Analysis of progressive change in automated visual fields ... two consecutive abnormal results (GHT borderline or outside normal limits) and at least five subsequent field tests Clinica

Analysis of Progressive Change in Automated VisualFields in Glaucoma

Scott D. Smith, Joanne Katz, and Harry A. Quigley

Purpose. To detect and estimate the rate of progression of visual field loss in subjects withglaucoma who undergo long-term automated perimetric visual field testing.

Methods. Automated visual field data were obtained for subjects with glaucomatous visual fieldloss and a minimum of seven threshold field tests over at least 4.5 years. Univariate linearregression was performed with respect to mean deviation (MD), corrected pattern standarddeviation (CPSD), mean thresholds of clusters corresponding to the Glaucoma Hemifield Test(GHT), and thresholds of 52 individual test locations. Subjects were classified as progressive orstable (unchanged or improved) based on the slope and statistical significance of theseparameters. Adjusted P values were used to maintain the overall type 1 error at 5%.

Results. One hundred ninety-one subjects with a mean follow-up period of 7.1 years (range,4.5 to 10.5 years) and a mean number of visual field tests of 9.5 (range, 7 to 16) were included.Twenty-four subjects (12.6%) showed progression in MD (mean slope [95% confidence inter-val], -1.26 [-1.50, -1.01] dB/year), and 27 (14.1%) showed progression in CPSD (meanslope [95% confidence interval], 0.71 [0.58, 0.84] dB/year). Thirty-five subjects (18.3%) hads i progressive GHT cluster. The mean slope in progressive clusters ranged from —1.51[-1.82, -1.20] to -2.84 [-3.39, -2.29] dB/year. Thirty-six subjects (18.8%) had ̂ 1 progres-sive individual test locations. Fifty-two subjects (27.2%) were classified as progressive basedon progression of CPSD, 2:1 cluster and/or s=l point.

Conclusions. Fewer than 1 in 3 subjects progressed by any one of the criteria for progressionover an average of 7.1 years. Rates of progression that could be statistically confirmed werein the range of approximately 1 to 5 dB/year, depending on the number of fields, thevariability over time, and the parameter assessed (global indices, GHT clusters, or individualpoints). No correlation between initial visual field status and the rate of progression wasfound. A minimum of approximately 5 years of follow-up with annual perimetry would berequired to detect significant changes in the visual field by linear regression. Invest Ophthal-mol Vis Sci. 1996; 37:1419-1428.

A he goal of methods designed to detect progressionin automated visual fields is to distinguish betweenfluctuation and a true decline in visual function. Themagnitude of inter-test variability is high'"4 and tendsto be greater in patients with glaucoma than in normalsubjects,5"9 rendering this task more difficult. Numer-ous techniques have been developed to detect field

From the Dana Center for Preventive. Ophthalmology, The Wilmer OphthalmologimlInstitute, The Johns Hopkins University, Baltimore, Maryland.Supported in part by United States Public Health Service research grants EY09130and RR04060 from the National Institutes of Health.Submitted for publication August 28, 1995; revised January II, 1996; acceptedFebruary 28, 1996.Pnyfmelary interest category: N.liefmnt requests: Joanne Katz, Tlie Johns Hopkins University School of Hygiene andPublic Health, Room 5515, 615 N. Wolfe Street, Baltimore, MD 21205-2103.

progression,10 30 but no widely accepted standard ex-ists.

Linear regression is a simple method to estimatetrends in longitudinal data such as those of serial auto-mated perimetry. It has the potential to identify thosepersons whose trend is sufficiently strong to exceedthe variability in the data and thereby to reach statisti-cal significance. To make reasonable estimates of therate of change with this technique, several visual fieldexaminations are required.19 Different parameters de-rived from visual field tests have been evaluated byregression analysis, including global visual field indi-ces and raw or age-adjusted threshold values of indi-vidual test locations or clusters of points.1618"27'30 It isthought that glaucomatous visual field loss tends to

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1420 Investigative Ophthalmology & Visual Science, June 1996, Vol. 37, No. 7

occur in local zones and at different rates in the upperand lower hemifields. This has suggested the potentialusefulness of cluster analysis, such as that used in theGlaucoma Hemifield Test (GHT)31 to identify loss infocal zones in each hemifield.

Previous studies"318"2730 evaluating visual fieldprogression by regression analysis have been limitedby small sample size, short period of follow-up, orboth. Our large data base of automated visual fieldsallows us to evaluate the usefulness of regression ofglobal indices, mean thresholds of clusters of pointscorresponding to those of the GHT, and thresholdsof individual test locations in identifying field progres-sion in a large number of patients with glaucoma whohave long-term follow-up.

METHODS

Visual field data were obtained from the patient database of the Glaucoma Service at the Wilmer Institute,which contains results of more than 50,000 examina-tions performed on the Humphrey Field Analyzer(Humphrey Instruments, San Leandro, GA). This database includes patients referred to glaucoma specialistsfor tertiary care and those followed up in a primaryophthalmic care service. Patients were identified whohad taken seven or more threshold visual field tests(program 24-2 or 30-2) over a period of at least 4.5years. Visual field results for these patients were trans-ferred to microcomputer using the Statpac for Win-dows software package (Humphrey Instruments). Weincluded in this study the field results of persons withtwo consecutive abnormal results (GHT borderline oroutside normal limits) and at least five subsequentfield tests. Clinical records were reviewed, and eyeswere included if they met the following criteria: visualfield loss attributed to glaucoma based on the assess-ment of the clinician at the time of initial evaluation orfirst abnormal field and no history of endophthalmitis,retinal detachment, penetrating keratoplasty, cataractextraction, or posterior capsulotomy during follow-up. Eyes with initial end-stage visual field loss (meandeviation < — 25 dB in the first and second fields)were excluded. For all patients, diagnosis of glaucomasubtype was based on the results of comprehensiveophthalmic examination, including slit lamp and di-lated fundus examination, gonioscopy, and visual fieldevaluation. For those patients in whom both eyes qual-ified, one eye was assigned randomly for inclusion.

Visual field data were transferred to minicom-puter, and univariate linear regression was performedwith time as the independent variable. Regressionanalysis was performed with respect to two global indi-ces, mean deviation (MD) and corrected pattern stan-dard deviation (CPSD). A similar analysis was per-formed for the mean thresholds of the 10 clusters

FIGURE l. Definition of the clusters of the Glaucoma Hemi-field Test (GHT).

corresponding to those of the GHT (Fig. 1) andthresholds of the 52 individual test locations examinedin program 24-2, excluding the two locations nearestthe blind spot. For test locations with multiple thresh-old measurements, the mean value was used in theanalysis.

The slopes of the lines fit by regression of MD,mean thresholds of GHT clusters, and thresholds ofindividual test locations that were significantly lessthan zero (negative) were defined as progressive.Slopes for CPSD that were significantly greater thanzero (positive) were also defined as progressive. Sig-nificant slopes of the opposite sign (positive for MD,clusters, and individual points, and negative forCPSD) were considered to be improved. All nonsig-nificant slopes and those that were improved wereconsidered stable. Slopes for MD and CPSD were con-sidered statistically significant if the P <, 0.025. Forthe 10 GHT clusters, a significant slope for each clus-ter was identified by P < 0.005. For individual loca-tions, a slope was identified as significant by P s 0.001.These P values were chosen to insure an overall type1 error of no more than 1 in 20 (5%) for each categoryof parameters analyzed (global indices, GHT clusters,and individual test locations).

To estimate the expected period of time requiredby linear regression to detect a statistically significanttrend under different conditions, a statistical modelwas generated based on the visual field data of subjectsclassified as progressive. The inter-test variability ofvisual field parameters was estimated by the root meansquare error of the corresponding linear regressionfor each subject with a significant slope in CPSD, >1GHT cluster and/or >1 point. This statistic representsthe observed variation not accounted for by the pre-dicted regression slope. The standard error of theslope was calculated by v£(2, — T)2 = (root meansquare error)/sqrt(Z(f, — T)2), where t, = the time of


Visual Field Progression in Glaucoma 1421

TABLE l. Number (%) of Subjects Having Laser Procedures and/or Trabeculectomy DuringFollow-up by History of Glaucoma Surgery

Prior Procedure

NoneLaser onlySurgery onlyBothTotal

None

63 (33.0)14 (7.3)9 (4.7)3 (1.6)

89 (46.6)

Procedures During Follow-up

Laser Only

56 (29.3)1 (0.5)4 (2.1)0 (0.0)

61 (31.9)

Surgery Only

6 (3.1)9 (4.7)3 (1.6)2 (1.0)

20 (10.5)

Both

18 (9.4)3 (1.6)0 (0.0)0 (0.0)

21 (11.0)

Total

143 (74.9)27 (14.1)16 (8.4)5 (2.6)

191 (100.0)

Laser procedures are trabeculoplasty or iridotomy.

each test since the initial examination. The test statis-tic t = slope/standard error was compared to criticalvalues of the t distribution with (n-2) degrees of free-dom, where n represents the number of fields in theseries. This procedure was repeated assuming equallyspaced annual and semiannual visual fields using dif-ferent values for slope and for root mean square errorscorresponding to the mean (weighted on degrees offreedom), 10th, and 90th percentile sample values toestimate average, low, and high long-term variability.

This research was conducted in accordance withthe tenets of the Declaration of Helsinki. Personalidentifiers were not maintained on the data base afterchart review. The Joint Committee on Clinical Investi-gations of the Johns Hopkins University School ofMedicine approved the study.

RESULTS

One hundred ninety-one subjects met the criteria forinclusion. Seventy-nine (41.4%) were male, and 112(58.6%) were female. Their mean age was 61.8 years(range, 10 to 88 years). Of the 184 subjects in whomrace was known, 111 (60.3%) were white, 72 (39.1%)were black, and one (0.5%) was Asian. The majorityof subjects (66.5%) had been referred for tertiary care,whereas the remainder (33.5%) were followed up inthe primary eye care service. Initial visual acuity was20/40 or better in 165 subjects (86.4%) and 20/50 to20/80 in 23 subjects (12%), and none had initial acu-ity less than 20/200. Thirty-six subjects (18.9%) lost>2 lines of acuity during follow-up. More than halfthe subjects (53.4%) underwent a glaucoma laser pro-cedure, trabeculectomy, or both during follow-up (Ta-ble 1). The majority of subjects (77%) had primaryopen angle glaucoma. There were 16 subjects (8.4%)with primary narrow angle glaucoma, 9 (4.7%) withexfoliation glaucoma, and 8 (4.2%) with pigmentaryglaucoma. The remaining 11 subjects (5.8%) hadother primary or secondary glaucomas, including con-genital, uveitic, steroid-induced, postsurgical, andangle recession glaucoma.

The mean number of visual fields during the fol-low-up period was 9.5 (range, 7 to 16). The meanperiod of time between the first and last field tests was7.1 years (range, 4.5 to 10.5 years). The mean initialMD was -8.7 ± 6.2 dB. The mean initial CPSD was6.2 ± 3.8 dB.

Linear regression of global indices identified 24subjects (12.6%) with a significant decline in MD and27 subjects (14.1%) with significant progression ofCPSD (Table 2). A significant decline in mean sensitiv-ity was identified in 92 (4.8%) of the 1910 GHT clus-ters analyzed (10 clusters per subject). The mean rateof decline in clusters that were progressive rangedfrom -1.51 to -2.84 dB/year (Table 2; see Fig. 1 fordefinition of GHT clusters). No relationship betweenthe region of the visual field and the likelihood ofprogression was present.

Linear regression of thresholds of individual testlocations resulted in 143 points (0.8%) identified asprogressive of the 17,368 locations analyzed (52 pointsper subject). The mean slope of those points classifiedas progressive was large, ranging from 14 to 73 timesgreater than the expected decline with age132 (Figs. 2and 3).

The observed inter-test variability differed consid-erably for global indices, mean thresholds of GHTclusters, and thresholds of individual test locations. Ofthe 191 subjects, the median variances of MD andCPSD were 4.6 dB2 and 2.1 dB2, respectively. For eachof the 10 GHT clusters, the median variance was be-tween 4.9 dB2 and 9.5 dB2. Median variances of indi-vidual test locations were between 5.6 dB2 and 23.3dB2 and were lowest in the central 10° of the field.

Many subjects showed improvement in both MDand CPSD (Table 3). Although 24 (12.6%) showed adecline in MD, 16 (8.4%) showed significant improve-ment. In 27 subjects (14.1%) CPSD worsened, whereasin 12 (6.3%) it improved. Among the 12 patients withimproved CPSD, the MD of their final visual fieldranged from +2 to —10 dB. The improvement, there-fore, was not related to the increasing uniformity of



TABLE 2. Mean Rate of Change of Global Indices and Average Threshold Values of the 10Clusters Corresponding to the Glaucoma Hemifield Test of Progressive and Stable Subjects

MDCPSDCluster Number

123456789

10

Number (%)

24 (12.6)27 (14.1)

9 (4.7)12 (6.3)10 (5.2)10 (5.2)8 (4.2)8 (4.2)9 (4.7)

10 (5.2)7 (3.7)9 (4.7)

Progressive

Mean Change [95% CI\ (dB/year)

-1.26 [-1.50, -1.01]0.71 [0.58, 0.84]

-1.51 [-1.82, -1.20]-2.00 [-2.60, -1.40]-2.69 [-3.24, -2.14]-2.53 [-3.14, -1.92]-2.84 [-3.39, -2.29]-1.91 [-2.48, -1.35]-2.14 [-2.72, -1.56]-2.07 [-2.68, -1.47]-1.80 [-2.53, -1.07]-1.74 [-2.45, -1.03]

Number (%)

167 (87.4)164 (85.9)

182 (95.3)179 (93.7)181 (94.8)181 (94.8)183 (95.8)183 (95.8)182 (95.3)181 (94.8)184 (96.3)182 (95.3)

Stable

Mean Change [95% CI\ (dB/year)

0.06 [-0.03, 0.15]-0.01 [-0.07, 0.05]

-0.14 [-0.26, -0.02]-0.14 [-0.25, -0.03]-0.05 [-0.16, 0.07]-0.05 [-0.17, 0.08]-0.02 [-0.14, 0.11]-0.12 [-0.21, -0.02]-0.12 [-0.23, -0.01]-0.06 [-0.17, 0.05]-0.04 [-0.15, 0.08]

0.00 [-0.13, 0.13]

MD = mean deviation; CPSD = corrected pattern standard deviation; GHT = Glaucoma Hemifield Test. Significance for MD andCPSD: P < 0.025; GHT clusters; P < 0.005.Stable subjects are those unchanged and improved, n = 191.

the visual field that can occur with progression in thefinal stages of glaucoma.

Although 35 subjects (18.3%) had >1 progressiveGHT cluster, only 13 (6.8%) showed improvement ins i cluster. Only one person showed improvement inthree clusters, none showed improvement in >3 clus-ters, and in 6.3% of the subjects, >4 clusters worsened.

Regression of individual thresholds identified 36subjects (18.8%) with s i progressive location and 17(8.9%) with improvement in s i location. Twenty-onepersons (11%) had 2=2 locations with a decline insensitivity, whereas only three (1.6%) had s 2 loca-tions with improvement. Of the 21 subjects with s 2

-2.850.51

-2.550.61

-3.561.09

-3.020.91

-3.210.75

-2.970.16

-3.550.76

-5.84

-2.97

-2.270.38

-2.61

-2.900.58

-1.960.42

-4.351.73

-2.930.98

-2.670.25

-3.660.85

-1.58

-2.530.88

-2.260.14

-2.950.64

-3.860.80

-2.520.44

-2.11

-2.150.42

-2.380.56

-4.01

-3.530.64

-2.840.40

-3.400.55

-3.130.47

-2.600.86

-2.93

-2.570.46

-2.94

-2.930.72

-2.770.12

-3.450.31

-2.731.03

-2.530.38

-3.230.71

-0.840.26

-3.470.59

-2.460.45

-2.920.27

-3.180.20

-2.87

-4.751.56

-2.740.06

-3.120.33

-3.37

-3.21

FIGURE 2. Mean rate of change (dB/year) and standard errorby test location for points with a statistically significant nega-tive slope (P < 0.001). Standard errors for locations havingonly one observation are indicated by ( —).

progressive locations, 18 (85.7%) had >2 progressivelocations that were adjacent. Two of the three subjectswith improvement at >2 locations improved at adja-cent points.

Based on this analysis, criteria for the classificationof a series of visual fields as progressive were selected(Fig. 4). Patients were categorized as having a deterio-ration in CPSD, >1 GHT cluster, and/or >1 individ-ual test location. Of these criteria, CPSD classified thefewest as progressive, whereas the cluster and pointcriteria identified roughly equal numbers as such. Al-though there was some overlap of the persons de-tected by these criteria, each classified some persons

-0.090.08

-0.10 -0.140.08 0.08

-0.05 -0.160.08 0.08

-0.080.07

-0.120.08

-0.210.08

-0.200.07

-0.250.08

-0.090.07

-0.070.07

-0.160.08

-0.130.08

-0.180.07

-0.150.07

-0.230.06

-0.120.06

-0.120.07

-0.010.08

-0.070.07

-0.110.08

-0.260.07

-0.220.07

-0.130.06

-0.280.08

-0.130.07

-0.020.08

-0.060.08

-0.110.08

-0.240.08

-0.120.07

-0.110.06

-0.250.08

-0.10'0.07

-0.020.08

-0.080.08

-0.060.07

-0.140.07

-0.210.08

-0.040.06

-0.120.07

-0.070.06

-0.010.07

-0.110.08

-0.230.07

-0.130.08

-0.050.08

-0.050.07

-0.080.06

-0.060.07

-0.060.07

FIGURE 3. Mean rate of change (dB/year) and standard errorby test location for points without a statistically significantnegative slope (P < 0.001).



TABLE 3. Number of Subjects WithProgression or Improvement in MD, CPSD,GHT Clusters, and Individual TestLocations

MDCPSDNumber of Clusters

01234-10

Number of Points01234-29

Progressive

Number ofPatients (%)

24 (12.6)27 (14.1)

156 (81.7)18 (9.4)3 (1.6)2 (1.0)

12 (6.3)

155 (81.2)15 (7.9)7 (3.7)4 (2.1)

10 (5.2)

Improved

Number ofPatients (%)

16 (8.4)12 (6.3)

178 (93.2)10 (5.2)2 (1.0)1 (0.5)0 (0.0)

174 (91.1)14 (7.3)

1 (0.5)2 (1.0)0 (0.0)

n = 191.MD = mean deviation; CPSD = corrected pattern standarddeviation; GHT = Glaucoma Hemifield Test.Significance for MD and CPSD: P < 0.025; GHT: P < 0.005;individual locations: P< 0.001.

as progressive who were not detected by the other two.If progression was indicated by satisfying any one ofthese criteria, 52 subjects (27.2%) were classified asprogressive.

If the pointwise criterion for progression was al-tered to require two or more progressive points, 45patients (23.6%) were classified as progressive bymeeting one or more of the CPSD, cluster, or pointcriteria. With this definition, no additional subjects

CPSD> 1 GHTCluster

Total52/191 (27.2%)

> 1 PointFIGURE 4. Classification of subjects as having visual field pro-gression according to three criteria: statistically significantincrease in corrected pattern standard deviation (CPSD) (P< 0.025), significant decline in mean sensitivity of s i clus-ter corresponding to the Glaucoma Hemifield Test (GHT)(P < 0.005), or significant decline in s i individual testlocation (P < 0.001). Fifty-two patients (27.2%) met one ormore of these criteria.

CPSD>1GHTCluster

> 1 PointFIGURE 5. Classification of subjects as having visual field im-provement according to three criteria: statistically significantdecrease in corrected pattern standard deviation (CPSD) (P< 0.025), significant increase in mean sensitivity of s i clus-ter corresponding to the Glaucoma Hemifield Test (GHT)(P < 0.005), or significant increase in s i individual testlocation (P< 0.001). Thirty-three patients (17.3%) met oneor more of these criteria.

were identified as progressive based on individual testlocations who were not already identified by the GHTcluster regressions.

The greatest number of subjects was classified asimproved by individual test locations (Fig. 5). Eigh-teen subjects (9.4%) had s=l point improved, 13(6.8%) showed improvement in CPSD, and 13 (6.8%)improved in ^1 cluster. Thirty-four subjects (17.8%)were classified as improved by one or more criteria.Less overlap was seen in the classification of improve-ment than of progression, particularly between CPSDand the other criteria. No subject was classified asimproved by all three criteria.

Subjects who underwent laser procedures, surgi-cal procedures, or both during follow-up were signifi-cantly more likely to be classified as progressive thanthose who underwent no procedures (Table 4). Blacksubjects referred for specialized glaucoma care were3.6 times more likely to be classified as progressivethan those in the primary eye care service (x*,P < 0.002). The proportion progressing was similar inprimary and tertiary care among white subjects. There

TABLE 4. Visual Field Progression by Historyof Laser Procedure and/or Trabeculectomy

Procedures Total Progressive (%)

NonePast onlyF/U onlyPast and F/U

63268022

12 (19.0)3 (11.5)

30 (37.5)7 (31.8)

Past = laser and/or surgery before first visual field; F/U = laserand/or surgery during follow-up period.X2 for procedure during F/U versus no procedure during F/U: P= 0.003; Overall **: P = 0.02.Laser procedure = iridotomy or trabeculoplasty.



TABLE 5. Rate of Progression of MD andCPSD in 52 Progressive Subjects by InitialVisual Field Status as Indicated by CPSDGreater or Less Than 5 dB

Mean InitialDefect (dB)

MDCPSD

Mean Slope(dB/year)

MDCPSD

^5 dB (n =

-4.563.12

-0.810.67

Initial CPSD

22) >5 dB (n = 30)

-11.488.62

-0.780.23*

* Difference significant; P = 0.001.MD = mean deviation; CPSD = corrected pattern standarddeviation.

was no difference in the mean baseline visual fieldstatus of stable (MD = -8.84 ± 6.14 dB, CPSD = 6.16± 3.88 dB) and progressive (MD = -8.55 ± 6.38 dB,CPSD = 6.30 ± 3.53 dB) subjects.

To evaluate the relationship between initial visualfield status and the rate of visual field change in pro-gressive subjects, the 52 subjects who met one or moreof the criteria for progression were categorized basedon initial CPSD (Table 5). No significant differencewas found in the rate of decline of MD between sub-jects with a more severe (>5 dB) compared with aless severe (^5 dB) initial defect in CPSD. The rateof change of CPSD, however, was significantly greaterin subjects with less initial field loss (P = 0.001). Inaddition, the proportion of subjects with statisticallysignificant progression in CPSD was greater amongthose with a smaller initial defect (68.2% versus 40%,P = 0.05). Classification of subjects on the basis ofinitial MD above or below —5 dB gave similar results.

The results of our model of the time requiredfor linear regression to detect statistically significanttrends in visual field parameters indicate that the ex-pected period of time is directly related to the degreeof long-term variability (indicated by the root meansquare error) and inversely related to the rate of pro-gression (Table 6). For a given rate of change, detec-tion of progression requires the shortest time forCPSD and an intermediate period of time for GHTclusters. The expected time required to reach signifi-cance for any of the parameters decreases by approxi-mately 25% to 30% by doubling the frequency of ex-amination.

DISCUSSION

The results of this study demonstrate that statisticallysignificant trends that correspond to clinically note-

worthy change in several automated visual field param-eters can be identified in a proportion of patients withglaucoma who undergo long-term follow-up. The rateof deterioration we measured is similar to that pre-viously reported. O'Brien and coworkers26 performedlinear regression on the mean threshold value andclusters of points in 40 patients whose automatedthreshold perimetry extended over 44.9 ± 17.4months. In subjects with a statistically significant de-cline, the mean rate of loss across the entire field was— 1.39 dB/year, and, in point clusters, it varied from— 1.09 to —2.14 dB/year. Our results were similar, witha mean slope of —1.25 dB/year for MD and meanslopes ranging from —1.51 dB/year to —2.84 dB/yearfor the 10 GHT clusters in those subjects with a sig-nificant rate of decline. In individual points showinga significant decline, the mean rate of change wasgreater, ranging from approximately 2 to 6 dB/yearin our subjects. Stable patients also had mean slopessimilar to those reported by O'Brien, who found amean rate of change across the field of —0.07 dB/year and a range of 0.25 to —0.14 dB/year in pointclusters. Our results showed a mean rate of change ofMD of 0.06 dB/year, and rates ranging from 0.00 to-0.14 dB/year in the GHT clusters.

We determined the type of regression functionbased on visual inspection of the data. This gave noindication that a better fit would be obtained with anonlinear rather than a linear function. Because visualfield data were recorded in decibels, a linear declinerepresents an exponential decay in retinal sensitivity.Although loss of sensitivity could occur at greater thanan exponential rate, we found nothing in our data tosuggest that another model would improve the results.The long follow-up period in this study reduced thelikelihood that episodic progression would result in apoor estimate of long-term change by a linear fit.

Many of the subjects in this study had been inex-perienced in automated perimetry at the beginningof follow-up. However, this did not appear to resultin a learning effect in a significant number of pa-tients,33"36 which might mask visual field progres-sion and lead to an underestimation of the propor-tion of progressive subjects. Only 3 of the 16 subjectswith a significant trend toward improvement in MDshowed a considerable increase in MD during theirsecond examination to suggest that learning hadoccurred. The long follow-up period, the large num-ber of fields per patient, and the small number ofpatients exhibiting learning reduce the importanceof this effect on our results.

A strong correlation was found between visualfield progression and a history of glaucoma laser ther-apy, surgical therapy, or both during follow-up (Table4). This association suggests that clinical parametersassociated with disease progression, including the cli-



TABLE 6. Expected Number of Years Required to Detect Progression of CPSD, MeanThreshold of a GHT Cluster, or Threshold of an Individual Point by Linear RegressionWith Evenly Spaced Visual Field Examinations

CPSD Slope (dB/year)

0.5123

GHT Ouster Slope(dB/year)

1234

Individual Point Slope(dB/year)

12345

Low

7654

10776

1410987

One Field per Year

Average

9755

12987

16121098

Long-Term

High

13976

151098

191311109

Variability

Low

53.532.5

7543.5

1075.554.5

Two Fields per Year

Average

74.53.53

9654.5

1286.565.5

High

106.54.54

117.565

14.59.57.56.56

MD = mean deviation; CPSD = corrected pattern standard deviation; GHT = Glaucoma Hemifield Test.Significance for CPSD: P < 0.05; GHT: P < 0.005; individual point: P < 0.001.Long-term variability was estimated by the root mean square error of 52 progressive subjects. Low, average, and high variabilitycorrespond to the observed 10th percentile, mean, and 90th percentile root mean square error, respectively. The range of slopes showncorresponds to the approximate range for each parameter among progressive subjects.

nician's assessment of the visual fields, occurred morefrequendy among subjects identified as progressive byour criteria. The high rate of progression in blacksubjects referred for specialty care compared to whitesubjects may have been caused by the existence ofdifferent referral patterns according to race in thispopulation.

The rate of change of different visual field param-eters was not uniform. In progressive patients, GHTclusters declined at a greater rate than did MD, andindividual points declined at an even greater rate.These variations in the rate of change are accountedfor both by the localized nature of glaucomatous fieldloss and by the increased stringency with which statisti-cal significance was defined for GHT clusters (P <0.005) and for individual points (P < 0.001) in ouradjustment for performance of multiple statisticalcomparisons. This greater degree of stringency wasused to reduce the number of points or GHT clustersreaching significance from chance alone (overall type1 error), which is very high if a cutoff of P = 0.05is chosen (Table 7). This adjustment increased ourconfidence in the progressive nature of abnormalpoints and clusters and reduced the number of im-proved points and clusters; hence, there were rela-

tively few in comparison to the number that were pro-gressive.

Other studies have adjusted for this effect in dif-ferent ways. Noureddin and coworkers25 investigatedpointwise progression of the visual field in subjectswith low-tension glaucoma. They defined a clinicallysignificant rate of decline as —2.4 dB/year and re-quired that points deteriorate at this rate or greaterand to reach significance at P < 0.05. This definitionclassifies points that lose as much as 93% of their grosssensitivity over 5 years as stable, but it may still permitone or more points to be progressive because ofchance alone with greater than 5% probability. Wer-ner and coworkers18 evaluated 10 sectors of the visualfield by linear regression and required that slopesreach statistical significance in two adjacent or anythree sectors. Of 30 subjects with a mean of 6.5 fields,their method classified 10 (33%) as progressive. Suchdifferences between studies in the definition of pro-gression make the comparison of results difficult tointerpret.

Among subjects categorized as progressive, therewas no relationship observed between baseline visualfield status and the rate of decline in MD. A greaterprobability of statistically significant progression of



TABLE 7. Probability of Number ofAbnormal Points or Clusters ResultingFrom Chance

Pointwise Analysis (52 Points)

Abnormal PointsResulting From Chance

Probability

P = 0.05

0.93060.74050.48540.26170.11740.04450.0145

P = 0.001

0.05070.00130.00000.00000.00000.00000.0000

Ouster Analysis (10 Ousters)

Abnormal ClustersResulting From Chance P = 0.05

0.40130.08610.0115

Probability

P = 0.005

0.04890.00110.0000

Values are for pointwise (52 points) or cluster (10 clusters)analysis of Humphrey visual fields as a function of choice ofsignificant P value.

CPSD and a greater mean slope of CPSD were ob-served in those with less severe initial field loss. Thesimilarity in the rate of change of MD in the twogroups suggests that these differences in CPSD do notreflect greater progression with early field loss. Rather,the fact that CPSD reaches a maximum and returnstoward zero as the field increases in uniformity withend-stage loss implies that those with greater initialloss are nearer the point of maximum CPSD and haveless room to show progression. Although the point atwhich CPSD peaks is not certain and probably variesbetween individuals, our results demonstrate that it isa less sensitive indicator of progression in those withmore severe initial field loss (CPSD < 5 dB). As aresult, the GHT and point criteria are important fordetecting progression in these patients.

Empirical methods to detect change compare asingle visual field to the results of one or two earliertests.10"14 The Glaucoma Change Probability (GCP),14

for example, compares the current field to the meanof two baseline examinations using empirical data toestimate the expected degree of variability of stablepatients with glaucoma at each point based on testlocation and baseline defect depth. Although fewertests are required to perform this analysis, the resultsof additional tests are not considered in making thepointwise statistical comparisons. In contrast, linearregression uses all the data from a series of fields to

estimate change. As more data are accumulated overtime, the statistical power to identify a significanttrend increases if the magnitude of variability is con-stant. In addition, if the two baseline fields in theGCP are for any reason not representative of the truebaseline, the comparison made by this method is moreunstable than with regression.

Birch and coworkers30 used the pointwise linearregression method of Noureddin25 and the GCP toevaluate progression in 36 series of fields of subjectswith glaucoma followed up for a mean period of 40months. For linear regression, they defined a declineof ^ 1 dB/year as clinically significant. Progression wasdetermined by the presence of two or more non-edgepoints with a statistically significant slope (P < 0.05).For GCP, progression was determined by the presenceof two adjacent non-edge points significantly worsethan baseline. By these criteria, 56% of subjects wereclassified by pointwise linear regression as progressive,whereas 25% were classified as progressive by GCP.The difference in the proportion of progressive pa-tients may be a result of the more restrictive criteriafor progression in GCP, requiring that two abnormalpoints be adjacent. In this series, only 14% of subjectswere classified as progressive based on subjective eval-uation of clinical records, including disc photographsand visual fields. Whether this discrepancy resultedfrom inaccuracy in classification by the statistical algo-rithms or by the subjective clinical evaluation is uncer-tain.

The period of time required to detect progressionby linear regression is influenced by the underlyingrate of progression, the degree of fluctuation of visualfield parameters, and the frequency of examination(Table 6). Because of greater variability of individualpoints and GHT clusters, for any given rate of progres-sion, these require a longer period of time to reachsignificance than does CPSD. However, because CPSDis a global index influenced by the entire field, it tendsto change less rapidly than do progressive points andclusters. As a result, a similar period of time is requiredto detect change in each of the parameters when itfalls in the range of the observed mean slope of pro-gressive subjects in our sample. Based on annual ex-aminations and average variability, the time requiredto detect a change in CPSD of 0.75 dB/year is approxi-mately 8 years. Nine years are required to detect achange in a GHT cluster of 2 dB/year, and 10 yearsare needed to detect a change of 3 dB/year in anindividual point.

The degree of long-term variability also influencesthe time required to detect progression. For personswith high compared with average variability, the timerequired to reach significance increases by 10% to40%, depending on the rate of progression (Table6). Variability has a greater influence at low rates of



progression because the underlying trend can bemasked more easily by random variation.

The amount of visual field loss that may occurbefore progression is confirmed may be great. Thiscan be reduced to some extent by increasing the fre-quency of examination. By doubling the frequency,the time to detection can be reduced by 25% to 30%(Table 6), and the expected amount of loss beforedetection (slope X time to detection) can be reducedconsiderably. The increase in statistical power gainedby frequent examination may be particularly im-portant for persons with high long-term variability orfor those with critical field loss in whom early detec-tion of progression is essential.

Our model is based on the actual value of theunderlying rate of progression of each visual field pa-rameter. In the clinical setting, this value is unknownbut is estimated from the visual field data. As a result,random error in the estimate of the slope leads tovalues larger or smaller than the true rate of progres-sion. The period of time at which statistical signifi-cance is reached varies accordingly but, on average,corresponds to the expected value reported.

Given the relative lack of specificity of MD forglaucoma change, we chose not to use MD in ourset of potential criteria for visual field progression.Comparison of global indices from Octopus perimetryhas shown that corrected loss variance has significantlybetter sensitivity and specificity than does mean defectin predicting glaucoma progression as assessed by clin-ical evaluation.23 A person with a significant declinein Humphrey MD resulting from glaucoma, therefore,would likely be detected by CPSD (analogous to cor-rected loss variance) or our other criteria that aremore sensitive to localized loss. Inclusion of MD asa criterion would be unlikely to increase the overallsensitivity for detection of progression but could re-duce specificity. In these data, only two people had asignificant decline in MD that was not identified asprogressive by the localized criteria. This small num-ber probably results from the exclusion of subjectswho underwent cataract extraction or posterior capsu-lotomy during follow-up.

Each of the three potential criteria for the defini-tion of progression has specific advantages and disad-vantages. The global index, CPSD, has less variabilitythan the GHT clusters or individual points and maydetect localized change not represented adequatelyby the GHT clusters. Estimation of slopes of individualpoints can detect changes in small areas of the fieldthat are not large enough to influence significandythe CPSD or GHT clusters, but these generally requirea greater rate of change to achieve statistical signifi-cance because the variability of individual locations isgreater. The GHT clusters provide a good compro-mise. Their variability is intermediate between that of

CPSD and individual points, yet they appear to retainfairly high sensitivity to localized change.

The trends we identified were statistically and clin-ically significant. The mean rate of change of manyGHT clusters and individual points exceeded 20 dBover 10 years in progressive patients. Such trends wereevident in more than 25% of subjects. This proportionseems small because a large number of patients hadbeen referred for tertiary care and underwent laserand surgical intervention. This may reflect a lack ofsensitivity of our criteria for visual field progression.However, we interpret the result as indicating a highdegree of stability in the majority of patients.

Because no standard for the identification of vi-sual field progression exists, it is difficult to determinethe true sensitivity and specificity of this, or any,method for the detection of field progression. Al-though optic nerve and nerve fiber layer characteris-tics are useful in monitoring glaucoma progressionearly in its course, these become less reliable in per-sons who have reached a level of moderate to severevisual field loss. Because many subjects were at thisstage when follow-up began, no independent valida-tion of our criteria for progression was possible. How-ever, the low proportion of subjects with improvementrelative to the proportion with progression suggeststhat the observed decline was real in most progressivesubjects because trends resulting from random varia-tion were equally likely to occur in either direction.

Our results demonstrate that regression analysiscan be a useful statistical tool to identify objectivelysignificant trends in the visual field. The period oftime necessary to detect significant change can be con-siderable, however, and is strongly influenced by therate of progression, die magnitude of long-term vari-ability, and the frequency of examination. This tech-nique can nevertheless provide valuable informationto assist the clinician in the long-term managementof patients with glaucoma.

Key Words

glaucoma, linear regression, perimetry, visual field progres-sion

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