Myopia is a common ocular disorder, with an estimated

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1 Clinical and Epidemiologic Research Myopia Stabilization and Associated Factors Among Participants in the Correction of Myopia Evaluation Trial (COMET) The COMET Group Department of Preventive Medicine, Stony Brook Medicine, Stony Brook, New York Correspondence: Leslie Hyman, Department of Preventive Medicine, Stony Brook Medicine, Health Sciences Center Level 3, Stony Brook, NY ; edu. Submitted: May 13, 2013 Accepted: October 9, 2013 Citation: The COMET Group. Myopia stabilization and associated factors among participants in the Correction of Myopia Evaluation Trial (COMET). Invest Ophthalmol Vis Sci. 2013;54: DOI: / iovs See the appendix for members of the Writing Committee (listed alphabetically) and for members of the Correction of Myopia Evaluation Trial (COMET) Group. PURPOSE. To use the Gompertz function to estimate the age and the amount of myopia at stabilization and to evaluate associated factors in the Correction of Myopia Evaluation Trial (COMET) cohort, a large ethnically diverse group of myopic children. METHODS. The COMET enrolled 469 ethnically diverse children aged 6 to younger than 12 years with spherical equivalent refraction between 1.25 and 4.50 diopters (D). Noncycloplegic refraction was measured semiannually for 4 years and annually thereafter. Right eye data were fit to individual Gompertz functions in participants with at least 6 years of follow-up and at least seven refraction measurements over 11 years. Function parameters were estimated using a nonlinear least squares procedure. Associated factors were evaluated using linear regression. RESULTS. In total, 426 participants (91%) had valid Gompertz curve fits. The mean (SD) age at myopia stabilization was (4.17) years, and the mean (SD) amount of myopia at stabilization was 4.87 (2.01) D. Ethnicity (P < ) but not sex or the number of myopic parents was associated with the age at stabilization. Ethnicity (P ¼ 0.02) and the number of myopic parents (P ¼ 0.01) but not sex were associated with myopia magnitude at stabilization. At stabilization, African Americans were youngest (mean age, years) and had the least myopia (mean, 4.36 D). Participants with two versus no myopic parents had approximately 1.00 D more myopia at stabilization. The age and the amount of myopia at stabilization were correlated (r ¼ 0.60, P < ). CONCLUSIONS. The Gompertz function provides estimates of the age and the amount of myopia at stabilization in an ethnically diverse cohort. These findings should provide guidance on the time course of myopia and on decisions regarding the type and timing of interventions. Keywords: myopia, myopia stabilization, Gompertz function, associated factors, myopia progression Myopia is a common ocular disorder, with an estimated prevalence of 33% among adults in the United States, 1 reflecting an increase of 66% over the past 30 years. 2 Among Asian populations, the prevalence is even higher, with rates as high as 37% by age 9 years among Chinese children in Singapore 3 and approximately 60% among adolescents aged 11 to 17 years in rural China. 4 Myopia, even at moderate levels, is associated with other ocular complications and visual impairment, 5 7 rendering the increased prevalence a concern. The course of myopia typically follows a pattern that begins with an initial emmetropic phase, followed by a myopic shift (onset) that usually occurs in the early school years, which is then followed by a period of rapid myopization that tends to plateau in the mid to late teenage years. 8 Additional and more modest progression may occur during early adulthood before fully stabilizing. 9 Although many studies have examined myopia development and progression, most focus on a short period, and information about its full course is limited. Having a better understanding of the full course of myopia, including its period of slowing and the age and the amount of myopia expected at stabilization in various populations (e.g., different ethnic groups), is important for guiding recommendations for frequency of eye examinations, continuing need for prescription changes, and possible timing for interventions such as refractive surgery. The time course of myopia was characterized by Goss and Winkler 10 using two lines to describe the myopia progression and stabilization phases of 299 young myopes. For each eye, a straight line representing the progression phase of myopia was estimated using at least three observed data points before age 15 years; the stabilization phase was represented by a horizontal line at a level determined by the average refractive error for all data points after 17 years. The age at which the two lines intersected was considered the age at myopia cessation, and the average of this myopia cessation age was found to range from to years for girls and to years for boys based on four different methods. This approach implied a sudden transition of myopia from the progression phase (one line) to the stabilization phase (another line). From more recent investigations, it does not appear that this is a typical pattern of eye growth. 11 The application of mathematical growth functions such as Gompertz functions has also been used to describe the course of myopia. Such functions are determined by a limited number Copyright 2013 The Association for Research in Vision and Ophthalmology, Inc. j ISSN:

2 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7872 of parameters that are biologically consistent with the different phases of myopia. Thorn et al. 8 successfully fit Gompertz functions 12 to longitudinal refraction data from 72 eyes of 36 children of predominantly white ethnicity who were followed from their premyopia status through the myopization process, ending with stabilization of myopia at a particular age and dioptric level. These results demonstrated that the Gompertz function provides good fits to longitudinal refraction data and provides parameters that can be related to underlying biological characteristics. Results from that study 8 showed the estimated mean age at myopia stabilization to be 15.2 years and the average amount of myopia at stabilization to be 3.2 diopters (D). The Correction of Myopia Evaluation Trial (COMET) began as a multicenter, randomized clinical trial to evaluate whether progressive addition lenses (PALs) slow the rate of progression of juvenile-onset myopia compared with conventional singlevision lenses (SVLs). 13,14 The overall 3-year treatment effect was 0.20 D less myopia with PALs, a difference that was statistically significant but clinically inconsequential. 15 The availability of 11 years of longitudinal refraction data from the COMET cohort, a large ethnically diverse group of myopic children, provides a unique opportunity to (1) describe the long-term course of myopia, (2) estimate the age and the amount of myopia at stabilization using Gompertz functions, and (3) evaluate associated factors. METHODS Study Population Participants eligible for these analyses were part of the COMET cohort who had study measurements, including cycloplegic and noncycloplegic refractions, taken annually for 11 years and noncycloplegic refractions also taken semiannually for the first 4 years, beginning with the clinical trial phase when they wore their assigned lenses of PALs or SVLs. After 5 years, the COMET became a longitudinal, observational study of risk factors for myopia progression and stabilization; at that time, participants in consultation with their parents and study optometrist could opt to remain in their original lens assignment or switch to the alternative spectacle lens type or to contact lenses. At baseline, the COMET cohort included 469 ethnically diverse children aged 6 to younger than 12 years with spherical equivalent refractive error between 1.25 and 4.50 D in each eye, no more than 1.50 D of astigmatism, and less than 1.00 D of anisometropia (spherical equivalent). Participants were recruited from four colleges or schools of optometry located in Birmingham, Alabama; Boston, Massachusetts; Houston, Texas; and Philadelphia, Pennsylvania. Additional details of the baseline characteristics, study design, and results have been published previously The COMET and protocols conform to the tenets of the Declaration of Helsinki. The research protocols were reviewed and approved by the institutional review boards of each participating institution. Informed consent (parents) and assent (children) were obtained. The COMET participants were considered for inclusion in the present analyses if they had at least 6 years of follow-up and a minimum of seven refraction measurements over 11 years. Only right eye data were used for these analyses because of the high correlation between right eye and left eye spherical equivalent refractions (SERs). 15 Only two participants underwent refractive surgery, which was reported at the 11-year visit; therefore, their refraction data from that visit were omitted from these analyses. Based on the longitudinal SER data collected over 11 years, individual Gompertz functions were fit to each of the participant s refractive measurements to model individual progression and subsequent stabilization of myopia. Additional steps were undertaken to ensure the quality of the curve fits and to select the cohort for inclusion in these analyses as described below. Procedures Refractive error (sphere, cylinder, and axis) was measured both by noncycloplegic autorefraction and by autorefraction following the administration of 2 drops of 1% tropicamide in both eyes using a Nidek ARK 700 autorefractor (Nidek, Gamagori, Japan). Five readings were taken per eye, converted to SER values, and then averaged. To maximize the number of data points available for curve fitting, noncycloplegic refractions were used as the outcome variable for these analyses because they were measured at 6-month intervals for the first 4 years and annually thereafter, while cycloplegic refraction was only measured annually throughout the study. Comparison of noncycloplegic and cycloplegic measures showed mean (SD) differences of 0.19 (0.22) D at baseline 14 and 0.23 (0.27) D on average throughout the 11-year follow-up period, with noncycloplegic measures more myopic than cycloplegic measures. Attempts were made to obtain refractive data from both parents of all COMET participants using noncycloplegic autorefraction following the COMET protocol when possible. 16 Otherwise, parental refractions were collected from lensometry, a written prescription, a clinical record, or a report from an eye care provider. 16,17 Curve Fitting Process The process for fitting the Gompertz curves to the COMET participant data involved several steps. These include (1) applying the Gompertz function, defined below; (2) evaluating and applying values for the imputation of data points for the initial emmetropic phase of myopia; and (3) using a nonlinear least squares procedure to estimate the function parameters, described below. Growth Function for Myopia (Gompertz). A fourparameter Gompertz curve was used to model the SER of the right eye over time. This function has a general pattern of initial stability (emmetropia) before the onset of myopia, followed by a rapid acceleration of myopia, slowing of progression, and then stabilization of the SER to a constant level. Using R to represent the refractive error (SER) of the right eye at a given age t for each participant, the Gompertz function for refractive error was specified as follows: R ¼ R e þ R c 3 0:07295 aðt t 0 Þ This function followed the approach proposed by Thorn et al., 8 where for each participant R e is the SER before the onset of myopia and R c is the change in SER from R e to the final asymptotic myopia level; is a constant based on an a priori definition of myopia progression onset and the nature of the double exponential function (i.e., peak acceleration into myopia), which happens when 7.295% of the myopization change is achieved, 8 and is not determined by the data at hand. The variable a is the shape parameter, with larger a (0 < a < 1) values representing slower myopia progression from the emmetropic phase, and t 0 is the age at peak myopia acceleration. Based on the individual Gompertz growth curves fitted from the above formula, the following clinically relevant outcomes were estimated for each individual (eye) with a valid curve fit. First, the final level of myopia (asymptotic value) was estimated directly from the fitted curve as follows:

3 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7873 TABLE 1. Sensitivity Analysis: Comparison of Different Imputation Schemes With the Selected Imputation Values Imputation Scheme Imputed Premyopic Ages, y Imputed Premyopic SER Within 1 y of Age Stabilization, % Within 0.50 D of Myopia at Stabilization, % 1 3 þ0.30 (cohort aged 8 y), 0.50 (cohort aged 6 7 y) þ0.30 (cohort aged 8 y), 0.50 (cohort aged 6 7 y) , 4 þ0.30 (cohort aged 8 y), 0.50 (cohort aged 6 7 y) ,4, (both age cohorts) ,4,5 þ0.50 (both age cohorts) SER final ¼ R e þ R c The age at stabilization, defined as the age at which the estimated SER was within 0.50 D of the asymptote (R e þ R c ), was then calculated as follows: Age stable ¼ ln½lnð0:5=r c þ 1Þ=ln 0:07295Š=ln a þ t 0 The amount of myopia at stabilization was the final level of myopia plus 0.50 D, calculated as follows: SER stable ¼ðR e þ R c Þþ0:50 D In addition, the age at peak myopia deceleration (second inflection [i.e., the age at which the velocity of myopia slowing is at its peak]) was calculated as follows: Age at second inflection ¼ lnð 0:38=ln 0:07295Þ=ln a þ t 0 Imputation of Early Data Points. Gompertz curves use information from premyopic and postmyopic phases. Because all COMET participants were 6 years or older and had at least 1.25 D of myopia at the time of study enrollment, premyopic values were unavailable. Therefore, before the curves could be fit, it was necessary to impute data points for the initial emmetropic phase for each COMET participant. Several studies have shown that most children approach a near-emmetropic refraction by age 1 to 2 years and that the emmetropia remains stable until refractions subsequently become myopic. 18 In addition, the premyopic (emmetropic phase) spherical equivalent was observed by Thorn et al. 8 in a sample of 72 eyes from 36 children to have a mean (SD) of 0.34 (0.44) D. The previously reported results, as well as biological considerations, were used to guide the selection of the imputed early values to fit Gompertz curves for the COMET participants. Thus, the premyopia spherical equivalent was set at þ0.30 D at 3, 4, and 5 years of age for those COMET participants who were 8 years or older at baseline. In the earliest-onset case reported by Thorn et al., 8 the premyopic value for the SER was 0.75 D, and the value was 5.4 years for the age at onset. Using this maximum value case as a guide, the premyopic SER was set at 0.50 D for the COMET children aged 6 to 7 years at baseline. TABLE 2. Parameter Curve Fitting Starting Values and Constraints Younger Cohort, 6to7y Starting Values Constraints Older Cohorts, 8to<12 y Starting Values Constraints t 0 (onset), y 3 to to 10 5 a (slope) 0.50 None 0.50 None R e,d 1.0 to 1.0 None 1.0 to 1.0 None R c,d 2.0 to 10.0 None 2.0 to 10.0 None To evaluate the impact of the a priori selected imputation values for ages and levels of premyopic SER at early ages on the final curve parameters and the estimated age and the amount of myopia at stabilization, a sensitivity analysis was conducted. This was achieved by varying the imputed spherical equivalent and premyopia ages in five different imputation schemes (Table 1) and by refitting all participant curves for each new scheme. Based on the imputed values from each scheme, curve parameters and the age and the amount of myopia at stabilization were then estimated for each participant and compared with the selected imputation values. For example, the deviation in participant i between the final estimate for the age at stabilization and the estimate based on the imputation scheme j (range, 1 5) was computed as follows: Age at Stabilization D i ¼ Age StabilizationðfinalÞ i Age Stabilizationðimputation jþ i Small differences in the level of myopia (within 0.50 D) at stabilization and the age (within 1 year) at stabilization were considered to be indicative of robustness of the estimates that resulted from the selected imputation values. As summarized in Table 1 across the five schemes, a high percentage (98% 99%) of the estimated values for myopia at stabilization fell within 0.50 D of the selected values. Thus, the estimated amount of myopia at stabilization was considered extremely robust across the possible imputation schemes used for premyopic ages and SER levels, with minimal meaningful differences observed across estimated values regardless of the imputation scheme used. The age at stabilization was similarly robust across the different imputation schemes in the majority of participants (with the percentage of values within 1 year of the stabilization age ranging from 85% 96%). As an additional examination, the linear association between the age and the amount of myopia at stabilization and participant characteristics (i.e., ethnicity, sex, and parental myopia) was evaluated for each of the five imputation schemes. The factors found to be associated with the age at stabilization and the amount of myopia at stabilization and magnitude of the associations were similar in both magnitude and importance across all imputation scenarios (data not shown). The analyses above demonstrate that the results presented in this article were determined by longitudinal data from the participants, not by our choice of imputed values. Parameter Estimation. Parameters for the Gompertz function in the initial equation in the Methods section were estimated using the nonlinear least squares regression procedure available in PROC NLIN in SAS version 9.1 (SAS Institute, Cary, NC). To find the best starting values for each parameter for curve fitting, a grid search was used with ranges for each parameter given in Table 2. A modified Gauss-Newton approach was used for the iterative process, and 2000 maximum iterations were performed. Biological constraints on some of the parameters were also imposed. For example, the estimated age at myopia onset was constrained in the model to occur no earlier than age 3 years in the youngest

4 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7874 FIGURE 1. (a f) Examples of Gompertz curves. (a) Age 6 to 7 years (baseline age) with stable myopia estimated before the last study visit (MSE [a measure of curve fit quality], 0.03). (b) Age 6 to 7 years (baseline age) with stable myopia estimated after the last study visit (MSE, 0.02). (c) Age8 years or older (baseline age) with stable myopia estimated before the last study visit (MSE, 0.01). (d) Age 8 years or older (baseline age) with stable myopia estimated before the last study visit (MSE, 0.33). (e) Age 8 years or older (baseline age) with stable myopia estimated after the last study visit (MSE, 0.03). (f) Age 8 years or older (baseline age) with no myopia progression (MSE, 0.02). cohort (<8 years old at baseline) and age 5 years in the older cohorts ( 8 years old at baseline). The starting values of the parameters in the estimation procedure differed according to the baseline age group. Figures 1a through 1f show examples of Gompertz curve fits for two participants who were aged 6 to 7 years at baseline and four participants 8 years or older at baseline. These examples include participants with (1) stable myopia estimated by the time of the last study visit (Figs. 1a, 1c, 1d), (2) stable myopia estimated after the last study visit (Figs. 1b, 1e), and (3) no myopia progression (Fig. 1f). These figures include curve parameters, the imputed and observed values used for the curve, and estimated values for final myopia, which is the curve asymptote, defined by R e þ R c, the amount of myopia at stabilization (i.e., asymptote þ 0.50 D), and the stabilization age. Selection of the Cohort Used for Analyses Eligibility for the present analyses was determined by evaluating the curves for the quality of their fit based on a convergence threshold or mean squared residuals. Curves were included unless nonconvergence was found using a convergence threshold of 10 5 or a poor model fit, defined as a mean squared residual (observed SER minus the curve-based predicted SER) exceeding 0.40.

5 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7875 TABLE 3. Characteristics of the COMET Participants With Gompertz Curve Fits (n ¼ 426) n (%) Age at Baseline, y 8 Characteristic Overall, n ¼ , n ¼ 40* Myopia Progression After Baseline, n ¼ 329 No Myopia Progression After Baseline, n ¼ 56 Ethnicity African American 112 (26) 11 (27) 72 (22) 28 (50) Asian 33 (8) 2 (5) 29 (9) 2 (4) Hispanic 62 (15) 6 (15) 49 (15) 7 (12) Mixed 21 (5) 2 (5) 18 (5) 1 (2) White 198 (46) 19 (48) 161 (49) 18 (32) Sex Male 198 (46) 15 (38) 157 (48) 25 (45) Female 228 (54) 25 (62) 172 (52) 31 (55) Myopic parents, n None 35 (15) 3 (17) 30 (16) 2 (8) (48) 6 (33) 93 (50) 11 (46) 2 84 (37) 9 (50) 64 (34) 11 (46) * Excludes one participant without progression after baseline. P values based on v 2 tests comparing proportions across three groups for ethnicity, sex, and the number of myopic parents are P ¼ 0.007, P ¼ 0.46, and P ¼ 0.47, respectively. Based on a subset of participants with parental myopia data. Handling of Participant Curves With a Lack of Myopia Progression During Follow-up Following the fitting of curves for each participant s myopia, a group of curves based on these fits was identified with no or limited progression over the 11-year period, defined as less than a 0.75-D predicted change in myopia from baseline to stabilization. Given the pattern of childhood myopia progression observed by Thorn et al. 8 and in other investigations, 22 myopia in this group of children was considered likely to have already stabilized by the time the children were enrolled in the study. Therefore, baseline values were used to estimate the age and the amount of myopia at stabilization for these participants. Definition of Outcomes The age at stabilization and the amount of myopia at stabilization were the primary outcomes of interest. For the primary analyses, model-based estimates were determined, and distributions were summarized for both outcomes for all participants with valid Gompertz curve fits. The age at peak myopia deceleration was evaluated as a secondary outcome. Statistical Analysis A standard two-stage method for nonlinear mixed effects modeling was used to summarize myopia progression and subsequent stabilization for the entire cohort. 23 The first stage, described above, involved fitting individual Gompertz functions to each of the participant s refractive measurements. The second stage summarized individual curve parameters and curve-based estimates for the entire cohort as described below. Following the completion of the curve fitting process, curve-based estimates (e.g., the age and the amount of myopia at stabilization) were summarized and averaged across individual curves using summary measures (e.g., means) to provide curve-based estimates for the COMET cohort. Linear models for the age (in years) at stabilization and the amount of myopia (in diopters) at stabilization were fit using least squares regression. Multivariable models for outcomes of interest (the age at stabilization and the amount of myopia at stabilization) also were fitted using all available participant-level (time invariant) predictors (ethnicity, sex, and the number of myopic parents) as covariates in the models. Parental refractions were available in a subset of 229 among 426 participants. Parents were considered to have myopia if their SER was 0.75 D or less (the mean of both eyes) when defining the number of myopic parents. When evaluating the correlation between the amount of myopia in the parents with that in their offspring, the midpoint value of the parents was used. Wald tests and corresponding P values were computed to test the statistical significance of covariate effects in the model. RESULTS Curve Fits Ninety-four percent (440 of 469) of the COMET cohort had sufficient data points (at least seven) and years of follow-up ( 6 years) to be fit with a Gompertz curve. Fourteen of 440 participants were excluded because of either nonconvergence (n ¼ 3) or a poor model fit (n ¼ 11). The analyses presented below are based on the remaining 426 participants, representing 91% of the original cohort. The curves fit well for these participants, as reflected by a mean (SD) of mean squared errors (MSEs) of 0.06 (0.04); 99% of fits had MSEs of 0.22 or lower (i.e., better fit). The MSEs for the curves shown in Figures 1a through 1f of 0.03, 0.02, 0.01, 0.33 (the largest MSE), 0.03, and 0.02 indicate that the curve fits were good for all participants. Cohort Characteristics Overall, the participants with successful curve fits were ethnically diverse, with 26% reporting their ethnicity as African

6 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7876 TABLE 4. Curve-Based Estimates of the COMET Participants With Gompertz Curve Fits (n ¼ 426) Mean (SD) [Median] (Minimum, Maximum) Age at Baseline, y 8 No Myopia Progression After Baseline, n ¼ 56 Myopia Progression After Baseline, n ¼ , n ¼ 40* Overall, n ¼ 426 Curve-Based Estimate Age at beginning of peak myopia deceleration, y Not applicable (1.84) [10.92] (7.18, 14.89) (1.91) [11.88] (8.44, 20.88) Not applicable Age at stabilization, y (4.17) [15.17] (6.51, 40.47) (3.64) [15.24] (8.39, 23.52) (3.92) [15.70] (9.46, 40.47) (1.01) [10.76] (8.26, 11.98) Amount of myopia at stabilization, D 4.87 (2.01) [ 4.54] ( 13.10, 1.30) 6.85 (2.29) [ 6.40] ( 12.18, 2.49) 5.04 (1.74) [ 4.65] ( 13.10, 2.10) 2.52 (0.72) [ 2.41] ( 4.40, 1.30) Final myopia, D 5.37 (2.01) [ 5.04] ( 13.60, 1.80) 7.35 (2.29) [ 6.90] ( 12.68, 2.99) 5.54 (1.74) [ 5.15] ( 13.60, 2.60) 3.02 (0.72) [ 2.41] ( 4.40, 1.30) * Excludes one participant without progression after baseline. The final (asymptotic) level of myopia and the age and the amount of myopia at stabilization were based on the baseline values. The mean values for the age at peak myopia deceleration were compared between the cohort aged 6 to 7 years and those 8 years or older with progressing myopia after baseline using a two-sample Student s t-test (P ¼ ). The overall P values based on ANOVA tests comparing the mean values across three groups for the age at stabilization, the amount of myopia at stabilization, and final myopia are all less than American, 8% as Asian, 15% as Hispanic, 5% as mixed, and 47% as white; 54% were female (Table 3). In the subset of 229 participants with parental refraction data, 37% had two myopic parents, 48% had one myopic parent, and only 15% had no parent with myopia (Table 3). Data are also presented separately by baseline age categories (i.e., 6 7 years and 8 years) and for the older cohort by whether or not myopia progression occurred after baseline. Ethnicity distributions differed among the three groups (P ¼ 0.007); the frequency of white participants was higher and the frequency of African Americans was lower in the cohort aged 6 to 7 years and the cohort 8 years or older with progressing myopia compared with the group 8 years or older with no myopia progression. Consistent with this observation, the one participant aged 6 to 7 years whose myopia did not progress after baseline and is excluded from this age category in Table 3 was of African American ethnicity. Sex and the number of myopic parents did not differ significantly among the three groups (P ¼ 0.46 and P ¼ 0.47, respectively). Curve-Based Estimates The curve-based estimates for the age at peak myopia deceleration (i.e., the age at the second inflection point on the Gompertz curve), the age at stabilization, the amount of myopia at stabilization, and final myopia are summarized in Table 4. Overall, the mean (SD) estimated age at peak myopia deceleration was (1.94) years, and the mean (SD) age at myopia stabilization was (4.17) years. The mean (SD) amount of myopia at stabilization was estimated to be 4.87 (2.01) D; the mean final myopia value was 5.37 (2.01) D, which by definition was 0.50 D more myopia (Table 4). When comparing the age and the amount of myopia at stabilization across the three age and myopia progression status groups summarized in Table 4, statistically significant differences were observed among groups for the age at stabilization, the amount of myopia at stabilization, and final myopia (P < for all). As would be expected, those whose myopia did not progress during follow-up had earlier estimated ages at stabilization and less myopia at stabilization. In comparisons limited to the cohort aged 6 to 7 years and the cohort 8 years or older with progressing myopia after baseline, the younger cohort had significantly earlier ages at peak myopia deceleration (by a little more than 1 year; (P ¼ ), more myopia at stabilization and higher final myopia values by an average of 1.70 D (P < ) for both of these outcomes. The age at myopia stabilization was also younger for those aged 6 to 7 years, but this difference did not reach statistical significance (P ¼ 0.11). Age at Stabilization Based on the Gompertz curve based estimates, approximately half (48%; 203 of 426) of the overall COMET cohort had stable myopia (estimated SER within 0.50 D of the asymptote) by age 15 years. The proportion with estimated stable myopia increased to 77% (330 of 426) by age 18 years and to 90% (384 of 426) by age 21 years. By age 24 years, the curves of almost all of the cohort (96%; 411 of 426) had achieved the curve-based definition of myopia stabilization. The estimated age at myopia stabilization varied significantly (P < ) by ethnicity (Table 5) and as further demonstrated in Figure 2, which shows the cumulative proportion of participants whose curves reached stable myopia as a function of age. From Figure 2, it appears that myopia in African Americans tended to stabilize the earliest, while myopia in other ethnic groups stabilized at more similar ages. By age 12 years, myopia was estimated to be stable in 37%

7 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7877 TABLE 5. Age at Myopia Stabilization and Associated Factors (n ¼ 426)* Participant Characteristic n Mean (SE) Age, y Difference (95% Confidence Interval) vs. Reference Group P Value Overall P Value Overall (0.20) Ethnicity African American (0.38) Reference - < Asian (0.71) 2.18 (0.61 to 3.76) Hispanic (0.51) 2.36 (1.11 to 3.62) Mixed (0.88) 1.96 (0.07 to 3.85) White (0.29) 2.53 (1.59 to 3.47) < Sex Male (0.30) Reference - - Female (0.28) 0.00 ( 0.79 to 0.80) Myopic parents, n None (0.72) Reference (0.41) 0.18 ( 1.80 to 1.44) (0.46) 0.80 ( 0.88 to 2.48) * Based on the estimated age at stabilization from the individual Gompertz curves (n ¼ 369) or observed baseline age in participants with stable myopia at their baseline visit (n ¼ 56). Based on Wald tests. Based on the subset with parental myopia data (n ¼ 229). P ¼ 0.11, test for two versus one parent with myopia; P ¼ 0.15, test for two versus one or no parents with myopia (combined group). FIGURE 2. Cumulative proportion of participants with stable myopia by ethnicity and the estimated age at stabilization (n ¼ 426). The overall cumulative proportion distributions are significantly different across ethnicity groups (P <.0001, log-rank test).

8 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7878 TABLE 6. Amount of Myopia at Stabilization and Associated Factors (n ¼ 426)* Participant Characteristic n Mean (SE) Myopia, D Difference (95% Confidence Interval) vs. Reference Group P Value Overall P Value Overall (0.10) Ethnicity African American (0.19) Reference Asian (0.35) 1.09 ( 1.87 to 0.32) Hispanic (0.25) 0.53 ( 1.15 to 0.09) Mixed (0.43) 0.76 ( 1.69 to 0.17) White (0.14) 0.68 ( 1.14 to 0.21) Sex Male (0.14) Reference - - Female (0.13) 0.26 ( 0.64 to 0.12) Myopic parents, n None (0.35) Reference (0.20) 0.15 ( 0.93 to 0.64) (0.22) 0.94 ( 1.75 to 0.13) * Based on the estimated amount of myopia at stabilization from the individual Gompertz curves (n ¼ 369) or observed baseline myopia in participants with stable myopia at their baseline visit (n ¼ 56). Based on Wald tests. Based on the subset with parental myopia data (n ¼ 229). P ¼ 0.008, test for two versus one parent with myopia; P ¼ 0.004, test for two versus one or no parents with myopia (combined group). (41 of 112) of African Americans compared with the other ethnic groups, whose proportions with stable myopia ranged from 13% (8 of 62) of Hispanics to 15% (5 of 33) of Asians (P < 0.001). This pattern persisted with increasing ages. For example, by age 15 years, while the proportion of African Americans with stable myopia had increased to 63% (71 of 112), the proportions with stable myopia in the other ethnic groups remained significantly lower, ranging from 39% (77 of 198) in white participants to 48% (30 of 62) in Hispanics (P ¼ ). By age 18 years, 90% (101 of 112) of African American participants had estimated stable myopia compared with 71% (140 of 198) of white participants and 76% of both Hispanics (47 of 62) and Asians (25 of 33), a significant difference (P ¼ 0.003). African Americans consistently had the highest cumulative rates of stabilization until 24 years and older, when myopia in most participants in all ethnic groups had stabilized based on the Gompertz curves. Consistent with the above results and as summarized in Table 5, when the age at stabilization was compared among all ethnic groups, African American participants had the youngest mean stabilization age of all ethnic groups (P < ). Ethnicity, sex, and the number of myopic parents were evaluated first in separate linear regression models and then in a final multivariable model for their potential association with the age at stabilization. Based on results of the separate univariate regression models summarized in Table 5, only ethnicity among these three factors was found to be associated with the stabilization age (P < ), with African Americans having the youngest age at myopia stabilization. Compared with each of the other ethnic groups, the mean age at stabilization in African Americans of years was significantly younger than that among Asians, Hispanics, and the mixed ethnicity group by approximately 2 years (P ¼ 0.007, P ¼ , and P ¼ 0.04, respectively) and 2.5 years younger than that in white participants (P < ). The stabilization age was not associated with sex or the number of myopic parents in these analyses. Only ethnicity (P ¼ 0.01) was associated with the estimated age at stabilization in a model that included sex and parental myopia as covariates. These results are consistent with the findings of the univariate analysis. Amount of Myopia at Stabilization The amount of myopia at stabilization, obtained from the Gompertz functions, was associated with ethnicity and the number of myopic parents in a univariate model (P ¼ 0.02 and P ¼ 0.01, respectively, for the overall association) (Table 6). At stabilization, African Americans on average had the least myopia ( 4.36 D) and Asians the most ( 5.45 D), a difference of 1.09 D (P ¼ 0.005). African Americans also had significantly less myopia than white participants (P ¼ 0.004). In the subset of 229 participants with available parental refractive data, the amount of myopia at stabilization was similar for those with no or one myopic parent and almost 1.00 D more myopia for participants with two myopic parents. The 0.94-D difference in myopia at stabilization in participants with no versus two myopic parents was statistically significant (P ¼ 0.02; Table 6), as were the differences in the amount of myopia at stabilization between participants with one and two myopic parents (P ¼ 0.008) and two myopic parents (P ¼ 0.004) compared with one and no myopic parents combined. Ethnicity (P ¼ 0.02) remained associated with the estimated level of myopia (in diopters) at stabilization, and parental myopia was of borderline significance (P ¼ 0.05) when evaluated in a multivariable model. Sex was not associated with the amount of myopia at stabilization in univariate or multivariate analyses. Relationship Between the Age at Stabilization and the Amount of Myopia at Stabilization The age at myopia stabilization and the amount of myopia at stabilization were found to be correlated overall (r ¼ 0.60, P < ) and for each age cohort when analyzed separately (r ¼ 0.60, P < for those aged 6 7 years; r ¼ 0.63, P < for those aged 8 years; Fig. 3). For each increase in year of the age at stabilization, myopia at stabilization increased (SER more negative) by 0.29 D overall, by 0.37D for those aged

9 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7879 FIGURE 3. Relationship between the age at stabilization and the amount of myopia stabilization. 6 to 7 years at baseline, and by 0.27 D for those 8 years or older at baseline. Influence of PALs and SVLs Assignment on the Age and the Amount Myopia at Stabilization Because the COMET began as a clinical trial to evaluate whether PALs versus SVLs would slow myopia progression, we also investigated the role of lens type on the age and the amount of myopia at stabilization. The age and the amount of myopia were compared between the PAL (n ¼ 211) and SVL (n ¼ 215) participants with successful Gompertz curve fits. The age at stabilization was similar in the PAL (15.7 years) and SVL (15.5 years) groups, as was the amount of myopia at stabilization, which was 4.9 D for those in PALs and 4.9 D for those in SVLs. When the role of intervention with PALs was examined in a secondary analysis that excluded the 56 children with no myopia progression during follow-up, the age and the amount of myopia at stabilization also were similar in the two lens groups. An additional exploratory analysis was conducted in the subset of 70 COMET participants (36 PALs and 34 SVLs) with low accommodation and near esophoria at baseline, a group that demonstrated a larger benefit from wearing PALs than the overall cohort. 24 In this subgroup analysis of 70 participants, the estimated age at stabilization was 15.1 years in the PAL group and 16.5 years in the SVL group, an average difference of 1.4 years earlier in the PAL versus the SVL group, which was not statistically significant (P ¼ 0.23). However, the PAL group on average had 1.4 D less myopia at stabilization than the SVL group ( 4.2 D in the PAL group versus 5.6 D in the SVL group, P ¼ 0.004). In addition, 19% (7 of 36) of the PAL subgroup versus 3% (1 of 34) of the SVL subgroup were classified as having no myopia progression after baseline. Final Myopia in the COMET Participants and Refractive Error in Their Parents The availability of parental refraction data allowed for an additional analysis using Pearson s correlation coefficient (r) to evaluate the relationship between the final amount of myopia in the COMET participants and the refractive error in their parents, overall and stratified by the number of myopic parents. Parental SER was based on the midparent value. There was a modest, statistically significant overall correlation between parental SER and final myopia in their offspring based on 229 participants with parental refraction data (r ¼ 0.34, P < ). For the analyses stratified by the number of myopic parents, final myopia in the offspring also was moderately and significantly correlated with parental myopia in participants with one (n ¼ 110) and two (n ¼ 84) myopic parents (r ¼ 0.29, P ¼ and r ¼ 0.35, P ¼ 0.001, respectively) but not in those with no (n ¼ 35) myopic parent (r ¼ 0.07, P ¼ 0.70).

10 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7880 Age at Peak Myopia Deceleration For each participant, the Gompertz functions provided an estimate of the age at peak myopia deceleration (the second inflection point). Peak myopia deceleration for all participants with myopia progression after baseline (n ¼ 369) occurred at the mean (SD) age of (1.90) years, a mean (SD) of 4.5 (2.2) years before myopia stabilization occurred. As summarized in Table 4, the time between peak myopia deceleration and myopia stabilization was similar for the cohort aged 6 to 7 years and the cohort 8 years or older with progressing myopia, which was on average 4.7 (2.0) years and 4.4 (2.2) years, respectively. Possible relationships between the age at peak myopia deceleration and ethnicity, sex, and the number of myopic parents were explored based on all participants with progressing myopia after baseline (n ¼ 369). Ethnicity but not sex or the number of myopic parents was predictive of the age at peak myopia deceleration. The average age at peak myopia deceleration was 11.2 years for African Americans, which was significantly younger than the average ages at slowing for Hispanics of 12.4 years and for white participants of 12.2 years, with differences between African Americans and each of these ethnic groups of 1.2 years (P ¼ ) and 1.1 years (P < ), respectively. DISCUSSION Overview The COMET is the most comprehensive longitudinal study of myopia progression and stabilization to be conducted to date. In the large ethnically diverse COMET cohort with juvenileonset myopia, Gompertz functions were fit successfully to the longitudinal refractive data in 91% of participants. For the participants whose myopia progressed during the 11 years of the study, the Gompertz function characterized the entire period during which the myopia progression rate slows and the refraction stabilizes. Importantly, in the group with progressing myopia after baseline, the results clarified that peak myopia deceleration (maximum slowing) occurs an estimated average of 4.5 years before a stable refraction is attained. The successful application of the Gompertz functions to the COMET cohort confirms and extends the results by Thorn et al. 8 among a smaller, more homogeneous sample of 36 children of predominantly white ethnicity (72 eyes). From these two studies, it is clear that myopia progresses in an almost linear manner, then slows, and gradually stabilizes. Although we were unable to examine the onset of myopia based on observed COMET data, the sensitivity analysis showed that the choice of the imputed, premyopia data points based on knowledge from previous studies did not significantly affect the key outcomes of the age at stabilization and the amount of myopia at stabilization. In addition to characterizing the time course of myopia, this study also presents new information on estimates of the age and the amount of myopia at stabilization in the COMET cohort based on the Gompertz curves, as well as on associated factors. Comparisons With Curve-Based Literature Few studies have attempted to model the full course of myopia in individuals and to provide estimates of the age and the amount of myopia at stabilization, and the available studies have included mostly white participants. Therefore, comparisons between the COMET and the following two studies are based only on COMET participants of white ethnicity. No study to date has evaluated associations with ethnicity and the number of myopic parents. The estimated average age at stabilization in the COMET was slightly older than that provided by Goss and Winkler 10 for girls (16.3 vs years) and was similar for boys (16.4 vs years). However, their estimates were obtained using a less precise approach. The one previous study 8 that also used the Gompertz function to estimate the course of myopia in a smaller sample found an estimated age at stabilization of 15.2 years, which is similar to that observed in the COMET cohort (16.35 years). While the age at peak myopia deceleration also was similar in both studies (approximately age 12 years), the estimated final myopia level was approximately 2 D more myopic in the COMET cohort than in the study by Thorn et al. 8 Thus, there is general consistency that on average myopia stabilizes at approximately age 15 years, but the final amount of myopia may vary depending on the population studied. Factors Associated With the Estimated Age and the Amount of Myopia at Stabilization Ethnicity. Our results showed the age at stabilization and the level of myopia at stabilization to be strongly correlated and influenced by similar factors. The age at stabilization (P < ) and the amount of myopia stabilization (P ¼ 0.02) both varied significantly across ethnic groups. African Americans were more likely to have an earlier age at peak myopia deceleration (approximately 1 year earlier than the other ethnic groups), have stable myopia at earlier ages (13.8 years compared with approximately 16 years in the other ethnic groups), and have less myopia at stabilization ( 4.36 D compared with approximately 5.0 D in the other ethnic groups). The ethnic differences in myopia stabilization observed in the COMET are not unexpected because differences in myopia progression among ethnic groups were observed previously in this cohort. During the first 3 years of the COMET, myopia progression was significantly slower in African Americans than in the other ethnic groups, a finding that is consistent with their lower amount of myopia at stablilization. 25 Asian children in the COMET showed the most myopia at stabilization and had significantly faster progression than African American COMET children during the first 3 years of the study. 25 While to the best of our knowledge data from other studies are not available on myopia stabilization in Asian children, rates of progression similar to those of the COMET children were found in studies conducted among Asian children in Hong Kong, 26 Singapore, 27 and the Shunyi district in China. 28 A report from the Collaborative Longitudinal Evaluation of Ethnicity and Refractive Error Study, 29 a multicenter observational investigation of refractive error in four ethnic groups from four different locations in the United States, found Asian children to have the highest prevalence of myopia. Prevalence studies among adults have also identified Asian populations as having more myopia 30,31 and African Americans as having less myopia. 2,32 Therefore, ethnic variation has been observed for all phases of the course of myopia. The differences in myopia prevalence among ethnic groups seem to be explained by a combination of genetic factors and environmental factors because increases in myopia prevalence have been observed across different ethnic groups among the same populations 2 (Saw SM, et al. IOVS 2011;52:AR- VO E-Abstract 2490) and because myopia prevalence for children of the same ethnic origins varies depending on where the children live and the environments to which they are exposed. 33 For example, children of Chinese origin living in Australia had lower levels of myopia than their counterparts living in Singapore. 34 Therefore, the ethnic differences in myopia stabilization may be influenced by factors in the visual or social environment that can occur during the different phases of myopia progression and slowing (e.g., changes in reading or studying patterns and time spent outdoors).

11 Myopia Stabilization and Associated Factors IOVS j December 2013 j Vol. 54 j No. 13 j 7881 Sex. No association was observed between sex and either the age at stabilization or the amount of myopia at stabilization, although we previously reported that girls had faster progression (by 0.16 D) than boys but no differences in axial elongation after 3 years. 25 Faster progression in girls was also observed in some studies 28,35 but not in other studies. 36,37 A recent study by Yip et al. 38 based on longitudinal data from the Singapore Cohort Study of the Risk Factors for Myopia found that children aged 6 to 14 years who had earlier growth spurts had myopia at an earlier age and had earlier ages at peak changes in SER and axial length. These findings were similar in girls and boys. The inconsistency of an association between sex and myopia prevalence and progression among different studies and the absence of an association with the age and the amount of myopia at stabilization in the COMET suggest that any relationship with sex, if it exists, would occur early in the course of myopia at ages when growth spurts may occur sooner in girls than in boys, would be modest, and would not be sustained over time. Number of Myopic Parents. The modest but statistically significant correlation found between the amount of myopia in parents and the amount of final myopia in their offspring overall and for those with one or two myopic parents supports an influence of parental myopia on myopia in their children. While the relationship between the number of myopic parents and myopia in their children is not a new observation, 16,39 the role of parental myopia on myopia stabilization has not been reported previously. These results regarding stabilization are consistent with a previous COMET study 16 showing that having two myopic parents was associated with more myopia progression in their children. Thus, the COMET findings indicate that the relationship between parental myopia and myopia in their children extends beyond progression to include the full course through stabilization. An additional analysis of the COMET parents found that a high level of myopia was associated with the level of education and, to a lesser extent, occupation. 17 It is possible that parents who are more myopic and have higher educational levels may encourage more reading or other behaviors that might influence the extent of myopia progression in their children and delay stabilization. Although results of recent genome-wide meta-analyses of refractive error suggest that multiple genetic factors are involved in the development of myopia and a 10- fold increased risk of myopia for individuals carrying the highest genetic load, 40 genetics has only a partial role in the course of myopia. Thus, reasons for the relationship between myopia in parents and their children are likely to include factors from a shared environment. Age. Although the general course of myopia in the cohort aged 6 to 7 years followed the same pattern of progression, slowing, and gradual stabilization as in the older cohort based on the Gompertz curves, this group had younger ages at peak myopia deceleration and stabilization and had more myopia at stabilization than those who were 8 years or older. This younger cohort also had faster progression and more myopia after the first 3 years of the study than the other age groups, although at baseline the amount of myopia was similar. 24 Furthermore, after 7 years of follow-up, those in this youngest cohort had a higher risk (hazard ratio, 6.6) of having myopia worse than 5.86 D compared with those who were 11 years old at baseline. 41 These observations suggest that myopia follows a similar course regardless of the age at which it occurs. However, having myopia at a younger age results in fast progression and earlier age at stabilization but results in more myopia at stabilization. Lens Assignment. Because the COMET began as a clinical trial, with participants randomized to PALs or SVLs, the question of whether intervention with PALs at a point after myopia progression had begun would effect the age or the amount of myopia at stabilization was explored. Results based on the full cohort showed no effect of lens type on the age or the myopia level at stabilization, indicating that the overall small but significant difference in progression observed between treatment groups 15 was not sustained over time. However, in an exploratory analysis based on the subgroup who had low accommodation and esophoria and who showed a larger benefit of wearing PALs than was found in the overall cohort, the level of myopia at stabilization was significantly lower in the PAL group than in the SVL group. 24 This observation raises the potential of a longer-lasting benefit to wearing PALs in these children. Study Strengths and Limitations A main strength of this study was the availability of carefully collected longitudinal refractive data over 11 years from a large ethnically diverse cohort with a range of patterns of myopia progression and stabilization and associated ocular conditions (e.g., large accommodative lags). The availability of these data allowed for fitting of individual curves to refractive data for the majority of COMET participants and provided curve-based estimates for each individual that could be averaged for the whole cohort, resulting in estimates that are generalizable to a large group of children with juvenile-onset myopia. The approach used to summarize the COMET data based on individual curve fits takes advantage of the availability of the longitudinal data to provide reliable estimates for the majority of the cohort. However, for those children whose myopia did not progress, their curve-based estimates for the age and the amount of myopia at stabilization were not reliable. Therefore, their baseline values, which were the best available estimates, were used for their age and the amount of myopia at stabilization. Baseline myopia for this group is a realistic estimate for the amount of myopia at stabilization. However, because myopia stabilization may have occurred before the baseline visit, using baseline age may overestimate the stabilization age (i.e., be older), a point to consider when interpreting the results. The inclusion of different subgroups of children such as those with limited myopia progression or early stabilization and those with large accommodative lags and near esophoria strengthens the generalizability of the results. Future Directions The present analyses have evaluated the course of myopia based on the SER. However, refractive changes are related to axial elongation, and it would be of interest to understand whether the relationships observed during the earlier stages of onset and progression change during the slowing and stabilization. In previous analyses in the COMET limited to the first 3 years of follow-up, a 0.5-mm change in axial length was associated with 1 D of myopia progression during the first 3 years of follow-up. 25 Future analyses of the COMET data will explore the nature of this relationship during the period of myopia slowing and stabilization. CONCLUSIONS Our results demonstrated that the Gompertz function can be used to describe the latter stage of longitudinal myopia progression and to provide estimates of the age and the amount of myopia at stabilization in an ethnically diverse cohort with juvenile-onset myopia. Furthermore, these observations clarify that myopia progression does not slow at a constant rate, as would be the case if it followed a logarithmic pattern of decay. Rather, the rate of myopia progression drops rapidly approximately 4 years before myopia stabilization is