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.

^{ 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 children

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }

^{ 10 }and adults.

^{ 11 }

^{ 11 }

^{ 12 }

^{ 13 }

^{ 14 }

^{ 15 }steep corneas,

^{ 12 }and thin

^{ 16 }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 }

^{ 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.

^{ 20 }

^{ 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.

^{ 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.

^{ 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.

^{ 27 }and logistic regression

^{ 28 }models and for the canonical and logistic models without Gullstrand lens power (because videophakometry is difficult to perform clinically).

*T*denote a random variable for the outcome of a predictive test or set of tests. A decision rule is defined by

*t*

_{0}, a threshold value of

*T*, such that if

*T*>

*t*

_{0}, the person is classified as positive (myopic) and if

*T*≤

*t*

_{0}, 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

*t*

_{0}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 }

^{ 30 }

^{ 31 }Let

*X*denote the predictive test

*T*for the nonmyopic population and

*Y*the test for the myopic group. Then θ =

*P*{

*X*<

*Y*}. An area ofθ = 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 }

^{ 35 }was extended based on the asymptotic normality of estimates of the θs to compare each method of prediction with the best of the other methods of prediction.

^{ 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 ratio

^{ 23 }; 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) .

^{ 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 .

^{ 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) .

^{ 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 }

^{ 19 }

^{ 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 }

Variable at Baseline (Grade 3) | Mean ± SD | Relative Risk | P Value |
---|---|---|---|

Mean cycloplegic autorefraction (sphere) (D) | 0.94 ± 0.71 | 0.040 | 0.0001 |

Vitreous chamber depth (mm) | 15.70 ± 0.69 | 1.760 | 0.0080 |

Axial length (mm) | 22.83 ± 0.70 | 1.910 | 0.0026 |

Gullstrand lens power (D) | 20.69 ± 1.36 | 0.793 | 0.0300 |

Corneal power (vertical meridian, third ring of the corneascope) (D) | 44.01 ± 1.60 | 1.162 | 0.0702 |

Anterior chamber depth (mm) | 3.67 ± 0.23 | 3.301 | 0.0798 |

Crystalline lens spherical volume (mm^{3}) | 135.74 ± 10.57 | 1.020 | 0.1499 |

Crystalline lens refractive index^{*} | 1.43 ± 0.0008 | 1.130 | 0.2244 |

Crystalline lens thickness (mm) | 3.46 ± 0.16 | 0.472 | 0.4343 |

Calculated crystalline lens power (D) | 23.74 ± 2.05 | 0.952 | 0.5015 |

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

Variable or Model | Area under the Curve, θ̂ | SE |
---|---|---|

Mean sphere | 0.875 | 0.028 |

Corneal power (vertical meridian) | 0.608 | 0.042 |

Gullstrand lens power | 0.605 | 0.042 |

Axial length | 0.614 | 0.045 |

Canonical | 0.892 | 0.023 |

Logistic | 0.893 | 0.024 |

Canonical without Gullstrand lens power | 0.884 | 0.025 |

Logistic without Gullstrand lens power | 0.885 | 0.026 |

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

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