;)
Once children become myopic, their eyes continue to grow and the degree of refractive error almost certainly increases. Being able to predict their future—how much their eyes will grow and how myopic they will become—would be valuable. The eyes of emmetropic and hyperopic children elongate,1,2 but myopic children undergo faster ocular growth that is not compensated by sufficient flattening and power loss from the cornea or crystalline lens needed to prevent myopia progression.3,4 A typical rate of progression of myopia in a 10-year-old child is −0.40 to −0.50 D per year but varies by sex, ethnicity, and age.5–8 Females, children of East Asian ancestry, and younger children tend to progress faster.9–15 Females progress an estimated −0.093 to −0.17 D per year faster than males.16,17 Chinese children are reported to progress −0.47 D more for 3 years than non-Chinese children.16 The effect of ethnicity seems to extend into the United States, as Asian American children progressed between −0.46 and −0.88 D faster for 3 years than Hispanic, Native American, and Black children.17 Older age is associated with slower progression. Seven-year-old children in the Singapore Cohort of the Risk Factors for Myopia (SCORM) study progressed −1.10 D per year compared with −0.40 to −0.50 D per year in 10-year-old children.6 Estimated annual progression rates from an ethnically diverse American sample ranged from −0.58 D per year at age 7 years to −0.16 D per year at age 13 years.17 Interestingly, recent research indicates that, although the average rate of progression slows with age, progression at a given age is largely independent of the age of myopia onset; that is, the average rate of myopia progression between ages 10 and 11 years is similar regardless of whether children become myopic at age 8 or 10 years.6,17,18 Myopia progression was faster in children with a greater number of myopic parents or at least one parent with more severe myopia.10,11,14,15,19 A more myopic refractive error at a baseline examination has also been associated with faster progression.10,15,20 Neither near work nor time outdoors has factored significantly or consistently into models of eventual amounts of myopia or rate of progression.6,17
Although there has been some progress in identifying risk factors for myopia progression, treatments to slow myopia progression place additional value on being able to identify the most rapidly progressing children. Although all children with myopia might benefit from these therapies, the fastest progressors may benefit the most. Clinical trialists may want to enroll samples enriched with higher proportions of children who will progress the fastest for demonstrating efficacy in the most at-risk populations. In addition, such a study sample potentially requires a smaller sample size to achieve the desired level of statistical power compared with a general sample, assuming that slow progressors are less likely to contribute to significant differences between the treated and control groups. This assumption has been challenged by Brennan and coworkers,21 who argue that treatment benefit seems evenly distributed across rates of progression when expressed in absolute terms of millimeter or diopters. Furthermore, they reported that measured annual refractive progression was a poor standalone indicator of progression in the following year.21 Expert panels have recommended against using prior progression as an entry criterion for myopia control clinical trials because of measurement error, bias, and ethical considerations.22,23 Nevertheless, surveys of pediatric ophthalmologists indicate that a rapid rate of progression (>1 D/y) is the main reason for their initiation of myopia control, and some recent clinical trials have used the previous rate of progression as an entry criterion.24–27 The results of SCORM provide some support for the use of history of progression. Their analysis of myopic Singaporean children 7 to 9 years old at baseline found an area under the receiver operating characteristic curve of 0.77 for the association between 1 year's myopia progression and subsequent 2-year progression, adjusted for age, sex, and ethnicity.28 The regression coefficient relating the two periods was low at 0.28, however, and fast progression of more than −1.00 D/y in the first year had a sensitivity and specificity of only 62.0 and 72.2%, respectively, for identifying progression faster than −0.58 D/y in the second year. Given their conclusion that “[p]ast progression may be inadequate as a standalone indicator,” the ability to predict future progression from past progression remains an open and important issue. The purpose of the current analysis is to examine the usefulness of 1 year's myopia progression as a predictor of the next year's rate of myopia progression while extending the work of Matsumura and colleagues28 by including axial length and using a more ethnically diverse sample with a broader range of ages.
METHODS
The Collaborative Longitudinal Evaluation of Ethnicity and Refractive Error (CLEERE) Study was a multicenter observational evaluation of ocular component development and risk factors for juvenile-onset myopia conducted in school-aged children (grades 1 to 8) at five clinical sites across the United States. It was an extension of the Orinda Longitudinal Study of Myopia that began in 1989 in Orinda, California, a predominantly White community. To expand racial/ethnic representation and generalizability, four sites were added: in 1997, Eutaw, Alabama (African American); Irvine, California (Asian American); and Houston, Texas (Hispanic); and in 2001, Tucson, Arizona (Native American). This research was reviewed by an independent ethical review board and conforms with the principles and applicable guidelines for the protection of human subjects in biomedical research. Informed consent and assent were provided by the parents and children, respectively. Consent procedures and study protocols were approved by each site's institutional review board.
The CLEERE Study’s measurement methods have been described previously in detail29; measurement methods for the main outcomes of interest are summarized as follows. Measurements were only made on the right eye. Axial length was the average of five measurements from A-scan ultrasonography (Allergan-Humphrey A-scan model 820, San Leandro, CA). Refractive error was measured using the average of 10 readings from autorefraction (Canon R-1 1989 to 2000 [Canon USA, Lake Success, NY], Grand Seiko WR-5100K 2001 to 2010 [Grand Seiko Co., Hiroshima, Japan]). Both measurements were performed under cycloplegia, 30 minutes after one drop of proparacaine 0.5% and either two drops of tropicamide 1.0% if iris color was less than grade 2 or one drop each of tropicamide 1.0% and cyclopentolate 1.0% when iris color was grade 2 or darker.30,31 Parents provided information about children's sex, race/ethnicity, and activity levels. For race/ethnicity, parents selected one of six designations: American Indian or Alaskan Native; Asian or Pacific Islander; Black, not of Hispanic origin; Hispanic; White, not of Hispanic origin; or other. These choices corresponded to the categories used by the National Institutes of Health in 1997 when CLEERE began. The activity levels of interest in this study were reading and outdoor/sports hours gathered from parent responses to these specific questions selected from a larger annual survey: “During the school year, how many hours per week (outside of regular school hours) would you estimate this child: 1) Studies or reads for school assignments; reads for fun (pleasure); watches television; uses a computer/plays video games); and 2) engages in outdoor/sports activities?” The number of myopic parents was determined by parent-provided information about their refractive error history.32
For these analyses, CLEERE Study data were restricted to children with at least three consecutive annual visits with measurements of refractive error and axial length. A child with longer follow-up could have more than one of these triplets in the data set. To be included in this analysis, the child had to be between 7 and 14 years old (inclusive) at study entry with spherical equivalent refractive error between −0.75 and −5.00 D (inclusive) at the second of the three visits. The resulting data set comprised 2231 observations from 916 participants. The simple association between measured prior progression of myopia or elongation of axial length and measured future change was examined by looking at the correlation between [visit 3 − visit 2] differences and [visit 2 − visit 1] differences. Slopes were calculated using orthogonal regression in JMP (version 15.2.0; SAS Institute, Cary, NC). The mixed procedure in SAS software, version 9.4, of the SAS System for Windows was used to fit all models. Models predicted values for refractive error and axial length at visit 3 rather than change between visits 2 and 3. This approach avoided the issue of having values for visit 2 appear on both sides of the prediction equation. Predicted change was calculated as the difference between the model value at visit 3 and the observed value at visit 2. Participants were randomly assigned to either a model training set or a model test set using a 55%:45% split. Two optimal models were selected, one incorporating the change in refractive error and axial length between visits 1 and 2 (the “with prior change” model) and the other using only the values of axial length and refractive error at visit 2 (the “without prior change” model). Backward stepwise selection first identified a sequence of nested models involving age, sex, race/ethnicity, and visit 2 values for axial length and refractive error. Each subsequent step removed the predictor that least harmed the model's fit. The process terminated when a core set of predictors remained. The following cross-validation procedure was then used to choose the best of the nested models. The training set was divided into 10 subsets, a model was fit using 9 of the 10 subsets, and then prediction error was estimated against the remaining test subset. This process was repeated 10 times by using each of the 10 subsets as the test subset. This cross-validation was repeated 100 times. The model with the fewest predictors and a mean error within the 95% confidence interval of the model with the lowest average prediction error was selected as the best final model. The number of myopic parents, reading, and sports/outdoor activity levels were then added to the final model and evaluated.
Model performance was evaluated in several ways. The 95% limits for the difference between predicted change and actual change were estimated using residuals from orthogonal regression, once where the predictions used prior change and once without prior change. The ability of the models to classify children according to dichotomous outcomes of fast versus slow progression between visits 2 and 3 was evaluated for predicted progression rates of at least −0.375, −0.50, and −0.75 D/y. The corresponding axial elongation levels were at least 0.139, 0.185, and 0.278 mm/y (assuming a conversion factor of 2.7 D/mm). Classification performance was assessed using sensitivity, specificity, positive and negative predictive values, and misclassification rate. Sensitivity and specificity use denominators of true, measured fast and slow progression, respectively. Sensitivity is the percent of true fast progressors predicted by the model to be fast. Specificity is the percent of true slow progressors predicted by the model to be slow. In contrast, positive and negative predictive values use the model prediction of fast and slow as their respective denominators. Positive predictive value is the proportion of observations predicted to be fast that are in fact fast. Negative predictive value is the proportion of observations predicted to be slow that are in fact slow. Misclassification rate uses the entire data set as the denominator, with the numerator being those classified incorrectly (observations predicted to be fast that are in fact slow and observations classified as slow that are in fact fast). A good model will have high and balanced sensitivity and specificity, a high positive predictive value, and a low misclassification rate. A useful model will also identify an enriched sample, that is, a higher proportion of fast progressors than might be found in a general sample.
RESULTS
Subjects had a low mean ± standard deviation amount of myopia, −1.86 ± 0.97 D; were predominantly female; and had an average ± standard deviation age of 11.3 ± 1.4 years. The average rate of progression of myopia between visits 1 and 2 was −0.54 ± 0.36 D. Progression was accompanied by an axial elongation of 0.26 ± 0.22 mm with an age-related decrease in both progression and axial elongation between visits 2 and 3 (Table 1). The prior year’s myopia progression was significantly correlated with the next year’s progression (P < .001; Fig. 1A), but prior axial elongation was not correlated with future elongation (P = .33; Fig. 1B). The orthogonal regression slope of 0.98 for myopia progression suggests a high degree of correspondence, but the variance in future progression explained by past progression was low with an R2 = 0.015. Despite these low correlations, both past myopia progression and past axial elongation were significant terms in the best models predicting visit 3 spherical equivalent (Table 2) and axial length (Table 3). The reference sex was male, and the reference ethnic groups were Hispanic and Native American for refractive error and White, Hispanic, and Native American for axial length. Continuous variables were centered on the means presented in Table 1, meaning that the intercept provides an estimate of visit 3's refractive error or axial length values for a reference ethnic group male of average age and average ocular component values. The number of myopic parents, near work, and time outdoors were not significant parameters in any of the models.
TABLE 1 -
Characteristics of the subjects in the data set
|
Overall (N = 916) |
| Female |
525 (57.3%) |
| Visit 1 age (y) |
11.3 ± 1.4 |
| Ethnicity |
|
| Hispanic |
270 (29.5%) |
| White |
213 (23.3%) |
| Asian |
180 (19.7%) |
| Black |
134 (14.6%) |
| Native American |
111 (12.1%) |
| Other |
8 (0.9%) |
| Visit 2 SER (D) |
−1.86 ± 0.97 |
| Visit 1 to visit 2 change in SER (D/y) |
−0.54 ± 0.36 |
| Visit 2 to visit 3 change in SER (D/y) |
−0.36 ± 0.40 |
| Visit 2 AL (mm) |
24.07 ± 0.79 |
| Visit 1 to visit 2 change in AL (mm/y) |
0.26 ± 0.22 |
| Visit 2 to visit 3 change in AL (mm/y) |
0.19 ± 0.21 |
Mean ± standard deviation is presented for continuous variables and number (proportion) for categorical data. Data for subjects with more than one set of measurements were averaged before averaging across subjects. AL = axial length; SER = spherical equivalent refractive error.
FIGURE 1: (A) Myopia progression between visits 2 and 3 as a function of progression between visits 1 and 2. The rate of future myopia progression was significantly associated with past progression (P < .001), but the variance explained by past progression was low (R 2 = 0.015). (B) Axial elongation between visits 2 and 3 as a function of axial elongation between visits 1 and 2. There was no significant association between future and past axial elongation (P = .33).
TABLE 2 -
Parameter estimates for predictors in models of visit 3 SER, one using only visit 2 information (without prior change) and one using visit 2 information in addition to the change in SER and the change in AL between visits 1 and 2 (with prior change)
| Predictor |
Without prior change |
With prior change |
| Intercept |
−2.11 (P < .001) |
−2.13 (P < .001) |
| Visit 2 age (y) |
0.071 (P < .001) |
0.060 (P < .001) |
| Female |
−0.10 (P < .001) |
−0.079 (P < .001) |
| Visit 2 AL (mm) |
−0.064 (P < .001) |
NS |
| Visit 2 SER (D) |
1.0 (P < .001) |
1.0 (P < .001) |
| Asian American |
−0.19 (P < .001) |
−0.18 (P < .001) |
| Black |
0.051 (P = .06) |
0.072 (P = .007) |
| White |
−0.11 (P < .001) |
−0.076 (P = .001) |
| Visit 1 to visit 2 change in AL (mm) |
N/A |
−0.28 (P < .001) |
| Visit 1 to visit 2 change in SER (D) |
N/A |
−0.13 (P < .001) |
| Interaction between change in AL and change in SER |
N/A |
0.41 (P < .001) |
| Change in SER squared |
N/A |
0.10 (P < .001) |
Model parameters were estimated using the complete data set. AL = axial length; N/A = not applicable; NS = not significant; SER = spherical equivalent refractive error.
TABLE 3 -
Parameter estimates for predictors in models of visit 3 AL, one using only visit 2 information (without prior change) and one using visit 2 information in addition to the change in SER and the change in AL between visits 1 and 2 (with prior change)
| Predictor |
Without prior change |
With prior change |
| Intercept |
24.24 (P < .001) |
24.24 (P < .001) |
| Visit 2 age (y) |
−0.043 (P < .001) |
−0.040 (P < .001) |
| Visit 2 AL (mm) |
0.98 (P < .001) |
0.99 (P < .001) |
| Visit 2 SER (D) |
−0.034 (P < .001) |
−0.025 (P < .001) |
| Asian American |
0.099 (P < .001) |
0.092 (P < .001) |
| Black |
−0.045 (P < .001) |
−0.046 (P < .001) |
| Visit 1 to visit 2 change in AL (mm) |
N/A |
−0.19 (P < .001) |
| Visit 1 to visit 2 change in SER (D) |
N/A |
−0.14 (P < .001) |
| Interaction between change in AL and change in SER |
N/A |
−0.13 (P < .001) |
Model parameters were estimated using the complete data set. AL = axial length; N/A = not applicable; SER = spherical equivalent refractive error.
The signs on the coefficients in Tables 2 and 3 for age indicate that older children would undergo less progression and axial elongation between visits 2 and 3. Females became slightly more myopic, but sex was not a predictive factor for future values of axial length. The near unity values for the coefficients for refractive error and axial length indicate that visit 3 values for these variables were similar to visit 2 values. The signs on the coefficients for refractive error and axial length in the models predicting the other variable indicate that, not surprisingly, a longer-than-average eye at visit 2 will likely have more myopia at visit 3 and that a more myopic eye will have a longer axial length. Asian American children will become more myopic and have longer eyes than the reference ethic/racial groups, with the opposite occurring in Black children. The models using prior change data were more complicated, with interaction terms between change in refractive error and change in axial length. Refractive error also included a quadratic term for change in its model.
The similarity of the 95% limits for the differences between predicted change and actual change, regardless of whether or not prior change information is used, suggests that the inclusion of complex “with prior change” terms adds little useful information compared with what can be predicted using the simpler “without prior change” model (Table 4; Figs. 2A to D). Use of model terms for age, ethnicity, sex (for refractive error), and visit 2 biometric values improved the 95% limits by about a factor of 2 compared with using only the prior year's myopia progression or axial elongation. The mean absolute difference for prediction error provided a similar picture to the 95% limits and results depicted in Fig. 1, that is, that prior change adds little value in predicting future change. Regardless of use of prior change, the low values for the 95% limits do not indicate that the model provides an accurate prediction. The strongly linear relationships in Figs. 2A to D indicate a substantial systematic error in the model prediction. As evidenced by the slopes and intercepts of the linear regression, robust measured change between visits 2 and 3 was underestimated by the prediction, whereas mild change was predicted for those who actually showed relative stability. For example, the regression equation in Fig. 2A shows that measured myopia progression of −1.00 D was underestimated by −0.59 D by the model (predicted progression, −0.41 D) and no measured myopia progression was predicted to be progression of −0.35 D. The regression equation in Fig. 2C shows that measured axial elongation of 1.0 mm was underestimated by 0.76 mm (predicted elongation, 0.24 mm) and no measured axial elongation was predicted to be growth by 0.19 mm.
TABLE 4 -
Ninety-five percent Limits and mean absolute difference for prediction error (difference between predicted change and actual change between visits 2 and 3)
| Predictive model |
95% Limits |
Mean absolute difference |
| SER: without prior change (D) |
±0.22 |
0.31 |
| SER: with prior change (D) |
±0.26 |
0.30 |
| SER: none (D) |
±0.57 |
0.45 |
| AL: without prior change (mm) |
±0.14 |
0.17 |
| AL: with prior change (mm) |
±0.16 |
0.17 |
| AL: none (mm) |
±0.33 |
0.28 |
The 95% limits were calculated from residuals perpendicular to the orthogonal regression line. Prediction error was calculated for both the model without prior change data and the model with prior change data. “None” (no model used) assumed that the prior year's myopia progression of SER or elongation of AL would equal the next year's change. AL = axial length; SER = spherical equivalent refractive error.
FIGURE 2: Difference between predicted and measured future change (prediction error = observed future change minus predicted change) as a function of measured future change. The 95% limits for the prediction error are also depicted. The panels provide results for (A) myopia progression without prior change, (B) myopia progression with prior change, (C) axial elongation without prior change, and (D) axial elongation with prior change.
The ability of the prediction models to identify “fast” versus “slow” myopia progression as categorical variables was also evaluated using a series of cut-point values of change in refractive error and axial length (Tables 5, 6). Because prior change showed little added value, model performance results are only presented using predictions from models without prior change. As might be expected, the best balance between sensitivity and specificity occurred when the cut points for “fast” were close to the mean values for myopia progression and axial elongation shown in Table 1 (0.36 D and 0.19 mm). This ratio (0.36/0.19) suggests an overall conversion factor of 1.9 D/mm instead of the 2.7 D/mm assumed when assigning the cut points. More extreme cut points resulted in reduced sensitivity, increased specificity, and reduced misclassification, particularly for refractive error. For example, the model without prior change only identified 4.9% of those who actually progressed by −0.75 D and 36.4% of those whose axial elongation was 0.278 mm or more. The misclassification and false-positive rates decreased at faster-than-average cut points. This pattern is expected but not necessarily desirable. By definition, observations of fast progression will become less frequent at cut points that are greater than the average rate of change for the sample. A majority of misclassifications for myopia progression and axial elongation were false-negative misidentification of slow rather than false-positive misclassification of fast, as the cut points became larger. The false-positive rate would be expected to decrease, as observations of faster than average change became less frequent.
TABLE 5 -
Without prior change model performance in terms of sensitivity, specificity, misclassification rate, false positives, and false negatives
| Cut points for “fast” between visits 2 and 3 |
Sensitivity |
Specificity |
Misclassification rate |
False positives |
False negatives |
| −0.375 D |
60.8 (56.2–65.3) |
63.2 (58.9–67.4) |
37.9 (34.9–41.0) |
50.8 (45.6–56.0) |
49.2 (44.0–54.4) |
| −0.50 D |
32.2 (27.2–37.4) |
84.6 (81.5–87.3) |
33.5 (30.6–36.6) |
30.1 (25.2–35.4) |
69.9 (64.6–74.8) |
| −0.75 D |
4.9 (2.2–9.5) |
98.9 (97.9–99.5) |
16.6 (14.3–19.1) |
5.5 (2.6–10.2) |
94.5 (89.8–97.4) |
| 0.139 mm |
75.9 (72.2–79.4) |
42.7 (37.9–47.6) |
38.4 (35.4–41.6) |
64.5 (59.4–69.3) |
35.5 (30.7–40.6) |
| 0.185 mm |
62.2 (57.7–66.6) |
61.6 (57.2–65.8) |
38.1 (35.1–41.2) |
52.4 (47.2–57.6) |
47.6 (42.4–52.8) |
| 0.278 mm |
36.4 (31.0–42.1) |
87.6 (84.8–90.0) |
28.3 (25.5–31.3) |
30.2 (24.9–36.0) |
69.8 (64.0–75.1) |
Results are given as percent (95% confidence interval).
TABLE 6 -
Without prior change model performance in terms of positive and negative predictive values
| Cut points for “fast” between visits 2 and 3 |
Positive predictive value |
Negative predictive value |
Model predicted to be “fast” |
Yield using model |
Yield without model |
| −0.375 D |
60.0 (55.5–64.5) |
64.0 (59.6–68.2) |
48.2 (45.0–51.4) |
29.0 (26.1–31.9) |
47.6 (44.4–50.8) |
| −0.50 D |
52.4 (45.4–59.4) |
70.2 (66.9–73.5) |
21.2 (18.7–23.9) |
11.1 (9.2–13.2) |
34.6 (31.6–37.6) |
| −0.75 D |
47.1 (23.0–72.2) |
84.0 (81.6–86.3) |
1.7 (1.0–2.8) |
0.8 (0.4–1.6) |
16.5 (14.2–19.0) |
| 0.139 mm |
63.5 (59.7–67.2) |
57.5 (51.8–63.0) |
67.9 (64.9–70.8) |
43.1 (40.0–46.3) |
56.8 (53.6–59.9) |
| 0.185 mm |
59.9 (55.4–64.3) |
63.8 (59.4–68.1) |
49.8 (46.7–53) |
29.9 (27.0–32.8) |
48.0 (44.8–51.2) |
| 0.278 mm |
56.9 (49.7–64) |
75.3 (72.1–78.3) |
19.9 (17.4–22.5) |
11.3 (9.4–13.5) |
31.1 (28.2–34.1) |
The percent of subjects predicted by the model to undergo “fast” change is also presented at various definitions of fast change. Model yield is the product of positive predictive value and those predicted to undergo fast change. The yield without use of the model is the percent of subjects in the study who changed by at least the criterion amount. Results are given as percent (95% confidence interval).
Positive predictive values were moderate in size across all categories of fast myopia progression and axial elongation with only small to moderate decreases as the cut points became larger. The model predicted fewer children to be fast progressors, however, at those more extreme definitions. The final yield of children likely to experience fast change was therefore very low, as low as 0.8% if the cut point was −0.75 D (Table 6). Practically applied, if a clinical trial screened 1000 children who had the demographic and ocular component characteristics of the CLEERE data set and the entry criterion was predicted progression of at least −0.75 D, only 17 would be enrolled and only 8 would be likely to actually progress by at least −0.75 D. In contrast, enrolling 100 children similar to CLEERE subjects without predictive screening would likely yield 17 who progressed by at least −0.75 D.
DISCUSSION
The predictive models derived from CLEERE data for children 7 to 14 years of age for refractive error and axial length at the third visit of a 3-year period depended primarily on demographic factors such as age, sex, and race/ethnicity rather than the change in refractive error or axial length in the previous year. Other factors, notably near work and time outdoors, were not significant predictive factors. Previous publications from CLEERE have already reported that near work was not a risk factor for increased risk of either myopia onset or rate of myopia progression.5,33,34 Time outdoors reduced the risk of the onset of myopia but had no effect on the rate of progression.5,33,34
The number of myopic parents increased the risk of myopia onset33,34 but was not related to myopia progression.17 The effect of parental myopia on the rate of progression in studies other than CLEERE is mixed. Although the age needed to reach stabilization of progression in the Correction of Myopia Evaluation Trial was not related to the number of myopic parents, the Correction of Myopia Evaluation Trial found that the amount of parental refractive error was related to the amount of their child's myopia progression over a 5-year period.19,35 This discrepancy might be due to analyzing parental myopia as a continuous variable rather than the categorical variable of number of myopic parents. Results from SCORM indicated that the number of myopic parents along with sex and race only made a slight improvement of 0.02 to the area under the receiver operating characteristic curve for models of myopia progression.6
Although demographic factors were expected to be related to the rate of change, more surprising was how little meaningful information on past change contributed to model predictions about the future. Axial elongation between visits 1 and 2 was not significantly correlated with elongation between visits 2 and 3. The prior year's myopia progression was correlated with the next year's progression but weakly with a low R2 of 0.015. The slope from orthogonal regression was a robust 0.98, much larger than the slope of 0.25 to 0.28 from ordinary least squares regression reported using SCORM data, but SCORM did not report their R2 for comparison.28 Past changes were significant terms in the prediction models of both refractive error and axial length; however, incorporating this information made no difference to the mean absolute difference between predicted and actual change (Table 4) and either made little difference or increased the 95% limits for prediction error (Table 4; Fig. 2). The poor performance for axial elongation may be due in part to the imprecision of measurement in the CLEERE Study. These were A-scan ultrasound data, and more precise partial coherence interferometric methods with improved repeatability are in common use now.36,37 Even though not as precise, ultrasound measurements still showed meaningful associations between myopia progression and axial elongation with significant correlations (P < .001) between both visits 1 and 2 (r = 0.47) and visits 2 and 3 (r = 0.40).
One goal of predicting the rate of change is for the clinician treating myopic children and the researcher planning a clinical study to prioritize the fast progressor. The current study results suggest that the most effective strategy for sample enrichment is through demographics of age, sex, race/ethnicity, and baseline refractive error and/or axial length values rather than history of refractive error and/or axial length change. Sample enrichment seems most efficient when the data predict a high average progression rate, that is, when roughly a 50/50 split will occur around that desired high average rate of progression. Whether sample enrichment is cost-effective depends on how difficult it is to identify and enroll high-risk children. Assuming a goal of having 16 to 17 fast progressors at the completion of a study, the more cost-effective approach would depend on the resources needed to screen 2000 children but only follow the 34 fast progressors identified by the model compared with just enrolling and following 100 unscreened children. Cost-effectiveness is not the only consideration, however. Prioritizing enrollment based on demographic data raises issues of generalizability. Young Asian females' myopia may progress the fastest but may not produce results that generalize to all myopic children. The mechanisms of progression are unlikely to be different, but the degree of treatment efficacy across sex and age in particular may come into question. Finally, consideration of the ethical issue of justice dictates that the burden of research should not fall to one group.
Previous studies have used a strategy of recruiting only those with faster progression of at least −0.50 D or more in the previous year.26,27 This strategy of enrolling fast progressors may be more effective in the first year compared with subsequent years. Average change in later years will probably decrease because of regression to the mean and the expected age-related decline in myopia progression and axial elongation. These effects could be substantial. For example, myopia progression for the single-vision control subjects in a clinical trial of prism and bifocal correction was a rapid −0.93 D in the first year26 but closer to that predicted by demographic factors of age and ethnicity in the second year at −0.61 D.6,17 Children from the CLEERE Study who progressed at least −0.75 D between visits 1 and 2 (average progression, −1.06 D) progressed by an average of −0.46 D between visits 2 and 3, only slightly higher than the average progression for the entire sample (−0.36 D; Table 1). Furthermore, CLEERE children who had axial elongation of at least 0.278 mm between visits 1 and 2 (average elongation, 0.48 mm) had an average elongation of 0.19 mm between visits 2 and 3, the same as the average for the entire sample (Table 1). If a more extreme cut point of axial elongation of at least 0.395 mm was chosen between visits 1 and 2, one that aligned with the 1.9 D/mm conversion factor and −0.75 D of progression, the average elongation of 0.59 mm between visits 1 and 2 decreased to only 0.20 mm between visits 2 and 3. Enrollment of consistently fast-progressing individuals would be advantageous for a clinical trial; however, change was not consistent enough in the current study to suggest that they can be reliably identified based on short-term data.
Clinicians may be aware of individuals whose myopia progression seems consistently fast or slow, contrary to the conclusions of this analysis. Observation over longer periods might confirm a child’s status as a consistently fast or slow myopia progressor. One study limitation is that the current results are based on only 1 year, and progression extends over a longer time frame.35 Waiting years to establish a dependably fast rate of progression seems impractical, however, and detrimental to the care of the child because additional diopters of myopia accrue during an extended period of observation before treatment. Initiating myopia control as early as possible seems the best approach even with considering that studies of myopia control longer than 3 years are rare and the period over which myopia control continues to reduce progression and elongation is questionable.21 In the Blue Mountains Eye Study of adults 49 years or older, 43% (15 of 35) of the participants who developed myopic retinopathy had refractive errors less myopic than −5.00 D.38 Reducing the overall burden of myopia-related complications requires reducing the final refractive error and axial length among all myopes, even those with low or moderate values.39 The inclination to wait and see how much progression occurs before initiating treatment runs counter to that goal. A more evidence-based approach would be to treat myopia whenever it appears because identifying who will progress rapidly is difficult and any reduction in the eventual amount of myopia is beneficial.
CONCLUSIONS
The associations between prior year and future year myopia progression or axial elongation were too weak to provide useful predictive information, alone or in combination with other input variables. Myopia progression and axial elongation were best predicted by demographic factors of age, race/ethnicity, and baseline biometric values. Female sex was a significant factor for a more myopic refractive error at visit 3 but not for a longer axial length. Parental history of myopia and environmental variables such as near work and time outdoors did not add to the accuracy of predictions of future change. Individual demographic and ocular data made acceptable predictions about fast versus slow change when the cut point was close to the average for the sample as a whole; however, these classifications became inefficient when used to identify an enriched sample of children likely to have faster rates of change. Strategies for sample enrichment such as recruitment of children of a specific age, sex, and race/ethnicity or who have shown past rapid rates of change are ethically problematic or likely ineffective over the duration of a clinical trial. These findings suggest that it is inadvisable to delay myopia control to establish a high rate of pre-treatment progression. Initiation of myopia control should not depend on history of progression.
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