Nonlinear behavior of certain optic nerve head parameters and their determinants in normal subjects

Nonlinear Behavior of Certain Optic Nerve Head Parameters and Their Determinants in Normal Subjects Alicja R. Rudnicka, MSc, PhD1 Chris Frost, MA, DipStat,2 Chris G. Owen, MSc, PhD,3 David F. Edgar, FCOptom4 Objective: To investigate the relationship between the absolute area of certain optic disc parameters and a number of ocular dimensional characteristics and demographic factors in young, healthy subjects. Design: Cross-sectional study. Participants: One hundred twenty-one subjects, aged 16.5 to 35.4 years participated, encompassing a wide range of refractive error from ⫹4 diopters (D) to ⫺25.75 D. One eye from each subject was randomly selected for examination. Main Outcome Measures: Absolute size of the optic disc parameters: optic disc area (DA), neuroretinal rim area (NRA), optic cup area (CA), and peripapillary atrophy area (PA). Methods: Absolute sizes of optic disc parameters were determined from digitized photographic color transparencies, taking into consideration the magnification of the fundus camera and human eye. Relationships between the absolute size of the optic disc features and axial length, crystalline lens thickness, anterior chamber depth, ocular refraction, front surface keratometry, age, and gender were examined. Results: Axial length, lens thickness, front surface keratometry, and age demonstrated positive associations with all optic disc parameters, and anterior chamber depth and ocular refraction demonstrated negative associations in all cases. Multiple regression analysis revealed that the associations observed univariately for age, anterior chamber depth, lens thickness, front surface keratometry, and ocular refraction were confounded by axial length for all disc parameters. After taking logs, DA and NRA exhibit an exponential relationship with axial length, whereas PA and CA exhibit a linear relationship with axial length. DA and NRA increase by approximately 3% per millimeter increase in axial length at 20 mm and up to 40% for DA and 50% for NRA at an axial length of 35 mm. PA and CA are estimated to increase by 26% (10%– 44%) and 10% (5%–16%), respectively, per millimeter increase in axial length. Females have approximately 5% smaller DA and 7% smaller NRA than males, but these effects are not statistically significant (P ⬎ 0.2). From the multiple regression analysis, females have 31% larger optic cup areas (1%–57%, P ⫽ 0.03) and 24% smaller PA (42% smaller to 5% larger P ⫽ 0.06) than males, but these effects are of borderline statistical significance at 5%. Conclusions: Of the ocular biometric factors considered, axial length seems to be the most important predictor of the absolute area of the optic disc parameters. No association exists between any disc parameter and age in this sample of subjects less than 40 years of age. Females exhibited smaller values for DA, NRA, and PA than did males, differences that were not statistically significant, and larger CA (P ⫽ 0.03). Ophthalmology 2001;108:2358 –2368 © 2001 by the American Academy of Ophthalmology. It is generally accepted that quantitative evaluation of the optic disc features in glaucoma should take into consider-

Originally received: August 28, 2000. Accepted: June 28, 2001. Manuscript no. 200649. 1 Wolfson Institute of Preventive Medicine, St. Bartholomew’s and The Royal London School of Medicine and Dentistry, London, England. 2 Medical Statistics Unit, London School of Hygiene and Tropical Medicine, London, England. 3 Department of Public Health Sciences, St. George’s Hospital Medical School, London, England. 4 Department of Optometry and Visual Science, City University, London, England. Supported in part by a grant from the Applied Vision Research Unit, City University, London, England. Reprint requests to Dr. Alicja R. Rudnicka, MSc, PhD, Wolfson Institute of Preventive Medicine, St. Bartholomew’s and The Royal London School of Medicine and Dentistry, Charterhouse Square, London EC1M 6BQ, England.

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© 2001 by the American Academy of Ophthalmology Published by Elsevier Science Inc.

ation the absolute size of the optic disc. Relatively larger optic discs have been reported to be more susceptible to nerve atrophy in glaucoma.1– 4 Chi et al3 demonstrated by use of a mathematical model that nerve fibers of larger discs may be more susceptible to high-pressure damage or displacement and concluded that the absolute size of an optic disc may be a risk factor in glaucomatous visual field loss development. Substantial differences both between individuals and different studies have been reported for the absolute size of the optic disc,5–7 and there is considerable overlap of measurements between normal and glaucomatous populations.8 –10 Some of the variability between different studies regarding the absolute size of the optic disc can be explained by the demographics of the subject samples and the method used to correct for the magnification of the human eye and fundus imaging system.11–14 The purpose of this study is to investigate the relationship between the absolute area of a range of optic disc ISSN 0161-6420/01/$–see front matter PII S0161-6420(01)00821-1

Rudnicka et al 䡠 Determination of Optic Nerve Head Parameters in Normal Subjects parameters (optic disc, optic cup, neuroretinal rim, and peripapillary atrophy) and a number of dimensional characteristics in a group of young, healthy, normal subjects. There are inconsistencies in the literature as to whether any associations exist between the size of optic disc parameters and ametropia or axial length. Some studies have found no correlations between disc area and axial length or between disc area and spherical equivalent refraction.7,15–18 Others have reported statistically significant positive correlations between disc area and axial length19 or refractive error.20 Studies have suggested that optic disc parameters may be affected by age,17,21 and may differ between the genders.16,20,22 To date, the aforementioned literature in this area has concentrated mainly on correlation coefficients and linear regression analyses. Few studies have performed multiple regression techniques.18,20,21 This study will examine the effect of a number of factors on optic disc parameters. Limitations of assuming a linear relationship between optic disc parameters and these factors are examined.

Material and Methods Sample Young healthy individuals, without any ocular or systemic pathosis, were recruited from the academic and undergraduate populations of City University. Most of the myopic patients were obtained from the Contact Lens Department of Moorfields Eye Hospital and were attending for routine contact lens follow-up appointments. Ethics Committee approval was obtained. Informed consent was sought from a total of 127 healthy subjects aged 16.5 to 35.4 years. At least 30 subjects had more than 10 diopters (D) of myopia. Suitable individuals were invited to attend for a routine eye examination. Inclusion criteria were as follows: ● ● ● ● ● ● ●

Visual acuity of 6/9 or better. Spectacle astigmatism less than or equal to 3.00 D. Intraocular pressure ⬍21 mmHg. No sign of any past/present ocular disease. Free of any systemic disease and not taking any medications. If the patient wore contact lenses, there should be no signs of any contact lens related ocular insult. No known family history of glaucoma.

Eligible subjects underwent the following order of tests on one eye only selected randomly (contact lens wearers were asked to leave their contact lenses out on the day of these measurements): ●

●

● ● ●

Front surface keratometry (FSK) using the Allergan Humphrey 410 automated keratometer (Allergan Humphrey, San Leandro, CA), an average from five readings was obtained. One drop of 0.4% benoxinate instilled and A-scan ultrasonography using the Allergan Humphrey 820 ultrasonic biometer in the semiautomatic mode, an average from five readings was obtained. Goldmann applanation tonometry. One or 2 drops of 1% tropicamide were instilled, and a cycloplegic refraction was carried out. Fundus photography was performed with the Carl Zeiss Jena Retinophot fundus camera 40° field (Carl Zeiss Jena, Jena, E. Germany) and Kodak Ektachrome 200 film (EastmanKodak, Rochester, NY). Optic nerve head and peripapillary crescents were centered within the camera field. The field of

view allowed the entire area of interest to be captured, including myopic eyes with large areas of peripapillary atrophy and high levels of ocular magnification. All images were taken using the same camera setup throughout.

Determination of the Size of the Optic Disc in Absolute Units Optic disc features were demarcated using established criteria: the optic disc area (DA) is defined as the entire retinal aspect of the optic nerve as delineated by the inner aspect of the scleral ring of Elschnig7,15,23; the cup margin, and hence its area, is defined by a change in the slope along the inner edge of the neuroretinal rim and not by a pallor change; the neuroretinal rim area (NRA) is outlined by the margins of the optic disc and optic cup. Blood vessels were included in the NRA if they were clearly embedded in neural tissue.8 If a vessel was isolated within the cup and not attached to neural tissue, it was obviously part of the cup and not the rim.15 Changes in direction of vessels in the optic disc were also used as a guide to neuroretinal rim edge. This topographic definition of the intrapapillary disc structures has been widely used and is generally accepted. Approximately half of the sample in this study did not have physiologic cupping, which challenges the preceding definitions. In these circumstances, cup area (CA) would be zero, and using the preceding definition the entire surface aspect of the optic disc would be considered to be neuroretinal rim. However, blood vessels entering and leaving the retina occupy space within the optic disc. In eyes without physiologic cupping, NRA was delineated using two methods. ● ●

NRA1: the entire surface aspect of the disc was assumed to be neuroretina. NRA2: the neuroretina was determined as the disc area minus the area occupied by the passage of blood vessels through the center of the optic disc.

The total area of peripapillary atrophy (PA) was also outlined if present. No distinction was made between the different possible types of PA, because the tissue boundaries were frequently indistinct, and typically a gradual transition between different types of atrophy was observed. The true size of a retinal feature, t, is related to the image size in the photographic film plane, s, by the equation t ⫽ pqs

(1)

where, p and q are the magnification correction factors of the fundus imaging system and the human eye, respectively. If the image size is measured as an area, then the equation becomes t 2 ⫽ 共pq兲 2 s 2

(2)

This is a well-established approach, and full details have been published elsewhere for the determination of p and q.13,14 Bennett et al13 demonstrated that the value for q was also dependent on the angular eccentricity of the retinal feature with respect to the optical axis of the eye. The value of q was determined for an eccentricity of 15°, which is the approximate eccentricity of the optic disc. The personalized schematic eye approach13 was used, which requires data obtained from A-scan ultrasound biometry (anterior chamber depth, lens thickness, and vitreous chamber depth), front surface keratometry, spectacle refraction, and refracting distance. The published value for the magnification correction factor, p, for the nontelecentric Carl Zeiss Jena Retinophot fundus camera was used.14 By use of ray tracing techniques, ocular refraction was determined as the refraction measured from the first principal plane of the eye.13

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Ophthalmology Volume 108, Number 12, December 2001 Table 1. Mean, Standard deviation for Ocular Biometric Factors along with the Median, Interquartile Range, Maximum, and Minimum Values for the Optic Disc Parameters Biometric Factors

N

Mean (Standard Deviation)

Minimum

Maximum

Axial length (mm) Anterior chamber depth (mm) Lens thickness (mm) Keratometry (mm) Ocular refraction (D) Age (yrs)

122 122 122 122 122 122

25.81 (2.54) 3.71 (0.32) 3.70 (0.26) 7.78 (0.27) ⫺4.93 (5.17) 23.38 (3.88)

22.01 2.60 3.15 7.28 ⫺20.25 16.5

34.60 4.53 4.70 8.35 4.28 38.0

Median (IQR) (mm2)

Minimum (mm2)

Maximum (mm2)

Optic disc parameter Optic disc area Neuroretinal rim area (1)* Neuroretinal rim area (2)* Optic cup area Peripapillary atrophy area

122 122 122 63 73

2.05 1.72 1.69 0.58 0.70

(1.74 (1.50 (1.45 (0.45 (0.42

to to to to to

2.52) 2.10) 2.08) 0.69) 1.49)

1.17 0.84 0.83 0.23 0.12

9.15 9.15 9.02 2.07 36.23

*These refer to the two different measures of neuroretinal rim area delineation described in the Methods section. D ⫽ diopter; IQR ⫽ interquartile range.

Throughout, analysis incorporating ametropia was performed using ocular refraction. Photographic slides were digitized to a Kodak Photo CD with a resolution of 3072 ⫻ 2048 pixels. Images were imported using Paint Shop Pro version 4.12 (Jasc Software, Inc., Eden Prairie, MN) Shareware and converted into 24-bit tagged image format files to a resolution of 768 ⫻ 512. This allowed images to be viewed using ImageJ software (ImageJ 1.16, NIMH, Bethesda, MD) on a 14-inch VGA monitor (resolution 800 ⫻ 600). This software package allows optic disc features to be delineated manually using the mouse and gives the exact pixel area contained within a demarcated area. Calibration revealed that 1 pixel was equivalent to 0.046 mm in the photographic film plane.

Statistical Analysis Statistical analysis was performed using Intercooled Stata 6.0 for windows software (STATA Corporation, College Station, TX). The primary aim of this analysis was to identify which of the following factors, axial length, anterior chamber depth, crystalline lens thickness, ocular refraction, FSK, gender, and age, are important predictors of the absolute size of the optic disc parameters and to describe the nature of any associations. Graphical inspection of the optic disc parameters showed a lognormal distribution, and the between-subject variability of the optic disc parameters tended to increase with increasing axial length, myopia, lens thickness, FSK, age and decreasing anterior chamber depth. A logarithmic transformation of the optic disc parameters was performed, which stabilized the variance before performing linear regression (see Appendix). Univariate regression models were performed for all explanatory variables, and in all instances the natural logarithm of the optic disc parameter was modelled. Explanatory variables, which were found to be related univariately, were included in a multiple linear regression analysis to compare the combined effects of each factor. The general form of the multiple regression model is given in the Appendix. After the log transformation, visual inspection of the data revealed a curved relationship between the optic disc parameters, except cup area, and some of the explanatory variables. A standard statistical technique for examining curvature is to include a quadratic term of the relevant variable and formally test its inclusion

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in the model using the F test. In the presence of statistically significant curvature, an exponential model24 was used (see Appendix). In terms of interpretation and prediction the exponential has advantages over the quadratic model, because it allows for the curvature in the relationship, but is not symmetrical like the quadratic. For CA and peripapillary atrophy area (PA), the relationship between the size of these features and the predictor variables was limited to eyes exhibiting these features. All effects were transposed back from the log scale and are reported in terms of the percentage change in the absolute optic disc parameter per unit increase of each explanatory variable, along with the corresponding 95% confidence intervals. P values are given when appropriate.25 Plots of the residuals were inspected for goodness of fit. Throughout statistical significance is taken as a probability of less than 5%.

Results Data are available for 122 normal individuals aged 16.5 to 38 years; mean age was 23.38 years. Five individuals (4%) failed to attend the eye examination. Females make up 57% of the sample. Table 1 summarizes the ocular biometric factors and shows a wide range of axial length from 22.01 mm to 34.60 mm. The range of ocular refraction (⫹4.28 D to ⫺20.25 D) corresponds to a range of mean spherical spectacle refraction from ⫹4 D to ⫺25.75 D. An optic cup was present in 52% (n ⫽ 63), and PA in 60% (n ⫽ 73) of subjects. Because the optic disc parameters were not normally distributed, Table 1 gives the median and interquartile range of their absolute size. Graphical inspection of the data showed all optic disc parameters to increase in size with increasing axial length, myopia, age, lens thickness, keratometry, and decreasing anterior chamber depth. From Figure 1 there seems to be a curved relationship between optic disc area (DA) and all variables except age and an increase in variance as DA increases. Corresponding graphs for NRA1, NRA2, and PA are similar to those for DA. In general, there was less evidence of any association between cup area and any of the explanatory variables. A log transformation of the optic disc parameters stabilized the variance before performing any

Rudnicka et al 䡠 Determination of Optic Nerve Head Parameters in Normal Subjects

Figure 1. Disc area plotted against (A) axial length, (B) ocular refraction, (C) anterior chamber depth, (D) lens thickness, (E) front surface keratometry, and (F) age.

linear regression. This is evident for DA by comparing Figures 1A and 2A. Axial length, lens thickness, front surface keratometry, and age demonstrated positive associations with all optic disc parameters, and anterior chamber depth and ocular refraction demonstrated negative associations in all cases. Table 2 gives the predicted change in the optic disc parameters for the stated change in each explanatory variable along with the R2 values from univariate regression analyses. The strongest associations (highest R2 values) are with axial length followed by ocular refraction. For example, 51% of the variability in logDA is explained by linear regression against axial length alone compared with 38% by ocular refraction. DA, NRA, and CA are predicted to increase by approximately 10% to 11% per mm increase in axial length (Table 2). The 95% confidence intervals (CI) are consistent with an increase from 8% to 12% for DA, 9% to 14% for both measures of NRA, and from 5% to 16% for CA. Overall, the strongest relationship is between logPA and axial length, with an R2 of 71% (r ⫽ 0.84). PA is predicted to increase by more than 40%, on average, per millimeter increase in axial length, with a 95% CI from 35% to a 50% increase in area. For each diopter increase in ocular refraction toward myopia, DA increases by, on average, 4% (95% CI, 5%– 3%). Similar findings are reported for NRA and CA (Table 2). The magnitude of the association with PA is larger, with an approximately 16% increase in PA per diopter increase in ocular refraction toward myopia (95% CI, 13%–18%). For anterior chamber depth, lens thickness, and FSK the effect sizes in Table 2 for DA and both measures of NRA are similar for

these three disc parameters. DA and NRA are estimated to increase by approximately 5% to 6%/0.1-mm increase in lens thickness, 4%/0.1-mm increase in front corneal radius, and to decrease by 4%/0.1-mm increase in anterior chamber depth. In all cases the 95% CI excludes zero, and all effects are therefore statistically significant at less than the 5% level. The magnitude of the associations are highest for PA, and /0.1-mm increase in anterior chamber depth, lens thickness, and corneal radius PA is predicted to decrease by 12%, increase by 24%, and increase by 7%, respectively. However, the 95% CI associated with corneal radius is consistent with no effect. Age showed a weak but statistically significant positive linear relationship with all optic disc parameters, except CA. DA and NRA increase by approximately 2% per year and PA by 9% per year (Table 2). Although females have smaller optic discs and NRAs than males by 5% and 7%, respectively (Table 2), these effects are not statistically significant (P ⫽ 0.44, 0.28, 0.27, respectively). Mean DA in females is 2.14 mm2 (95% CI, 1.97 mm2–2.34 mm2) and 2.25 mm2 (95% CI, 2.05 mm2–2.47 mm2) in males. Mean NRA in females, whichever measure of NRA is used, is 1.76 mm2 (95% CI, 1.61 mm2–1.92 mm2) and in males 1.90 mm2 (95% CI, 1.70 mm2–2.12 mm2). Females were found to have 41% smaller PA and 27% larger CA than males, but these effects are of borderline statistical significance (P ⫽ 0.04, 0.03, respectively) and should be interpreted cautiously. Mean cup area in females is 0.67 mm2 (95% CI, 0.58 mm2– 0.79 mm2) and in males 0.53 mm2 (0.46 mm2– 0.60 mm2); mean peripapillary atrophy in females is 0.74 mm2 (95% CI, 0.57 mm2– 0.97 mm2) and in males 1.26 mm2 (95% CI, 0.79 mm2–2.01 mm2). In general, the associations are weaker for CA, which has the lowest R2 values (Table 2), and, other than the gender difference already described, cup area is only statistically significantly related to axial length, ocular refraction, and keratometry. Subjects with longer axial lengths tended to be more myopic, older, have thicker crystalline lenses, flatter corneas, and shallower anterior chamber depths. In particular, there was a very high negative correlation (r ⫽ ⫺0.93) between axial length and ocular refraction. Because of this high correlation between the two strongest explanatory variables and the resultant potential for model instability caused by collinearity, it was essential that all multiple regression models allowed for the curvature in the relationships, particularly between axial length and DA and NRA. For DA (P ⬍ 0.001) and NRA (P ⬍ 0.001) there was clear evidence of curvature with axial length only, whereas for PA (P ⫽ 0.09) and CA (P ⫽ 0.18) the curvature with axial length was less apparent. For this reason exponential modeling of axial length was used only for DA and NRA. The exponential model allows for the rate of change in the size of DA and NRA to be relatively less at shorter values of axial length compared with longer axial lengths. Figure 2 shows the fitted exponential curve obtained when an exponential term in axial length only is fitted (Eqn. 4 of Appendix). R2 values for the DA and NRA models are slightly larger than for the corresponding linear models. Table 3 shows the predicted percentage changes in DA, NRA1, and NRA2 for a 1-mm increase in axial length. From the exponential model the percent change depends on the initial axial length and so is presented for a variety of different axial lengths. DA and NRA increase by approximately 3%/mm in axial length at 20 mm, but at axial lengths of 25 mm, 30 mm, and 35 mm, this increases to approximately 7%, 16%, and 40% for disc area and 7%, 18%, and 50% for both measures of NRA, respectively. Once axial length was modeled using the exponential model (Appendix Eqn. 4) for DA and NRA, further addition of other explanatory variables to the model (anterior chamber depth and

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Ophthalmology Volume 108, Number 12, December 2001

Figure 2. Predicted values from exponential model are indicated by the black line for (A) disc area and (B) neuroretinal rim area (NRA1) plotted on a log scale against axial length. Predicted values from linear regression against axial length are indicated by the black line for (C) peripapillary atrophy area and (D) optic cup area plotted on a log scale against axial length.

ocular refraction, either as a linear or exponential terms, lens thickness, FSK, age, and gender as linear terms) did not explain a statistically significant proportion of the residual variation (in all cases F test P ⱖ 0.05). Having adjusted for axial length, DA and both measures of NRA are estimated to increase by approximately 2% per diopter increase in ocular refraction, but the 95% CI shows the results are consistent with an effect between a 1% decrease and a 4% increase. For DA and NRA the exponential model in axial length alone is an acceptable model, and plots of the residuals support this (Figure 3). For CA and PA there was insufficient evidence of nonlinearity with any of the explanatory variables. In contrast to the univariate analysis, the 95% CI from multiple linear regression analysis (Appendix Eqn. 3) for the associations between CA and ocular refraction and keratometry are consistent with no effect (in both cases P ⬎ 0.55). However, /1-mm increase in axial length CA increases by on average 11% (95% CI, 5%–16%), which is similar to the univariate analysis. Females have 31% larger CA (95% CI,

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1%–57%, P ⫽ 0.03). For PA, multiple regression analysis shows axial length to be the only statistically significant association, and the effect has reduced and PA is predicted to increase by 26%/ 1-mm increase in axial length (95% CI, 10%– 44%), per diopter increase in ocular refraction toward myopia, PA is predicted to increase by approximately 6% (95% CI, from 12% increase to 1% decrease), but this effect is not statistically significant at the 5% level. For anterior chamber depth, lens thickness, and age, effect sizes reduced to approximately 1%, and in all cases the 95% CIs are consistent with no effect. Females have 23% smaller PA, but the 95% CI is consistent with 42% decrease to a 4% increase (P ⫽ 0.09). For all optic disc parameters once axial length was modeled using the appropriate model, the other explanatory variables did not explain a statistically significant proportion of the residual variance, apart from the possible difference in CA and PA between the genders. The association between DA and NRA is log-exponential in axial length and log-linear in axial length for CA and PA. For completeness plots of the residuals are included in Figure 3

Rudnicka et al 䡠 Determination of Optic Nerve Head Parameters in Normal Subjects Table 2. Summary of Univariate Regression Analysis. Predicted Percentage Change in Optic Disc Parameters is Per Unit Increase in Explanatory Variable

Predicted Change in Optic Disc Parameter for Stated Increase Optic Disc Area n ⫽ 122

1-mm increase in axial length 1-D increase in ocular refraction 0.1-mm increase in ACD 0.1-mm increase in LT 0.1-mm increase in keratometry 1-year increase in age Females vs. males

Neuroretinal Rim Area (1) n ⫽ 122 2

%

R

10.3 (8.4, 12.3) ⫺4.1 (⫺5.0, ⫺3.2) ⫺4.4 (⫺6.2, ⫺2.7) 5.4 (3.1, 7.8) 4.2 (1.9, 6.6) 1.8 (0.2, 3.4) ⫺4.8 (⫺16.2, 8.0)

0.51 0.38 0.17 0.16 0.10 0.04 0.01

%

R2

11.4 (9.3, 13.6) ⫺4.5 (⫺5.5, ⫺3.5) ⫺4.1 (⫺6.0, ⫺2.1) 6.2 (3.7, 8.7) 3.8 (1.3, 6.5) 1.9 (0.1, 3.7) ⫺7.3 (⫺19.2, 6.5)

0.51 0.39 0.12 0.17 0.08 0.04 0.01

*Effect sizes associated with ocular refraction are negative because the effect is calculated per unit increase in ametropia (i.e. increasing positive value).

and show that these regression models are a reasonable fit to the data.

Discussion The values for DA, NRA, and CA agree with previous studies,8,15,16,19,20,26,27 with slightly larger average values reported by others.7,18,28,29 Differences between studies may be partly attributed to the magnification correction methods used to convert image size measurements into absolute units and the demographics of the sample. Jonas et al30 reported up to a 10-fold variation in DA, with a higher mean value for DA of 6.87 mm2, but their sample contained a larger proportion of subjects with higher degrees of myopia. An increase in the interindividual variation in optic disc size with increasing myopia was also reported, and this supports the observations in this study. It was important to stabilize this variance by performing a log transformation before regression analyses. Heijl and Mo¨ lder17 demonstrated that in subjective evaluations of fundus photographs larger discs were more often classified as glaucomatous, whether they were glaucomatous or not, whereas smaller discs were more likely to be classified as normal. Thus, cohorts obtained from clinics where patients are attending for suspect glaucoma, for example, may contain a higher proportion of larger size optic discs than a random sample taken from the general population. The Baltimore Eye Sur-

vey31 found glaucomatous patients to have larger optic discs than adults without glaucoma, but the effect was not significant at the 5% level. Univariate analysis showed a statistically significantly positive relationship between axial length and all optic disc parameters, and in all cases axial length was the strongest predictor compared with the other factors. Some studies have found no correlation between disc area and axial length or between disc area and spherical equivalent refraction.7,15–18 These studies predominantly included subjects with relatively lower degrees of ametropia and a narrower range of axial lengths. Others have reported weak correlations between disc area and axial length.19 Jonas et al30 found a correlation between disc area and axial length, and disc area and refraction in a group of myopes of more than ⫺8 D but not in a group of subjects with less than 8 D of myopia.7 A larger cross-sectional study, in agreement with this study, found an increase in disc area and NRA with increasing myopia.20 Others have not found NRA to be associated with axial length or ocular refraction.7,15,29 Although there are discrepancies in the literature as to whether the absolute sizes of optic disc parameters are related to axial length or ocular refraction, this does not necessarily imply that the studies are in complete disagreement. This study has shown that the logarithm of the optic disc parameters DA and NRA exhibit a nonlinear relationship with axial length, which seems to be reasonably well explained by the exponential growth model described. If this expo-

Table 3. Predicted Percentage Change in Optic Disc Area and Both Measures of Neuroretinal Rim Area (NRA1, NRA2) per Unit Increase in Axial Length at the Specified Levels of Axial Length, Using the Exponential Model (equation 4). Predicted % Change in Optic Disc Parameter for 1-mm Increase in Axial Length at Various Levels Axial Length

Optic Disc Area n ⫽ 122

Neuroretinal Rim Area (1) n ⫽ 122

Neuroretinal Rim Area (2) n ⫽ 122

1-mm increase in axial length at 20 mm–21mm 25 mm–26 mm 30 mm–31mm 35 mm–36mm

%, R ⫽ 0.56 2.8 6.5 15.7 40.1

%, R ⫽ 0.58 2.7 6.9 17.8 49.9

%, R2 ⫽ 0.58 2.8 6.9 17.7 48.8

2

2

Log (DA) ⫽ 0.344 ⫹ 0.0052 exp[(axial length in mm)⫻ 0.168]. Log (NRA1) ⫽ 0.168 ⫹ 0.0037 exp[(axial length in mm)⫻ 0.181]. Log (NRA2) ⫽ 0.149 ⫹ 0.0040 exp[(axial length in mm)⫻ 0.178].

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Ophthalmology Volume 108, Number 12, December 2001 the Explanatory Variable, along with the 95% Confidence Intervals, R2 for each Model and Sample Size (n) in Explanatory Variable (95% Confidence Interval) Neuroretinal Rim Area (2) n ⫽ 122 2

%

R

11.4 (9.4, 13.6) ⫺4.5 (⫺5.5, ⫺3.5) ⫺4.1 (⫺6.0, ⫺2.2,) 6.2 (3.7, 8.7) 3.9 (1.3, 6.5) 1.9 (0.2, 3.7) ⫺7.4 (⫺19.3, 6.2)

0.51 0.40 0.12 0.17 0.07 0.04 0.01

Optic Cup Area n ⫽ 63 % 10.0 (4.6, 15.7) ⫺3.1 (⫺5.5, ⫺0.01) ⫺2.7 (⫺5.9, 0.5) 1.3 (⫺3.2, 6.0) 4.7 (1.0, 8.4) ⫺0.1 (⫺2.8, 2.6) 27.3 (3.4, 56.7)

Peripapillary Atrophy Area n ⫽ 73 R

2

0.19 0.10 0.04 0.01 0.10 ⬍0.01 0.10

%

R2

42.4 (35.0, 50.2) ⫺15.7 (⫺18.1, ⫺13.3) ⫺11.9 (⫺17.6, ⫺5.9) 23.6 (14.5, 33.4) 6.6 (⫺2.4, 16.5) 9.4 (3.5, 15.7) ⫺41.0 (⫺64.4, ⫺2.3)

0.71 0.67 0.17 0.30 0.03 0.13 0.06

ACD ⫽ anterior chamber depth; D ⫽ diopter; LT ⫽ lens thickness.

nential relationship is accepted, study samples that primarily include subjects with lower degrees of ametropia, typically less than 6 D, would encompass a relatively narrow range of axial length (between approximately 23 and 26 mm), and are unlikely to elicit any statistically significant relationship between these disc parameters and axial length unless the sample is very large. In Figure 2, the exponential curve in this region is fairly flat. Similarly, if the study sample contains a large proportion of subjects with higher degrees of myopia, and therefore longer axial lengths, a positive relationship is more likely to be found between these optic disc parameters and axial length. At relatively longer axial length the gradient of the exponential curve becomes steeper. The advantage of the current analysis is that it avoids the arbitrary division of the sample by degree of ametropia or axial length, and this partly explains why some studies have differed in their findings. The exponential model describes the relationship between axial length and DA and NRA adequately, such that the other factors are no longer important predictors. The effects observed in the univariate analysis were confounded by axial length. DA and NRA increase by approximately 3%/mm increase in axial length at 20 mm, but at axial lengths of 25 mm, 30 mm, and 35 mm, this increases respectively to approximately 7%, 16%, and 40% for DA and 7%, 18%, and 50% for NRA. The fact that the DA and NRA increase with increasing axial length is biologically plausible. It has been shown that the size of the optic disc in 107 freshly enucleated eyes is governed by the size of the scleral canal.7 It is very likely that the size of the scleral canal increases as the globe becomes stretched with axial extension in myopia. This increase in the scleral canal area is accompanied by an increase in the DA and, consequently, the NRA. There is no biologic reason to expect this elastic behavior of the sclera to be linear. It is possible that stretch forces at the posterior pole behave nonlinearly and may explain the exponential increase in DA and NRA on a log scale with axial elongation. An increase in PA with increasing axial length is not surprising, because myopic crescents are believed to be a direct result of scleral expansion associated with the axial elongation in myopia.32,33 The variability in PA increased with increasing PA and with increasing axial length and

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myopia. A log transformation stabilized this variance, and the relationship between PA and axial length became linear, with no evidence of residual nonlinearity. Although PA is thought to be a risk factor for glaucomatous neuropathy,6,7,34 it is not clear whether physiologic PA carries the same increased risk. Once axial length was modeled linearly, the other factors were no longer important predictors for PA and CA, apart from a possible difference between males and females. PA is estimated to increase by approximately 26% and CA by 10%/mm increase in axial length. The associations between CA and axial length and between CA and refraction are comparatively weak. However, others have not found any association between cup area and axial length7 or refraction.20,35 In contrast to DA and NRA, PA and CA do not exhibit any residual curvature after a log transformation. PA and CA exhibit a constant proportionate change in size per unit increase in axial length. This differing observation may be due in part to the fact the PA and CA are physiologic features not present in all eyes, and the analysis is limited to eyes exhibiting these two features. PA is usually present in myopic eyes, which tend to have longer axial lengths and larger optic discs. At shorter values of axial length, where the optic disc is smaller (and NRA smaller), PA is not found with the same frequency. The data used in the analysis of PA are constructed of a particular subgroup of the eyes used in the analyses for DA and NRA. Similar reasoning can be applied to CA, only half of the sample had physiologic cupping, and it was noted that at longer axial lengths CA was observed with reduced frequency. Cup/disc area ratio was shown to be related to axial length and to intraocular pressure by Tomlinson and Phillips.36 They believed that the higher cup/disc area ratio observed in longer eyes is a reflection of an association between DA and axial length. An association between larger discs having larger optic cups has been reported.5,15,17,19,23,26 Intercorrelations between the optic disc parameters have not been reported in this study. A general observation in this study was that subjects with higher myopia tended not to have an optic cup, whereas in subjects with moderate/low myopia it was observed more frequently. The position of the lamina cribrosa is more anterior in myopic eyes than in nonmyopic eyes,33 which gives the cup

Rudnicka et al 䡠 Determination of Optic Nerve Head Parameters in Normal Subjects

Figure 3. (A) Normal residual plot and (B) residuals plotted against axial length, from exponential model in axial length for optic disc area. (C) and (D) Normal residual plots for peripapillary atrophy area and optic cup area, respectively, from multiple linear regression.

a shallow appearance and limits the amount of optic cupping that is possible. The fact that axial length has been elicited, as a central predictor of DA, NRA, and PA may not be surprising, because it is one of the most important factors governing ametropia and consequently the magnification offered by the human eye. All methods of ocular imaging giving the absolute size of retinal features will take account of the eye’s refractive power, and it is now generally accepted that this is strongly related to axial length and ametropia. What is important is to describe the nature of this relationship as clearly as possible, especially because there is conflicting evidence in the literature. This study’s analysis offers an explanation to link studies. If indeed axial length was not related to the size of the optic disc parameters and the associations observed were produced by systematic error of the magnification correction procedure used, the relationships should have been the “same” for all optic disc parameters. This is not the case.

The nature of these associations is different as are their magnitude and strengths, being very much weaker for CA. Furthermore, the systematic error would have to be considerable to produce these results, which the authors believe to be highly unlikely. Previous work has shown agreement between the size of optic disc dimensions estimated planimetrically and the size of the scleral canal in enucleated eyes.6 If an association exists between the optic disc parameters and axial length, it is very likely that an association with ocular refraction will also be observed, because these two factors are so strongly correlated with each other. An additional possible source of variation is that spectacle refraction is often used in the analysis instead of corneal vertex refraction or ocular refraction. Although the former is the standard clinical measure of ametropia, for analytical purposes the latter two are preferred, because the influence of vertex refracting distance is taken into consideration and standardizes the degree of ametropia. This becomes more

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Ophthalmology Volume 108, Number 12, December 2001 important with higher degrees of ametropia. The current results show that once axial length is taken into consideration, ocular refraction does not explain a statistically significant proportion of the residual variation in the optic disc parameters over and above that already explained by axial length. The univariate analysis agrees with previous work showing a marginal difference in DA and NRA between the genders,15,18,20,26,29 with females having approximately 5% smaller DA and 7% smaller NRA than males, but these effects were not statistically significant. Others have found females to have statistically significantly smaller horizontal disc diameters16,22 than males. PA was found to be considerably smaller in females univariately, but in the multiple regression model gender was of borderline statistical significance (P ⫽ 0.09), with females having 23% smaller PA than males. Females had, on average, 31% larger CAs than males by the multiple regression analysis, but this difference is of borderline statistical significance (P ⫽ 0.03) and should be interpreted cautiously. Other studies have not reported any differences between males and females for cup area.20,35 An association was demonstrated between age and DA, NRA, and PA in this study, but these relationships were confounded by axial length. In the exponential models for DA and NRA the effects associated with age are greatly reduced and are not statistically significant at the traditional level of 0.05 in all cases. The independence of disc size and NRA with age agrees with previously published work in normal populations having older age profiles.15,16,22,29,37 The univariate analysis showed PA to increase by on average 9% per year increase in age (145% per decade), but this effect was markedly reduced in the multiple regression analysis and was not statistically significant. The association between age and axial length in this sample most likely confounded the association between age and PA. In agreement with other studies no association was found between cup area and age.7,20,35 An understanding of the interrelationships between optic disc parameters in people with different ocular characteristics is required if clinical diagnostic criteria partially rely on the size of these optic disc parameters. Of the ocular biometric factors considered, axial length seems to be the most important predictor of the absolute area of the optic disc parameters. In multiple regression analyses associations between the explanatory variables and the optic disc parameters were all confounded by axial length. This does not mean that ocular refraction is not important, because it is inextricably linked to axial length, and this is true for the other biometric factors. We confirm that there is no association between the optic disc parameters and age in this sample of subjects less than 40 years of age. Females exhibited smaller values for DA and NRA than males, which were not statistically significant, and borderline statistically significant differences for PA and CA. In addition, the two different methods described to demarcate the neuroretina produced different values, as expected, for absolute size, but the relationships with the other variables produced virtually identical results. It should be stated that the findings in this study relate to

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normal subjects with similar distribution of ocular biometric factors, age, and gender. If the preceding analysis were to be repeated in a group of glaucoma patients, the relationships observed may be different.

Appendix Statistical Modeling To stabilize the heterogeneity of variance exhibited by the optic disc parameters a logarithmic transformation was performed before linear regression analysis. If this is not done, the assumptions of a linear regression normal errors model would be invalid.38 In all instances the natural logarithm of the optic disc parameter was modeled. Explanatory variables, which were found to be related univariately, were included in a multiple linear regression analysis to compare the combined effects of each factor. The general form of the multiple regression model is given in equation 3. log共y i 兲 ⫽ ␣ ⫹

冘␤ x ⫹ ␧ j

j ij

i

␧i ⬃ N(0,␴ 2)

(3)

yi is the value for the relevant optic disc parameter for the each subject, i xij is the value of the jth explanatory variable for the ith subject. ␣ is the constant term in the model exp(␤j) –1 gives the proportionate change in y for a unit increase in xj. ⑀i is the error term and is assumed to be normally distributed with mean zero, variance ␴2. Although model 3 gives the combined effects of the predictor variables, problems arise when highly correlated variables, such as axial length and ocular refraction, are included in the model simultaneously. The parameter estimates are likely to be inaccurate if the correlation is strong and can produce misleading results for the separate effects of each covariate. This statistical phenomenon is termed collinearity. It can be overcome to some extent by addressing any inadequacies in the linear model by fitting a more appropriate model. Graphically there seems to be a curved relationship between each optic disc parameter, except cup area, and some of the explanatory variables even after log transformation. In the presence of statistically significant residual curvature after performing the log transformation, an exponential model was fitted.24 This nonlinear model allows for the curvature in the relationship but is not symmetrical like the quadratic model. The form of the exponential model is given in equation 4 for an optic disc parameter yi and for a single predictor, axial length. log(y i ) ⫽ b 0 ⫹ b 1 exp 兵b 2 ⫻ 共axial length兲 i 其 ⫹ ␧ i ␧i ⬃ N(0,␴2)

(4)

yi and ⑀i are defined as above b0 is the constant term in the model b1 and b2 are the effects associated with axial length Eqn. 4 was used as the baseline exponential model, and the addition of the other variables found to be statistically

Rudnicka et al 䡠 Determination of Optic Nerve Head Parameters in Normal Subjects Table 4. Parameter Estimates and 95% Confidence Intervals for Exponential Model in Axial Length for Optic Disc Area and Neuroretinal Rim Area Parameter Estimates (95% Confidence Interval)

Axial length (b1) Axial length (b2)

Optic Disc Area n ⫽ 122

Neuroretinal Rim Area (1) n ⫽ 122

Neuroretinal Rim Area (2) n ⫽ 122

0.0052 (⫺0.0114, 0.0218) 0.168 (0.078, 0.258)

0.0037 (⫺0.0076, 0.0149) 0.181 (0.093, 0.269)

0.0040 (⫺0.0082, 0.0163) 0.178 (0.091, 0.265)

Log (DA) ⫽ 0.344 ⫹ 0.0052 exp[(axial length in mm)⫻ 0.168]. Log (NRA1) ⫽ 0.168 ⫹ 0.0037 exp[(axial length in mm)⫻ 0.181]. Log (NRA2) ⫽ 0.149 ⫹ 0.0040 exp[(axial length in mm)⫻ 0.178].

significantly related to the optic disc parameters from the original univariate model were evaluated by the F test. First, linear terms were included. However, if the quadratic model revealed statistically significant curvature for a variable, exponential terms for these covariates were also evaluated. All effects are reported in terms of the proportionate change in the absolute optic disc parameter per unit increase of each explanatory variable, along with the corresponding 95% CIs. Plots of the residuals were inspected for goodness of fit.

Results Effectiveness of the log transformation is evident for DA comparing Figures 1 and 2, which show that the variance was stabilized. Similar graphical observations were made for the other disc parameters, and in all cases normal plots of the data were considerably improved by log transformation. Quadratic models revealed residual curvature with axial length for DA and NRA only (P ⬍ 0.001 in both cases). The quadratic model is useful to examine presence of curvature but has limitations. In particular, the fact that a quadratic model must have a minimum can introduce implausible nonmonotonic behavior. The exponential model in axial length was fitted, because it allows for the increasing rate of change in DA and NRA at increasing levels of axial length but is monotone. The quadratic and exponential models are not nested models and cannot be compared formally, but the latter succinctly captures the essential features and as such is preferred in terms of interpretation and prediction. Residual plots from the exponential model with just axial length support the goodness of fit of this model. Residual plots for NRA were similar to those shown for DA (Fig 3). Table 4 gives the parameter estimates and 95% CI from the exponential models in axial length for DA and NRA.

Technical Note STATA uses the Newton-Raphson iterative procedure to obtain parameter estimates. Initially, values for the coefficients were specified by an educated guess. Convergence criteria for successive parameter estimates and for the residual sum of squares were set to 0.00001. In all cases fewer than 20 iterations were required, and all models converged to a unique solution.

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