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Comparison of Ocular Component Growth Curves
among Refractive Error Groups in Children
Lisa A. Jones,
1
G. Lynn Mitchell,
1
Donald O. Mutti,
1
John R. Hayes,
1
Melvin L. Moeschberger,
2
and Karla Zadnik
1
PURPOSE. To compare ocular component growth curves among
four refractive error groups in children.
M
ETHODS Cycloplegic refractive error was categorized into four
groups: persistent emmetropia between ⫺0.25 and ⫹1.00 D
(exclusive) in both the vertical and horizontal meridians on all
study visits (n ⫽ 194); myopia of at least ⫺0.75 D in both
meridians on at least one visit (n ⫽ 247); persistent hyperopia
of at least ⫹1.00 D in both meridians on all visits (n ⫽ 43); and
emmetropizing hyperopia of at least ⫹1.00 D in both meridi-
ans on at least the first but not at all visits (n ⫽ 253). Subjects
were seen for three visits or more between the ages of 6 and 14
years. Growth curves were modeled for the persistent em-
metropes to describe the relation between age and the ocular
components and were applied to the other three refractive
error groups to determine significant differences.
R
ESULTS At baseline, eyes of myopes and persistent em-
metropes differed in vitreous chamber depth, anterior cham-
ber depth, axial length, and corneal power and produced
growth curves that showed differences in the same ocular
components. Persistent hyperopes were significantly different
from persistent emmetropes in most components at baseline,
whereas growth curve shapes were not significantly different,
with the exception of anterior chamber depth (slower growth
in persistent hyperopes compared with emmetropes) and axial
length (lesser annual growth per year in persistent hyperopes
compared with emmetropes). The growth curve shape for
corneal power was different between the emmetropizing hy-
peropes and persistent emmetropes (increasing corneal power
compared with decreasing power in emmetropes).
C
ONCLUSIONS Comparisons of growth curves between persis-
tent emmetropes and three other refractive error groups
showed that there are many similarities in the growth patterns
for both the emmetropizing and persistent hyperopes, whereas
the differences in growth lie mainly between the emmetropes
and myopes. (Invest Ophthalmol Vis Sci. 2005;46:2317–2327)
DOI:10.1167/iovs.04-0945
M
yopia is a common condition in the world today that
generates significant annual healthcare expenditures.
1
Sperduto et al.
2
estimated the prevalence of myopia in 12- to
17-year-olds in the United States in 1971 to 1972 to be 24%.
Although many studies have been performed in the area of
childhood myopia, there is limited information about the
course and progression of myopia and accompanying changes
in the ocular components over extended periods. Comparing
the course of component development in emmetropes and
children with refractive error provides a useful description of
the natural history of ocular growth.
Most of the information about the natural history of myopia
is obtained from the control groups of bifocal or drug treat-
ment studies.
3–11
Although these studies have investigated the
change in myopia with age, very few look at the accompanying
changes in the ocular components.
4,7
Later studies have con-
centrated primarily on axial length.
4–8,11
Pa¨rssinen and Lyyra
7
presented the results from a randomized
clinical trial evaluating the impact of bifocals with a ⫹1.75 D add,
compared with full correction with spectacles for distance vision
only versus full correction with spectacles for continuous wear.
Regression models of myopia progression over a 3-year period by
gender were presented. In the spectacle-wearing group, myopic
progression was faster in girls than in boys. The 60 slowest
progressors were compared with the 60 fastest progressors on
corneal power (both initial and final), final anterior chamber
depth, final lens thickness, and final axial length. There were
significantly more girls among the 60 fastest progressors. The only
statistically significant difference between the two groups was in
axial length, with the fastest progressors having an average axial
length of 0.88 ⫾ 0.76 mm longer than the slowest progressors.
7
Gwiazda et al.
6
presented results of the Correction of Myo-
pia Evaluation Trial evaluating single-vision versus progressive
addition lenses in children on the progression of myopia. Over
the 3 years of the study, the spherical equivalent progressed by
approximately 1.4 D in the single-vision lens group. An in-
crease in axial length of 0.75 mm over the same period showed
a significant correlation with change in refractive error (r ⫽
0.89).
Fulk et al.
5
conducted a single-vision versus bifocal lens
myopia progression trial, enrolling only myopic children with
near-point esophoria. Vitreous chamber depth increased ap-
proximately 0.48 mm after 30 months in the single-vision lens
group, whereas axial length changed by 0.49 mm.
Hyperopia has been studied far less often in either cross-
sectional or longitudinal studies.
12,13
Most data describe the
frequency of hyperopia in a given sample.
14
No studies discuss
the ocular components, their growth, or their relationship to
hyperopia in childhood.
One longitudinal study from an optometric practice exam-
ined refractive error for 6 years in 60 patients, beginning at age
7 years.
15
Whereas the number of myopes increased over the
years, the number of hyperopes remained unchanged (mean
change in the hyperopes: ⫹0.04 ⫾ 0.74 D). Ma¨ntyja¨rvi
16
found
little change in 46 hyperopes studied (mean change: ⫺0.12 ⫾
0.14 D/y). Hirsch
17
examined children at age 5 or 6 years and
then again at age 13 or 14 years. He found that all children who
From the
1
College of Optometry and
2
School of Public Health,
Division of Epidemiology and Biometrics, The Ohio State University,
Columbus, Ohio.
Supported by National Eye Institute Grants EY08893 and
EY014792, the Ohio Lions Eye Research Foundation, and the E. F.
Wildermuth Foundation.
Submitted for publication August 4, 2004; revised December 17,
2004, and February 11 and March 10, 2005; accepted March 29, 2005.
Disclosure: L.A. Jones, None; G.L. Mitchell, None; D.O. Mutti,
None; J.R. Hayes, None; M.L. Moeschberger, None; K. Zadnik,
None
The publication costs of this article were defrayed in part by page
charge payment. This article must therefore be marked “advertise-
ment” in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Corresponding author: Lisa A. Jones, College of Optometry, The
Ohio State University, 338 W. 10th Ave., Columbus, OH 43210;
ljones@optometry.osu.edu.
Investigative Ophthalmology & Visual Science, July 2005, Vol. 46, No. 7
Copyright © Association for Research in Vision and Ophthalmology
2317
were ⫹1.50 D or more hyperopic at age 5 or 6 years (n ⫽ 33)
and 88% of children who were between ⫹1.25 and ⫹1.49 D at
age5or6(n ⫽ 8) years remained hyperopic at age 13 or 14
years. These studies indicate that children with hyperopia are
more likely to remain hyperopic. Ocular components have not
been examined in hyperopes over time.
The studies evaluating refractive error over time have ad-
dressed some of the components that change as refractive
error changes, with particular attention to the increase in axial
length and vitreous chamber depth and the progression of
myopia. The purpose of this study was to generate and com-
pare the growth curves for the ocular components in school-
aged emmetropes, myopes, and hyperopes that are em-
metropizing and those with persistent hyperopia.
Understanding the growth of the various components of the
eye in detail may help to explain the different behavior of
refractive errors as a function of age: how myopes progress,
how emmetropes remain stable, why some hyperopes em-
metropize, and why others remain hyperopic. The results of
this analysis expand on the current literature by including
measures of crystalline lens shape and power in addition to
corneal power and axial dimensions.
METHODS
Subjects for these analyses were participants in the Orinda Longitudi-
nal Study of Myopia (OLSM).
18
Children were recruited from the
Orinda Union School District in California to participate in a longitu-
dinal study evaluating risk factors for myopia and the development of
the associated ocular components. Individuals and their parents pro-
vided informed consent according to the tenets of the Declaration of
Helsinki. Informed consent procedures and the study protocol were
approved by the University of California, Berkeley’s Committee for the
Protection of Human Subjects. Data presented herein were obtained
from 1989 through 2001. To be included in these analyses, the subject
had to have at least three visits between the ages of 6 to 14 years to
allow for the generation of ocular component growth curves.
The ocular components of the right eye only were measured.
Corneal anesthesia was used twice: once to minimize the discomfort
from the cycloplegic drops and later to allow ultrasonography. One
drop of 0.5% proparacaine was followed by two drops of 1% tropic-
amide, 5 minutes apart, for cycloplegia. Measurements were made 25
minutes after the initial instillation. Cycloplegic refractive error was
measured by autorefraction with an open-view infrared autorefractor
(model R-1; Canon USA, Lake Success, NY; no longer manufactured).
The left eye was occluded with an eye patch during autorefraction.
The autorefractor was set up so that the free viewing space was
illuminated from the examiner’s side of the instrument. The child
fixated 6/9 (20/30) size letters on a near-point test card viewed through
a ⫹4.00-D Badal lens. At least 10 autorefractor readings were taken
with the eye in primary gaze. Spurious readings, or acceptable ones
exceeding 10, were eliminated according to the following scheme and
rationale.
Because lapses in fixation result in off-axis refraction, such lapses
are marked by anomalous cylinder readings. We eliminated these
readings, whether there were more than 10 or not, by determining the
mode of the cylinder (magnitude) and eliminating any reading with
cylinder differing by more than 0.75 D from the mode. Blinking or eye
movement can also cause anomalous sphere readings. Sphere readings
that differed by more than 1.00 D from the mode of all sphere values
were also removed. After anomalous readings were eliminated, extra
readings were eliminated alternately from the beginning and the end of
the measurement series.
The 10 spherocylindrical refractions were averaged by using the
matrix method described by Harris.
19
This method treats each sphero
-
cylinder as a vector that can then be manipulated by standard linear
algebra matrices to provide means and standard deviations of sphere,
cylinder, and axis. Mean spherocylinders were also converted to hor-
izontal and vertical meridian refractions.
Corneal power in the vertical meridian was measured with pho-
tokeratoscopy (KERA 9-ring CorneaScope [Kera Corp., Santa Clara, CA]
from 1989 to 1990 and 1990 to 1991). One photograph was taken on
each occasion. The photograph was analyzed on a proprietary, video-
based, computer-assisted analysis system (KERA-Scan; Kera Corp.).
From 1991 to 1992 on, the topographic modeling system was used.
The third inferior ring (corresponding to a location roughly 1.5 mm
from the center) in the vertical meridian was selected for this analysis,
primarily because it was a reading free of contamination from lid
position and therefore obtainable in every child.
Crystalline lens radii of curvature were obtained with video pha-
kometry,
20
which is an updated version of still-flash photography
comparison ophthalmophakometry
21,22
that measures Purkinje images
I, III, and IV formed close to the optic axis by a collimated light source,
with digitized, computer analysis of multiple images. The child was
seated behind the instrument with an eye patch on his or her left eye
and instructed to fixate a red-light– emitting diode on a movable arm
while the reflected Purkinje images I, III, and IV were recorded. Lens
power was calculated with the Gullstrand-Emsley schematic eye indi-
ces of refraction for the aqueous and the vitreous (4/3) and the
crystalline lens (1.416).
23
An equivalent index and calculated lens
power were also found with an iterative procedure that produces
agreement between measured refractive error and that calculates by
using ocular component data from ultrasound and Purkinje image data
from phakometry.
Anterior chamber depth, lens thickness, and vitreous chamber
depth (average of five readings for each) were measured through the
dilated pupil with the an A-scan ultrasound unit (model 820; Allergan-
Humphrey, Carl Zeiss Meditec, Dublin, CA), with a handheld probe on
a semiautomatic measurement mode with a drop of 0.5% proparacaine
instilled in the right eye. Readings in which the retinal peak was
marked at other than its anterior-most point were discarded, either
online or after all five readings had been obtained.
The data entry and verification for 1989 through 1995 were con-
ducted by the Data Management Unit of the Survey Research Center at
the University of California at Berkeley. Data from 1996 through 2001
were entered and verified at the Optometry Coordinating Center at
The Ohio State University. All data were double-entered into databases
specifically designed for the study.
Children included in these analyses met the following criteria: Each
child attended at least three study visits between the ages of 6 and 14
years. A child was defined as a myope if both the horizontal and
vertical meridians of the right eye under cycloplegia were ⫺0.75 D or
more myopic at one or more visits. A child was defined as a persistent
hyperope if both the horizontal and vertical meridians were at least
⫹1.00 D or more hyperopic at all visits. Emmetropes were defined as
being between ⫺0.25 and ⫹1.00 D (exclusive) in both meridians at all
study visits. Children who began as hyperopes (horizontal and vertical
meridians at least ⫹1.00 D) at the first visit but did not demonstrate at
least ⫹1.00 D of hyperopia at all study visits were considered to be
emmetropizing hyperopes. Children not fitting one of these four cri-
teria were not included in the analysis.
Statistical Methods
Descriptive statistics (means and frequencies) were calculated for age
and for each of the ocular components at the child’s first examination.
Growth curves were generated relating age and each ocular compo-
nent: lens equivalent index, calculated equivalent lens power, Gull-
strand lens power, lens thickness, anterior chamber depth, axial
length, vitreous chamber depth, and corneal power. The curves were
generated in mixed models run on computer (SAS ver. 9.1; SAS Insti-
tute Inc., Cary, NC). This method allows for multiple points to be used
to generate each subject’s curve and then creates an “average” model
that incorporates the individual curves into an average curve, accord-
ing to the maximum likelihood. The model also allows for specification
2318 Jones et al. IOVS, July 2005, Vol. 46, No. 7
of the structure of the variance–covariance matrix to describe the
relation between the correlated longitudinal observations. Variance–
covariance matrices investigated were the unstructured and com-
pound symmetry matrices. Model parameters were determined by
maximum-likelihood methods.
24
Mixed modeling is particularly pow
-
erful because it allows for the presence of a variable number of data
points—that is, an otherwise eligible subject is not excluded for miss-
ing observations due to the potential for differing lengths of follow-up.
Missing data are handled within the iterative maximum-likelihood pro-
cedure, in which all available subject data were used, even in the
calculations. The maximum-likelihood procedure chooses the param-
eters that will maximize the likelihood of observing the given set of
sample data.
Growth curves were initially modeled for each component, includ-
ing only the data from emmetropic children.
25
In short, each outcome
was modeled as a linear function of several mathematical forms of age,
which included natural log, quadratic, age,
2
inverse(age), and in
-
verse[natural log(age)] and assuming points of inflection. In these latter
models, cut points based on age were included in the model to allow
the shape of the curve to vary before and after a given cut point. The
cut points were selected within 0.5-year increments from age 9 to 12
years, so that there was a sufficient number of data points both before
and after the cut point and so that the cut point was within the age at
which myopia might be expected to develop. Akaike’s information
criterion (AIC) values from each model were used to determine which
function of age and which variance– covariance structure best de-
scribed the ocular component changes.
26
The best model was consid
-
ered to be the one with the lowest AIC value, and model effectiveness
was assessed by the model
2
. The probability was used to assess the
significance of model fit. Once the best-fitting model for emmetropes
was determined, this functional form was applied to the data for the
myopes and for both groups of hyperopes, to derive curves for those
groups. Parameter estimates from each curve were then compared
with corresponding parameters from the emmetropic model. Allowing
each refractive group to have growth curves with their best-fitting
functional form would prevent comparisons between curves because
of the lack of a comparison method across models. By fixing the
functional form as the optimal model for the emmetropes, we main-
tained the ability to compare the estimated curves among refractive
error groups.
RESULTS
Two hundred forty-seven children were classified as myopic.
Of these, 76.1% were nonmyopic at baseline. There were 43
FIGURE 1. Description of the sub-
jects who were eligible and ineligible
for the analyses.
IOVS, July 2005, Vol. 46, No. 7 Refractive Error Growth Curves 2319
persistent hyperopes, 253 emmetropizing hyperopes, and 194
persistent emmetropes. Eight children who were emmetropic
at baseline became myopes during the course of the study.
Figure 1 presents the children available for analysis and the
reasons for exclusion. Males were 44.1%, 46.5%, 56.7%, and
46.5% of the myopes, persistent hyperopes, persistent em-
metropes, and emmetropizing hyperopes, respectively. Racial–
ethnic group was reported by a parent. Overall, whites ac-
counted for the majority of the sample (85.0%), with 0.4%
African American, 11.1% Asian, 2.0% Hispanic, 0.3% American
Indian and 1.1% “other” racial– ethnic group. The percentage
of children classified into each refractive error group by race or
ethnic group is shown in Table 1.
The number of visits per subject differed significantly
among refractive error groups (Table 2,
2
⫽ 139.96, P ⬍
0.0001), with the persistent emmetropes more likely to have
attended fewer visits than the myopes, the persistent hyper-
opes, or the hyperopes. Thirty-seven percent of the myopes,
42% of the emmetropizing hyperopes, and 33% of the persis-
tent hyperopes had a full eight visits. Only 15% of the persis-
tent emmetropes attended all eight visits. Mean years of fol-
low-up (⫾SD) were 3.7 ⫾ 1.9 for the persistent emmetropes,
5.0 ⫾ 2.0 for the myopes, 5.4 ⫾ 1.7 for the emmetropizing
hyperopes, and 4.6 ⫾ 2.1 years for the persistent hyperopes
(analysis of variance, P ⬍ 0.0001). Post hoc comparisons show
that the persistent emmetropes had a significantly shorter fol-
low-up period than did the myopes (P ⫽ 0.0023), the em-
metropizing hyperopes (P ⬍ 0.0001), and the persistent hy-
peropes (P ⬍ 0.0001). There was also a marginally significant
difference between the follow-up period of emmetropizing
hyperopes and persistent hyperopes (P ⫽ 0.046). The visits for
all subjects were overwhelmingly consecutive—that in, a sub-
ject who had three visits had three consecutive visits over a
2-year period, not visits spaced out over many years.
Baseline mean age and ocular component data for each of
the refractive groups are presented in Table 3. Because of the
differences in age between persistent emmetropes and the
other refractive error groups at baseline, comparisons of all
components were adjusted for age. Persistent emmetropes
changed, on average, ⫺0.19 ⫾ 0.24 D from their first to their
last visit. We saw very few emmetropic subjects with shifts
within the category. For example, of the subjects who started
at the higher end of emmetropia (ⱖ ⫹0.75 D both meridians),
only 5% fell below0Donthelast visit. This helps demonstrate
the stability of refractive error in the emmetropic group. The
myopes were evaluated to see whether there was evidence of
a group of stable myopes to compare to myopes who could be
identified as progressing myopes. Of the myopes, only 16
(6.5%) progressed 0.25 D or less over their visits. As a yearly
average, 86% of the subjects showed an average yearly change
of more than 0.25 D. Based on these data, there does not seem
to be strong evidence of a group of stable myopes among our
subjects.
At baseline, persistent emmetropes and myopes differed in
axial length, vitreous chamber depth, and corneal power after
adjustment for age. Persistent emmetropes differed from the
emmetropizing hyperopes in anterior chamber depth and axial
length and from the persistent hyperopes in lens refractive
index, calculated lens power, anterior chamber depth, axial
length, and vitreous chamber depth. Persistent emmetropes
had a significantly longer axial length, longer vitreous cham-
ber, and deeper anterior chamber than did the persistent hy-
peropes. In contrast, the persistent emmetropes had a signifi-
cantly shorter axial length and shallower vitreous chamber
depth than did the myopes. Figure 2 presents the spherical
equivalent refractive error data across age for each of the four
refractive error groups. By definition, the persistent hyperopes
remained hyperopic across age, whereas the emmetropizing
hyperopes approached the emmetropic group. The spherical
equivalent of the myopic group continued to become more
myopic until age 14 years.
The best models describing the relation between a given
ocular component and age derived from the persistent em-
metropes’ data using mixed models with an unstructured vari-
ance–covariance matrix are given in Table 4. These models
were applied to the data of the other three refractive error
groups. The probabilities indicate whether the shape of the
model for each of the other three groups (that is, comparisons
of the model parameters) differed significantly from that of the
persistent emmetropes. Growth curves did not differ when the
myopic group was separated into incident and prevalent
myopes (data not shown).
There was a decreasing rate of change in all refractive error
groups for crystalline lens index (Fig. 3), Gullstrand lens power
TABLE 1. Racial/Ethnic Status of Subjects as Classified by Parents
Racial/Ethnic
Group
Myopes
n (%)
Emmetropes
n (%)
Emmetropizing
Hyperopes
n (%)
Persistent
Hyperopes
n (%)
American Indian 1 (50.0) 0 1 (50.0) 0
Asian 59 (72.0) 16 (21.1) 6 (2.4) 1 (1.2)
African American 1 (33.3) 1 (33.3) 1 (33.3) 0
Hispanic 4 (26.7) 7 (46.7) 2 (13.3) 2 (13.3)
White 178 (28.4) 170 (27.1) 240 (38.3) 39 (6.2)
Other 4 (50.0) 0 3 (37.5) 1 (12.5)
TABLE 2. Number of Visits Attended, by Refractive Error Group
Number of
Visits
Myopes
n (%)
Emmetropes
n (%)
Emmetropizing
Hyperopes
n (%)
Persistent
Hyperopes
n (%)
3 59 (23.9) 96 (49.5) 21 (8.3) 12 (27.9)
4 11 (4.5) 14 (7.2) 28 (11.1) 5 (11.6)
5 15 (6.1) 7 (3.6) 29 (11.4) 3 (7.0)
6 45 (18.2) 45 (23.2) 42 (16.6) 8 (18.6)
7 25 (10.1) 3 (1.5) 26 (10.3) 1 (2.3)
At least 8 92 (37.2) 29 (15.0) 107 (42.3) 14 (32.6)
2320 Jones et al. IOVS, July 2005, Vol. 46, No. 7
(Fig. 4), and calculated lens power (Fig. 5), with no statistically
significant differences in shape between persistent em-
metropes and the other refractive error groups for any of the
models. Lens thickness (Fig. 6) showed a decrease in thickness
until approximately 9.5 years of age, with an increase in thick-
ness at older ages in all four refractive error groups. There were
no differences in model shape for this component as a function
of refractive error group.
Persistent emmetropes differed from persistent hyper-
opes in the shape of the model for anterior chamber depth
(Fig. 7). The persistent emmetropes displayed a faster deep-
ening of the anterior chamber at younger ages than did the
persistent hyperopes. A difference in the shape of the ante-
rior chamber depth model was also recorded between the
myopes and the persistent emmetropes but not between the
persistent emmetropes and the emmetropizing hyperopes.
The myopes’ anterior chamber depth growth curve had a
steeper slope than the growth curve for the persistent em-
metropes. The steeper slope indicates that the myopes’
anterior chamber deepening did not slow down with age as
much as in the persistent emmetropes. However, the differ-
ence was not substantial, as shown by the small differences
between parameter estimates. The statistical significance
associated with these small differences may be more a func-
tion of large sample size.
The persistent emmetropes’ axial elongation (Fig. 8) was
significantly slower at older ages in persistent emmetropes
than in persistent hyperopes. Myopes also differed significantly
in model shape of axial elongation, with the slope of the
myopes’ growth curve increasing at a higher rate than the
persistent emmetropes after age 10 years. The model shape for
axial length did not significantly differ between persistent
emmetropes and emmetropizing hyperopes.
For vitreous chamber depth (Fig. 9), myopes and persistent
emmetropes differed significantly in model shape. The slope of
the vitreous chamber depth growth curve in the myopes in-
TABLE 3. Demographics at Baseline by Refractive Error Group
Variable Myopes Emmetropes
Emmetropizing
Hyperopes
Persistent
Hyperopes
Spherical equivalent (D) ⫺0.49 ⫾ 1.38 0.54 ⫾ 0.22 1.36 ⫾ 0.48 2.45 ⫾ 0.92
Age (y) 7.98 ⫾ 2.1* 9.40 ⫾ 2.3 7.06 ⫾ 1.3† 7.94 ⫾ 2.1‡
Lens refractive index 1.430 ⫾ 0.01 1.429 ⫾ 0.01 1.432 ⫾ 0.01 1.434 ⫾ 0.01‡
Gullstrand lens power (D) 20.79 ⫾ 1.5 20.62 ⫾ 1.4 21.18 ⫾ 1.3 21.26 ⫾ 1.8
Calculated lens power (D) 23.94 ⫾ 2.2 23.63 ⫾ 2.0 24.98 ⫾ 2.0 25.58 ⫾ 2.5‡
Lens thickness (mm) 3.50 ⫾ 0.2 3.47 ⫾ 0.1 3.54 ⫾ 0.2 3.55 ⫾ 0.2
Anterior chamber depth (mm) 3.68 ⫾ 0.2 3.69 ⫾ 0.2 3.53 ⫾ 0.2† 3.44 ⫾ 0.3‡
Axial length (mm) 23.05 ⫾ 0.9* 22.93 ⫾ 0.7 22.30 ⫾ 0.6† 21.91 ⫾ 0.9‡
Vitreous chamber depth (mm) 15.87 ⫾ 0.9* 15.77 ⫾ 0.7 15.24 ⫾ 0.6 14.93 ⫾ 0.8‡
Corneal power (D) 44.30 ⫾ 1.4* 43.61 ⫾ 1.5 43.79 ⫾ 1.3 43.54 ⫾ 1.5
Data are expressed as the mean ⫾ SD.
* Myopes significantly different from emmetropes after controlling for age in post hoc testing,
␣
⫽
0.05.
‡ Persistent hyperopes significantly different from emmetropes after controlling for age in post hoc
testing,
␣
⫽ 0.05.
† Hyperopes significantly different from emmetropes after controlling for age in post hoc testing,
␣
⫽
0.05.
FIGURE 2. Spherical equivalent for
each of the four refractive groups
from age 6 to 17 years.
IOVS, July 2005, Vol. 46, No. 7 Refractive Error Growth Curves 2321
creased at a higher rate than in the persistent emmetropes after
age 10 years. There were no differences in model shape in the
slope of vitreous chamber depth growth curves between the
persistent emmetropes and the persistent or emmetropizing
hyperopes.
Myopes and persistent emmetropes differed significantly in
model shape of corneal power (Fig. 10). Myopes had a rela-
tively constant slope with age, whereas persistent emmetropes
had a slope that became increasingly negative with increasing
age. Emmetropizing hyperopes also differed from the persis-
tent emmetropes in model shape of corneal power with a
slightly increasing slope with age. Persistent emmetropes and
persistent hyperopes were not significantly different from each
other.
DISCUSSION
Comparison of the results of this study with previous studies is
limited in scope because of the difficulty of comparing growth
curves to mean change. Both Gwiazda et al.
6
(COMET Study)
and Fulk et al.
5
show increases in vitreous chamber depth and
axial length in myopes, similar to our myopia curves. The
COMET Study also shows similar results in increases in anterior
chamber depth. Likewise, there is no change in the corneal
radii component from COMET. Over the course of 3 years,
there was 0.03-mm change in corneal radii.
6
Our myopia
curves show little change in corneal power as well. The one
component that seems to be on a different path is lens thick-
ness. The COMET Study shows a mean change in lens thick-
TABLE 4. Best Model to Predict Changes with Age in Emmetropes for Each Ocular Variable
Ocular Component Models P
Crystalline lens index E: 1.427 ⫹ 0.162 䡠 age
⫺2
PH: 1.429 ⫹ 0.222 䡠 age
⫺2
0.4645
M: 1.428 ⫹ 0.079 䡠 age
⫺2
0.2563
EH: 1.429 ⫹ 0.121 䡠 age
⫺2
0.6064
Gullstrand lens power E: Age ⱕ 9 years 27.001 ⫺ 2.983 䡠 ln(age)
Age ⬎ 9 years 25.080 ⫺ 2.057 䡠 ln(age)
PH: Age ⱕ 9 years 26.399 ⫺ 2.522 䡠 ln(age)
Age ⬎ 9 years 24.408 ⫺ 1.654 䡠 ln(age) 0.6376
M: Age ⱕ 9 years 28.775 ⫺ 3.948 䡠 ln(age)
Age ⬎ 9 years 24.311 ⫺ 1.945 䡠 ln(age) 0.0608
EH: Age ⱕ 9 years 25.834 ⫺ 2.399 䡠 ln(age)
Age ⬎ 9 years 24.633 ⫺ 1.888 䡠 ln(age) 0.3166
Calculated lens power E: 21.850 ⫹ 133.590 䡠 age
⫺2
PH: 22.501 ⫹ 158.168 䡠 age
⫺2
0.2369
M: 21.244 ⫹ 149.618 䡠 age
⫺2
0.1972
EH: 22.251 ⫹ 129.020 䡠 age
⫺2
0.7366
Lens thickness E: Age ⱕ 9.5 years 3.799 ⫺ 0.041 䡠 age
Age ⬎ 9.5 years 3.352 ⫹ 0.006 䡠 age
PH: Age ⱕ 9.5 years 3.746 ⫺ 0.026 䡠 age
Age ⬎ 9.5 years 3.428 ⫹ 0.007 䡠 age 0.0954
M: Age ⱕ 9.5 years 3.841 ⫺ 0.046 䡠 age
Age ⬎ 9.5 years 3.389 ⫹ 0.002 䡠 age 0.1827
EH: Age ⱕ 9.5 years 3.778 ⫺ 0.036 䡠 age
Age ⬎ 9.5 years 3.363 ⫹ 0.007 䡠 age 0.5221
Anterior chamber depth E: 1.817 ⫺ 0.265 䡠 ln(age)
2
⫹ 1.441 䡠 ln(age)
PH: 2.773 ⫺ 0.062 䡠 ln(age)
2
⫹ 0.447 䡠 ln(age)
0.0048
M: 1.425 ⫺ 0.311 䡠 ln(age)
2
⫹ 1.749 䡠 ln(age)
⬍0.0001
EH: 1.381 ⫺ 0.349 䡠 ln(age)
2
⫹ 1.787 䡠 ln(age)
0.1054
Axial length E: Age ⱕ 10.5 years 20.189 ⫹ 1.258 䡠 ln(age)
Age ⬎ 10.5 years 21.353 ⫹ 0.759 䡠 ln(age)
PH: Age ⱕ 10.5 years 19.926 ⫹ 0.970 䡠 ln(age)
Age ⬎ 10.5 years 19.825 ⫹ 1.010 䡠 ln(age) 0.0273
M: Age ⱕ 10.5 years 18.144 ⫹ 2.391 䡠 ln(age)
Age ⬎ 10.5 years 17.808 ⫹ 2.560 䡠 ln(age) ⬍0.0001
EH: Age ⱕ 10.5 years 19.660 ⫹ 1.366 䡠 ln(age)
Age ⬎ 10.5 years 21.180 ⫹ 0.715 䡠 ln(age) 0.2231
Vitreous chamber depth E: Age ⱕ 10 years 13.154 ⫹ 1.211 䡠 ln(age)
Age ⬎ 10 years 14.754 ⫹ 0.513 䡠 ln(age)
PH: Age ⱕ 10 years 12.860 ⫹ 1.014 䡠 ln(age)
Age ⬎ 10 years 13.437 ⫹ 0.762 䡠 ln(age) 0.0743
M: Age ⱕ 10 years 11.297 ⫹ 2.228 䡠 ln(age)
Age ⬎ 10 years 10.907 ⫹ 2.416 䡠 ln(age) ⬍ 0.0001
EH: Age ⱕ 10 years 12.708 ⫹ 1.308 䡠 ln(age)
Age ⬎ 10 years 14.339 ⫹ 0.606 䡠 ln(age) 0.3867
Corneal power E: 42.131 ⫺ 0.566 䡠 ln(age)
2
⫹ 2.033 䡠 ln(age)
PH: 45.061 ⫹ 0.161 䡠 ln(age)
2
⫺ 1.033 䡠 ln(age)
0.4073
M: 44.253 ⫺ 0.009 䡠 ln 䡠 (age)
2
⫹ 0.008 䡠 ln(age)
0.0009
EH: 44.525 ⫹ 0.163 䡠 ln(age)
2
⫺ 0.704 䡠 ln(age)
⬍0.0001
Comparison models for myopes, persistent hyperopes, and emmetropizing hyperopes based on the
best model. The probability is for the comparison between the model for emmetropes and the corre-
sponding refractive error model. E, emmetropes; PH, persistent hyperopes; M, myopes; EH, emmetropiz-
ing hyperopes.
2322 Jones et al. IOVS, July 2005, Vol. 46, No. 7
ness over 3 years in the single vision lens group of ⫺0.01 mm.
In our study, over a similar age range of 6 to 11 years, there
appeared to be a decrease in lens thickness of approximately
0.14 mm before a leveling off. A potential reason for this is that
our myopic subjects were a combination of pre- and post-onset
myopes. The COMET subjects were always myopic. Lens thick-
ness should be studied in more detail before and after the onset
of myopia.
Comparisons between the persistent emmetropes and the
persistent hyperopes and between the persistent emmetropes
and the emmetropizing hyperopes show that the growth curve
shapes were similar in the groups, overall, with the exception
of anterior chamber depth and axial length. The differences
between the persistent hyperopes and the persistent em-
metropes were based on the position from which the groups
started at baseline. The persistent hyperopes started at a posi-
tion significantly different from the persistent emmetropes,
and their eyes were unable to grow enough to compensate for
the smaller size. Therefore, they were unable to emmetropize.
Persistent hyperopes had a higher amount of initial hyperopia
than did emmetropizing hyperopes.
It is noteworthy to see that the persistent hyperope’s eye
grows at all. It would be plausible to think that, because these
eyes remain hyperopic, any growth would in fact be absent.
Persistent hyperopia does not appear to be an error in growth
in childhood, and so the source is more likely to be at some-
time earlier in development. Treatments for hyperopia that
seek to speed growth may be limited in effectiveness, as the
FIGURE 3. Growth curve for crystal-
line lens index, using the best model
derived from emmetropic data and
applying it to the other three refrac-
tive groups.
FIGURE 4. Growth curve for Gull-
strand lens power, using the best
model derived from emmetropic data
and applying it to the other three
refractive groups.
IOVS, July 2005, Vol. 46, No. 7 Refractive Error Growth Curves 2323
problem may be more related to the way the eye develops in
size in infancy.
Conversely, persistent emmetropes and myopes were sim-
ilar on almost all variables at baseline, with the exception of
greater corneal power for myopes. Their differences appeared
for several components in the shape of the growth curves.
Components that varied are those related to the size of the eye:
vitreous chamber depth, anterior chamber depth, axial length,
and corneal power. The two most striking differences between
the myopes and persistent emmetropes were in axial length
and vitreous chamber depth. In myopes, both of these com-
ponents had a rate of growth that exceeded that of the persis-
tent emmetropes, with little or no decrease in slope, represent-
ing a lack of slowing of the growth as seen in persistent
emmetropes as the children reached older ages. Growth in the
myopes appeared to continue unchecked. There was little
change in the corneal power growth curve of the myopes,
whereas the persistent emmetropes experienced a decrease in
corneal power over the age range on the order of approxi-
mately 0.50 D—an interesting finding. Even in emmetropia,
change is going on. The components are not stable. A 0.5 mm
growth in axial length, on average, would lead to approxi-
mately 1.50 D of myopia without counterbalancing by a
change in lens power of a similar amount. These curves help to
establish what normal eyes do and show that normal eyes do
indeed grow.
The growth curves for myopes contained both prevalent
and incident myopes. We analyzed the myopic group based on
incident and prevalent myopia (data not presented). The dif-
ferences between these two groups were a function of that
FIGURE 5. Growth curve for calcu-
lated lens power, using the best
model derived from emmetropic data
and applying it to the other three
refractive groups.
FIGURE 6. Growth curve for lens
thickness, using the best model de-
rived from emmetropic data and ap-
plying it to the other three refractive
groups.
2324 Jones et al. IOVS, July 2005, Vol. 46, No. 7
time at which the subjects entered the study. Growth curves
for the incident myopes resembled those of the prevalent
myopes but were only offset vertically by the amount of myo-
pia that progressed in the intervening years after onset. How-
ever, some caution should be exercised when generalizing the
curves to individual myopes due to the difference in age of
onset.
Given the similarities of the emmetropic and myopic eye at
baseline, it appears the time frame for treatment and prediction
before the onset of myopia is relatively short. When the ability
to discriminate is limited to a short window in advance of
onset, more frequent pediatric eye examinations may be nec-
essary, to catch children at the critical time when onset would
be predictable. Effective treatments to prevent or delay onset
must also work within a similarly short period.
There is the potential that the shorter follow-up of persis-
tent emmetropes may have had an impact on the curves. Data
were available for persistent emmetropes across a range of
visits, so the modeling techniques applied should yield robust
estimates (data not presented). Given that the persistent em-
metropes were older at baseline, some of the length-of-fol-
low-up issue may be related to the study design. The staggered
entry at the study’s beginning and cutoff at grade 8 may have
yielded emmetropes who were only able to have three or four
visits. When we identified a child as an emmetrope at an older
age, it was more likely that he or she would continue to remain
an emmetrope. Children who were enrolled in grade 6 as an
emmetrope had the opportunity to have only three visits. It is
also possible that the length of follow-up is related to the lack
of incentive for an emmetropic child to continue to participate
FIGURE 7. Growth curve for ante-
rior chamber depth, using the best
model derived from emmetropic data
and applying it to the other three
refractive groups.
FIGURE 8. Growth curve for axial
length, using the best model derived
from emmetropic data and applying
it to the other three refractive
groups.
IOVS, July 2005, Vol. 46, No. 7 Refractive Error Growth Curves 2325
in the study. Because 76% of the emmetropes had their last
visits at age 13 or 14, we believe that the more likely reason is
the former than the latter. The strict criteria for classifying
persistent emmetropes also make them the most susceptible to
any measurement variability over the course of the study.
Although this has the effect of limiting the size of the em-
metrope sample, it would not be expected to introduce bias.
As a follow-up, all the potential growth curve models
tested on persistent emmetropic children
25
were applied to
each of the components within each of the refractive error
groups—that is, a total of 48 models for each refractive error
group–component pair. Just as for the persistent em-
metropic group, AIC values were used to determine the
most appropriate model to relate age and each ocular com-
ponent within each refractive error group. In several cases,
the persistent emmetropic model represented the best
model for a refractive error group or component (two mod-
els in myopes and one model in emmetropizing hyperopes).
For the remaining components, the AIC corresponding to
the persistent emmetropic model was often relatively close
(within 10%) to the AIC of the best model. There were three
cases in which the persistent emmetropic form AIC and the
best model differed by more than 10%, which infers that the
persistent emmetrope model was not a good fit for that data
(models not shown). Therefore, even after forcing the per-
sistent emmetropes’ models on other refractive groups, the
models seem to make an accurate representation of change
in an ocular component with age.
FIGURE 9. Growth curve for vitre-
ous chamber depth, using the best
model derived from emmetropic data
and applying it to the other three
refractive groups.
FIGURE 10. Growth curve for cor-
neal power, using the best model de-
rived from emmetropic data and ap-
plying it to the other three refractive
groups.
2326 Jones et al. IOVS, July 2005, Vol. 46, No. 7
This growth curve method has many potential applications
in the field of vision science. We are currently using it to
evaluate the onset of myopia based on time before and after
onset to determine changes in components and their relation
to its development. It also holds promise for studying the
modulation of components in the process of emmetropization,
by allowing for a detailed look at the stepwise growth over the
period.
CONCLUSIONS
Comparisons of growth curves between persistent em-
metropes and three other refractive error groups show that
there are many similarities in the growth patterns for both the
emmetropizing and persistent hyperopes, while the differ-
ences in growth lie mainly between the emmetropes and
myopes. Emmetropizing hyperopes and persistent em-
metropes have a similar pattern of growth. The curves of the
emmetropizing hyperopes represent a middle ground between
the persistent emmetropes and persistent hyperopes. This
gives a starting point to establish what constitutes “normal”
eyes and shows that emmetropic eyes do indeed grow. The
relation between the curves of the persistently emmetropic
eye and the ametropic eye support the concept that hyperopia
and emmetropia are more a product of initial size rather than
rate of growth, whereas emmetropia and myopia are distin-
guished more by growth than initial size.
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