities at each pair of points in the eye to define the clusters with the strongest relationship with another. Given the lack of an objective method to evaluate 10-2 visual field progression, 2 glaucoma specialists masked to all clinical data graded each visual field sequence of our sample and defined progression on the basis of their visual inspection and a modified version of the ParrisheHodappeAnderson criteria for progression. To be deemed as progressing, the visual field results were required to have 1 or a combination of the following patterns: (1) development of a new defect in a previously normal area of the field (defined as pattern deviation [PD] probability at P > 0.05) with a decrease of sensitivity 5 dB in the PD graph; (2) expansion of a previously abnormal area (defined as any cluster with PD probability at P < 0.05 in the PD graph); and (3) deepening in sensitivity of a previously abnormal area by 10 dB in the PD graph. Either of the patterns described had to be repeatable on the last 2 examinations when compared with the 2 baseline ones. Consensus was required to define progression versus stable. In cases where no consensus was reached, a third glaucoma expert adjudicated. For convergence validation purposes, we tested the performance of the progression criterion with the highest PIR in our final analysis in 2 ways: (1) We calculated the area under the curve (AUC) of the receiver operating characteristic (ROC) using the 102 visual field progression criteria results (progression vs. stable) as the binary classification variable and the 10-2 MD slope (dB/year) as the continuous variable. For comparison purposes, the same method was performed using the clinicians’ grading as the classification variable. The AUC-ROC is a statistical method that has long been used in medicine and other fields to test the performance of diagnostic tests and diagnostic criteria based on a reference binary classification system.42 It is based on the fact that any gain in sensitivity always happens at the cost of a decrease in specificity and vice versa. In an ROC curve, the true positive rate (sensitivity) is plotted in function of the false-positive rate (1-specificity) for different cutoff points of a parameter, which was the 10-2 MD rate of change in our study. Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular rate of 10-2 visual field change. The AUC-ROC is a measure of how well a parameter can distinguish between 2 diagnostic groups (progressing vs. stable). The “x” axis represents false-positive rates (1-specificity), and the “y” axis represents the sensitivity for the test. The values can range from 0.0 to 1.0, the latter meaning perfect performance, which would theoretically happen if a test had 100% sensitivity and 100% specificity (or 0% false-positives). The area below the diagonal line represents an AUC-ROC of 0.5, meaning the test has a 50% chance of providing the correct result, which is equivalent to guessing or flipping a coin. The goal is to have a curve above the diagonal line within the entire range of false-positive results (1-specificity, “x” axis). Values >0.7 (70%) are considered moderate to good; a value of 0.8, for instance, means that the test has an average sensitivity of 80% for all possible values of specificity.42 (2) Because the macular sensitivity correlates with the best-corrected visual acuity,19,43,44 we compared the number of Snellen chart lines lost during follow-up between progressing and stable groups on the basis of optimized PIR (OPIR). Statistical analyses were performed using STATA software (version 12.0; StataCorp LP, College Station, TX) and Mplus software (version 6.12; Muthen & Muthen Inc., Los Angeles, CA). The alpha level used to define statistical significance was set at 5%. Adjustments for multiple comparisons (e.g., Bonferroni, Tukey’s, and least significant difference) were not performed because these corrections may not be needed when the comparisons are complementary and only a few planned observations are performed.45
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Ophthalmology Volume 121, Number 3, March 2014
Results A total of 146 eyes of 146 patients were included in the study. Each eye underwent a median of 8 visual field tests (interquartile range [IQR], 6e13; range, 5e65) spanning a median of 7.5 years (IQR, 4.7e11.8; range, 1.5e21.1 years). Mean baseline 10-2 MD value was 12.0 dB (IQR, 6.7 to 17.8; range, 1.09 to 32.3 dB). Seventy-five eyes (51.3%) had a baseline MD
