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From 1 The Ohio State University College of Optometry, Columbus, Ohio; 2 School of Optometry, University of California, Berkeley; and 3 Office of Research, Biostatistics Program, 4 College of Medicine and Public Health, Division of Epidemiology and Biometrics, and 5 Department of Statistics, College of Mathematical and Physical Sciences, The Ohio State University, Columbus, Ohio.
Abstract
PURPOSE. The purpose of this study was to identify reliable predictors of the onset of juvenile myopia.
METHODS. The data from 554 children enrolled in the Orinda Longitudinal Study of Myopia (OLSM) as nonmyopes with baseline data from the third grade were evaluated to develop a predictive profile for later onset of juvenile myopia. Myopia was defined as at least -0.75 D of myopia in the vertical and horizontal meridians of the right eye as measured by cycloplegic autorefraction (n = 45 children). Chosen predictors were refractive error and the ocular components: corneal power, Gullstrand crystalline lens power, and axial length. Sensitivity and specificity were calculated. Receiver operating characteristic (ROC) curves were generated to evaluate and compare these predictors singly and combined.
RESULTS. Refractive error, axial length, Gullstrand lens and pod corneal power were all significant predictive factors for the onset of juvenile myopia. The best single predictor of future myopia onset in the right eye was the right eye’s cycloplegic autorefraction spherical refractive error value (mean sphere across 10 readings) at baseline. For a cut point of less than +0.75 D hyperopia in the third grade, sensitivity was 86.7% and specificity was 73.3%. The area under the ROC curve for this mean sphere was 0.880. Producing a logistic model combining mean sphere, corneal power, Gullstrand lens power, and axial length results in a slight improvement in predictive ability (area under the ROC curve = 0.893).
CONCLUSIONS. Onset of juvenile myopia can be predicted with moderate accuracy using the mean cycloplegic, spherical refractive error in the third grade. Measurement of other ocular components at this age improves predictive ability, albeit incrementally. Further improvements in the prediction of myopia onset will require the use of longitudinal data in addition to one-time measurement of refractive error and the ocular components.
Myopia has generated enormous research interest during the last century, particularly in the last 20 years. Research efforts now focus on human studies of risk factors for myopia development, animal models of myopigenesis, and myopia treatment trials.1 Most investigators in the refractive error research community would agree that the animal and human lines of investigation are converging in the following way. As basic scientists study the ways in which the eye grows, how eye growth might be modulated,2 3 4 and whether a pharmaceutical agent to control eye growth can be developed,5 clinical vision researchers investigate the genetic and environmental etiologic factors that accompany myopia development in children6 7 8 9 10 and adults.11
The particular anatomy of the ocular components has been investigated in numerous studies. Myopic eyes are associated with excessive axial length,11 12 13 14 15 steep corneas,12 and thin16 and less powerful crystalline lenses.17 However, all these investigations found their associations in samples that included prevalent cases of myopia and did not attempt to associate ocular component values with future myopia development. We have found previously that even premyopic eyes of children (presumably at genetic risk for the development of myopia because they have myopic parents) are longer and less hyperopic than the eyes of children not at such genetic risk.17
We believe that the clinical key to these converging lines of research lies in the ability to predict the onset of myopia long before it is clinically measurable by conventional refraction. If experimental models of myopia lead to a pharmaceutical agent for controlling abnormal eye growth and/or if ongoing studies of optical treatments for progressive myopia can be extended to preventing its onset, accurate prediction of myopia onset and identification of children at high risk for myopia onset will be crucial.
In the early 1960s, it was observed that children with less hyperopia at school entry were more likely to go on to develop myopia during their elementary school years.18 More recently, refractive error in infancy has been suggested as a predictor of future juvenile myopia.19 Both these studies identified refractive error at some point in time well before the onset of myopia as the relevant predictive variable.
Goss and Jackson20 21 22 23 have extended this analysis to include the ocular components, assessment of the binocular vision system, and parental history of myopia, but their prediction may occur too close to the onset of myopia (just 6 months prior) to prove ultimately useful. Goss and coworkers’ predictive analyses are conducted 6 months before the "last emmetropic visit." Thus, it is impossible to identify this critical visit until after the myopia has already occurred. Such a prediction scheme would make treatment administered before the onset of myopia logically impossible.
In this article we use baseline data from the Orinda Longitudinal Study of Myopia to evaluate the ability of refractive error and the ocular components to predict the onset of juvenile myopia.
Methods
The Orinda Longitudinal Study of Myopia employs a cohort design, in which children are enrolled in successive years at selected ages to provide initial cross-sectional data. Children participated in the study after they and their parents received an explanation of all study procedures. Parents gave consent for their children’s participation after all study procedures were explained in accordance with the tenets of the Declaration of Helsinki. The children are then followed for a variable number of years to provide longitudinal data. Data from 554 children from the Orinda Longitudinal Study of Myopia (age at baseline 8.60 ± 0.53 years; mean ± SD) whose right eyes were not myopic by the occasion of their third grade visit (i.e., their refractive error was more hyperopic than -0.75 D on cycloplegic autorefraction in either meridian) and who could provide baseline data from the third grade are reported here. (The third grade visit was chosen as baseline even though some children were enrolled as early as the first grade. The ocular componenets are very similar across children in the first grade and have "differentiated" to a certain extent by third grade. Third graders are still young enough that prediction of future myopia is meaningful in terms of eventual prevention.) Through 1994, 45 of them had developed myopia in the right eye (15 by grade 4, 11 by grade 5, 8 by grade 6, 5 by grade 7, and 6 by grade 8); we expect that more of these children will develop myopia as they are followed to older ages. The 554 children presented here are drawn from a larger sample of 678 children who were seen as third graders between 1989 and 1993. Of these, 148 were followed all the way through the eighth grade, and 23 were myopic by the third grade. Forty-seven children (6.9%) were lost to follow-up during this time period.
We measured the right eye’s ocular components and refractive error on the subject sample as described previously in detail.6 Specifically, we used the Canon R-1 autorefractor (Canon USA, Lake Success, NY) to measure refractive error, averaging 10 consecutive cycloplegic measures to produce a refraction value for the vertical and horizontal meridians and the mean sphere,24 the Kera photokeratoscope to measure corneal curvature, video phakometry to measure crystalline lens curvatures,25 and the Humphrey 820 model A-scan ultrasound unit (Humphrey Systems, Dublin, CA) to measure the eye’s axial dimensions, anterior chamber depth, crystalline lens thickness, and vitreous chamber depth. Although measurements of the various components were divided between three different examiners, each examiner measured the same components at each annual session. To facilitate the measurements, topical agents were used to induce corneal anesthesia (one drop of 0.5% proparacaine first and then a second drop just before ultrasonography), pupillary mydriasis, and cycloplegia (two drops of 1.0% tropicamide, instilled 5 minutes apart). A new case of myopia was defined as any child in the fourth grade or higher whose cycloplegic autorefraction results were –0.75 or more myopic in both the vertical and horizontal meridians.
Statistical Methods
First, we evaluated the relative risk of measured and calculated
ocular component values as measured at baseline. Table 1
shows the relative risk of a unit difference in each of the ocular
components for development of myopia as defined above. After this
proportional hazards analysis,26
models were built
maximizing the log likelihood. Important variables and potential cut
points for these variables were identified using the candidate
variables from the proportional hazards results. From this analysis,
continuous candidate predictor variables for further analysis emerged
at the 0.05 level of statistical significance, namely, the mean
cycloplegic sphere power from the 10 autorefraction measurements, the
corneal power in the vertical meridian from the third ring of the
photokeratoscope photograph, the Gullstrand lens power, and the axial
length, all as measured at baseline. However, these ocular components
are intercorrelated (certainly, in the case of vitreous chamber depth
and axial length, as one is contained fully in the other) and
contribute in an additive way to produce the eye’s refractive error.
Thus, analyses to determine the relative contribution of these
variables and their value in predicting myopia onset were conducted.
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The index from the canonical discriminant analysis is a linear combination of the four selected ocular component variables that best separates the myopic and nonmyopic groups among all possible linear combinations.
ROC Curves
For two well-defined groups (e.g., myopes versus nonmyopes),
let T denote a random variable for the outcome of a
predictive test or set of tests. A decision rule is defined by
t0, a threshold value of T,
such that if T > t0,
the person is classified as positive (myopic) and if T 
t0, the person is classified as
negative (nonmyopic). For a given threshold, sensitivity is the
probability that a myopic person is classified as myopic (true
positive) and specificity as the probability that a nonmyopic person is
classified as nonmyopic (true negative). The theoretical ROC curve is a
function of sensitivity versus (1 - specificity) as the threshold
t0 ranges over all possible values. On
the y-axis is sensitivity, or the true-positive fraction. On
the x-axis is (1 - specificity), the false-positive
fraction.29
One convenient global measure of the predictive accuracy of a
test or set of tests is the area under the corresponding ROC curve. The
area under the ROC curve measures the probability, denoted by 
, that
in a randomly selected pair of nonmyopic and myopic individuals the
predictive test(s) allows them to be correctly
identified.30
31
Let X denote the predictive
test T for the nonmyopic population and Y the
test for the myopic group. Then =
P{X < Y}. An area of
= 0.8, for example, means that a randomly selected individual
from the myopic group has a predictive test value, Y, larger
than the value X for a randomly selected individual from the
nonmyopic group 80% of the time. An unbiased estimate of
P{X < Y} is the area under
the empiric ROC plot, which is also the Mann–Whitney version of the
two-sample rank-sum statistic of Wilcoxon.32
33
34
Multiple Comparisons of ROC Curves
Point estimates (denoted as 
) and SEs for the area under
the curve () for the ocular components individually, combined by the
canonical discriminant analysis and logistic regression models, and
canonical and logistic indices without Gullstrand lens power curves
were calculated. Multiple comparisons with the best (MCB) analysis,
described by Hsu,35
was extended based on the asymptotic
normality of estimates of the s to compare each method of prediction
with the best of the other methods of prediction.
Results
To provide direct comparisons to previous studies,18 19 the mean sphere cycloplegic refractive error at grade 3 was evaluated (Table 2) as a predictor of myopia, producing a sensitivity of 86.7% and a specificity of 73.3%. Of course, some of the nonmyopic children in the right column of Table 2 may go on to develop myopia, so this analysis will be ongoing. The cut point of at least +0.75 D of hyperopia depicted in Table 2 was chosen so as to maximize the –2 log likelihood in a proportional hazards analysis. (For details, see Klein and Moeschberger, 1997.26 ) Shifting this cut point just 0.25 D in the myopic direction changes the sensitivity of this analysis to 68.9% and the specificity to 87.2%, illustrating the trade-off between sensitivity and specificity with a change in predictive criterion. Previous investigators demonstrated the predictive value of the ratio of axial length to corneal radius of curvature (AL/CR ratio) with a sensitivity of 88% and specificity of 57% for a cutoff of 3.02 for the AL/CR ratio23 ; we find a much lower sensitivity and only slightly higher specificity, even though the children in the previous study were similar in age distribution to our sample (Table 3) .
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, and SEs for the area under the curve
are presented in Table 4
. An MCB analysis comparing each of the individual components’ ROC
curves and the mean sphere ROC curve reveals that corneal power,
Gullstrand lens power, and axial length are each inferior to mean
sphere at the 
= 0.0001 level. Therefore, the mean sphere is
the best single predictor for myopia of all the variables tested. We
wanted to examine whether the other variables in combination with the
mean sphere would improve the predictive model over that using the mean
sphere alone. A separate MCB analysis comparing the mean sphere, the
canonical, the logistic, the canonical without Gullstrand lens power,
and the logistic without Gullstrand lens power ROC curves, give the
following 95% MCB simultaneous confidence intervals:
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= 0.05. Other confidence
intervals imply that the canonical model is either the best or is
within 0.0099 of the best model, the logistic model is either the best
or is within 0.0083 of the best model, the canonical without GLP model
is either the best or is within 0.0197 of the best model, and the
logistic without GLP model is either the best or is within 0.0203 of
the best model. As these four models are indistinguishable, the
logistic model can be chosen with confidence as the best model for
practical usage, but given the difficulty in assessing Gullstrand lens
power,25
the logistic model without Gullstrand lens power
included would be an acceptable substitute. The increment of improved
performance of the logistic model without Gullstrand lens power may be
seen in the ROC curve depicted in Figure 2
.
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Hirsch ventured into myopia prediction in the early 1960s, basing his analyses solely on noncycloplegic retinoscopy results at school entry (at 5–6 years of age) compared to the same measurement at the end of elementary school (13–14 years of age). He chose the same cut point as in our Table 2 and defined myopia at school exit as -0.50 D or more myopia (spherical equivalent). He achieved a similar result to ours, with only a slightly lower sensitivity of 81.5% and a similar specificity of 72.1%.18 Our results are based on cycloplegic autorefraction rather than noncycloplegic retinoscopy, and we would expect that as some of our current nonmyopes convert to future myopes, our predictive ability could increase. Our results confirm Hirsch’s, namely, that a low hyperopic refractive error is an important risk factor for future myopia. As we have discussed previously,36 this level of performance does not have the high level of both sensitivity and specificity needed to make decisions regarding which particular child should receive any potential treatment to prevent the onset of myopia (Figs. 1 2) .
Much later, Goss and Jackson compared values of the ocular components in children who became myopic (minus refractive error in both meridians of both eyes and -0.25 D or more myopic spherical equivalent in both eyes as measured by cycloplegic subjective refraction) 6 months after a nonmyopic measurement occasion compared to children who did not become myopic in the same time interval. Their predictions require knowledge of which measurement occasion is the "last emmetropic visit," which makes true prediction in the context of a preventive treatment impossible. They found a statistically significant difference only for the ratio of axial length to corneal radius of curvature in the vertical meridian (cut point of 3.02), producing a sensitivity of 88% and a specificity of 57%,23 a result our data do not confirm. This same study produced lower sensitivities and specificities for all other variables examined, including positive relative accommodation, the midpoint of the near fusional vergence range,22 heterophoria,21 and parental history of myopia.20
Although others have analyzed similar variables as predictors, namely, parental history of myopia19 37 38 and infant refraction,19 none of these has presented data on sensitivity and specificity, so their results cannot be compared meaningfully to ours. Our reanalysis of the data set based on a myopic infant refraction (any minus power in either meridian by noncycloplegic retinoscopy) revealed a range of sensitivities from 61.9% to 81.2% and a range of specificities from 59.1% to 63.2%, depending on the myopic "fate" of the emmetropic infants (not described in the original data set).36
We find that if a single measure is to be made for the purposes of predicting myopia onset in advance of the event, the single best measure of those we evaluated is the spherical portion of the prescription generated by cycloplegic autorefraction (Figs. 1 3) . If we combine the four ocular components discussed here—mean sphere, corneal power, Gullstrand lens power, and axial length, three of which can be readily measured with accessible clinical techniques—then the accuracy of prediction improves somewhat (Figs. 2 4) . It is vital that any attempts to predict future myopia onset choose predictors that can be used without advance knowledge of when the myopia onset occurs to prevent post hoc prediction models that do not truly foretell the future refractive error.
Some of the children who have not developed myopia have not been followed through grade 8 and may yet develop myopia. Nonetheless, these represent the first predictive models of myopia onset in the literature, using ocular component data gathered before the onset of myopia. Figures 3 and 4 enable the clinician to apply the corresponding formulas presented to actual data gathered in the third grade on an individual child to predict the likelihood that the child will go on to develop myopia of at least –0.75 D in both meridians by eighth grade. These models are the first to include both an evaluation of test performance and predictive power, giving clinicians a probability with which to interpret measurements made in young nonmyopes. Our results show that such predictive models are not yet adequate using refractive error and one-time measurement of the ocular components. These models will be refined over time as we add other features, such as longitudinal ocular component data, family history of myopia, and children’s near work, as well as increase the length of follow-up and the number of incident myopes.
The usefulness of ROC curve analysis lies in its ability to convey information about prediction across the entire range of sensitivity and specificity, enabling one to view these data in a more comprehensive way. It also presents the level of performance of batteries of tests conveniently. ROC analysis allows the investigator and/or clinician to focus on a range of interest on the ROC curve to evaluate the performance of a predictive test or set of tests.
For example, if a treatment is particularly effective, then the cut point pertaining to the portion of the ROC curve where sensitivity is maximized may be the interesting part of the curve, but if the treatment is effective but somewhat noxious or expensive, then the range of interest might be where sensitivity and specificity are nearly equally balanced. If a treatment had an idiosyncratic side effect in, for example, eyes not destined to become myopic, then the ROC curve range of interest would be in the region where 1 - specificity is minimized (or specificity is maximized).
In the case of myopia, treatments to actually prevent myopia onset, rather than just retard the progression of myopia already initiated, are still on the horizon, but many pharmaceutical agents are being investigated and patented for this purpose. If a topical eye drop is developed to modulate eye growth during childhood and the agent is effective, inexpensive, and has minimal side effects in children, then the range of interest in the ROC curve would be where sensitivity is perhaps emphasized slightly over specificity. A pharmaceutical or optical treatment where the therapy was worse than the cure (e.g., an eye drop that had to be used four times a day for 10 years of a child’s life from ages 6 to 16 years and so might be ultimately worse than developing –3.00 D of myopia) might lead to consideration of the range of the ROC curve where specificity was relatively more important.
Feasibility of the tests needed for accurate prediction are also a factor. If a test or battery of tests is expensive or difficult to perform in certain patients, its predictive ability might be moot. If a test is very accurate for prediction but difficult to administer, the ROC curve it can generate might be helpful in deciding whether to perform the test in the first place.
In summary, we document the value of cycloplegic refractive error and three optical ocular components in the prediction of juvenile myopia onset at least 1 year after the baseline measurement taken in the third grade. Mean sphere measured during the third grade school year provides sensitivity of 86.7% and specificity of 73.3% for the traditionally held baseline cutoff point of at least +0.75 D of hyperopia and produces an ROC curve with an area under the curve of 0.880. Adding corneal power, Gullstrand crystalline lens power, and axial length improve the myopia onset prediction slightly. Future analyses will add nonoptical factors such as parental history of myopia and children’s near work activities to these predictive models.
Footnotes
Reprint requests: Karla Zadnik, The Ohio State University College of Optometry, 338 West Tenth Avenue, Columbus, Ohio 43210-1240.
Supported by National Institutes of Health Grant EY08893.
Submitted for publication July 29, 1998; revised December 3, 1998; accepted January 29, 1999.
Proprietary interest category: N.
Presented in part at the annual meetings of the American Academy of Optometry, San Antonio, Texas, December, 1997; and of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, May, 1998.
References
This article has been cited by other articles:
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  Y.-F. Shih, T.-H. Chiang, and L. L.-K. Lin Lens Thickness Changes among Schoolchildren in Taiwan Invest. Ophthalmol. Vis. Sci., June 1, 2009; 50(6): 2637 - 2644. [Abstract] [Full Text] [PDF]
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J. J. Walline, L. A. Jones, L. Sinnott, R. E. Manny, A. Gaume, M. J. Rah, M. Chitkara, S. Lyons, and on behalf of the ACHIEVE Study Group A Randomized Trial of the Effect of Soft Contact Lenses on Myopia Progression in Children Invest. Ophthalmol. Vis. Sci., November 1, 2008; 49(11): 4702 - 4706. [Abstract] [Full Text] [PDF]
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L. A. Jones, L. T. Sinnott, D. O. Mutti, G. L. Mitchell, M. L. Moeschberger, and K. Zadnik Parental History of Myopia, Sports and Outdoor Activities, and Future Myopia Invest. Ophthalmol. Vis. Sci., August 1, 2007; 48(8): 3524 - 3532. [Abstract] [Full Text] [PDF]
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D. O. Mutti, J. R. Hayes, G. L. Mitchell, L. A. Jones, M. L. Moeschberger, S. A. Cotter, R. N. Kleinstein, R. E. Manny, J. D. Twelker, K. Zadnik, et al. Refractive Error, Axial Length, and Relative Peripheral Refractive Error before and after the Onset of Myopia Invest. Ophthalmol. Vis. Sci., June 1, 2007; 48(6): 2510 - 2519. [Abstract] [Full Text] [PDF]
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S.-M. Saw, W.-H. Chua, C.-Y. Hong, H.-M. Wu, W.-Y. Chan, K.-S. Chia, R. A. Stone, and D. Tan Nearwork in Early-Onset Myopia Invest. Ophthalmol. Vis. Sci., February 1, 2002; 43(2): 332 - 339. [Abstract] [Full Text] [PDF]
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D. O. Mutti, L. A. Jones, M. L. Moeschberger, and K. Zadnik AC/A Ratio, Age, and Refractive Error in Children Invest. Ophthalmol. Vis. Sci., August 1, 2000; 41(9): 2469 - 2478. [Abstract] [Full Text]
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D. Troilo, D. L. Nickla, and C. F. Wildsoet Form Deprivation Myopia in Mature Common Marmosets (Callithrix jacchus) Invest. Ophthalmol. Vis. Sci., July 1, 2000; 41(8): 2043 - 2049. [Abstract] [Full Text]
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D. O. Mutti, R. I. Sholtz, N. E. Friedman, and K. Zadnik Peripheral Refraction and Ocular Shape in Children Invest. Ophthalmol. Vis. Sci., April 1, 2000; 41(5): 1022 - 1030. [Abstract] [Full Text]
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