shows the flow diagram that resulted in the subjects who were eligible for the final analysis (i.e., those who had complete data for the variables of interest; refractive error, activity levels, and parental myopia) and sufficient follow-up. Overall, 514 subjects of 1038 with a third-grade visit (49.5%) had complete data and sufficient follow-up (i.e., either became myopic or were seen through eighth grade). The largest percentage of subjects who were excluded from the analyses did not have the opportunity for an eighth grade visit because the study closed before the subjects reached that grade (74%). Approximately 25% of the subjects without complete follow-up were in fourth grade when the study ended, approximately 25% were in the fifth grade and 25% were in the sixth grade. Half of the data among the remaining subjects lost to follow-up (23/46 subjects) was missing because of a missing activity variable.
Description of which subjects were excluded and the reason for exclusion.
shows a comparison of those with complete data to all those subjects with a third-grade visit who were not eligible for inclusion in the dataset because of incomplete follow-up or sufficient follow-up, but a missing variable of interest. In a comparison of parental history of myopia between these two groups, there were no statistically significant differences. Cycloplegic sphere was significantly different between the two groups, but the difference of 0.21 D is probably not clinically significant. Hours of watching television and hours of computer/video games were statistically significant, both being less than 1 hour per week different between the included subjects and those ineligible for inclusion. Hours of sports and outdoor activities were significantly different; the subjects with complete data had, on average, slightly more than 1 hour per week more of sports and outdoor activities.
Comparisons of Subjects with Complete Data and Subjects with Incomplete Data, Including Those with Insufficient Follow-up
Of the 514 eligible children, 111 (21.6%) became myopic by the eighth grade. The average age at the third-grade visit was 8.63 ± 0.39 years, and the average age at onset of myopia was 11.4 ± 1.5 years. The mean (± SD) of refractive error and activity hours in the third grade by child’s future myopia status, as well as the odds ratio, accompanying 95% confidence interval (CI), and probability are presented in . Of the activity variables, the number of hours of sports and outdoor activity per week in third grade was the only variable significantly associated with future myopia. The nonmyopic child participated in an average of 11.65 ± 6.97 hours per week of sports and outdoor activity, whereas the future myopic child participated in an average of 7.98 ± 6.54 hours per week (OR = 0.91, 95% CI = 0.87 – 0.94).
Univariate Results for Refractive Error, Activities, and Parental History for Child Myopia Status
also presents parental myopia data. Among children who remained nonmyopic, approximately 48% had a myopic mother, whereas 69% of the children who became myopic had a myopic mother (P < 0.001). Similarly, among children who remained nonmyopic, 44% had a myopic father, whereas 64% of the children who become myopic had a myopic father (P < 0.001). The number of myopic parents was associated with children’s future myopia. Among children who remained nonmyopic, almost 21% had two myopic parents, whereas 45% of the future myopes had two myopic parents (P < 0.001). Compared with the reference group (children with no myopic parents), the odds ratios for future myopia were significant: 2.17 and 5.40 for children with one or two myopic parents, respectively.
The areas under the ROC curves (AUC) associated with univariate logistic predictive models of future myopia are presented in . Variables from our previous model22
(mean sphere, axial length, and corneal power) are included, with mean sphere having the largest AUC (0.86), with number of hours per week of sports and outdoor activities and number of myopic parents being the next closest variables (0.68 and 0.66, respectively). The remainder of the activities had AUCs between 0.50 and 0.57. Of these, only hours per week spent reading had a statistically significant AUC. The confidence intervals of all the other activities’ AUCs included 0.50, indicating a predictive value no different from chance. provides plots of the ROC curves for those variables with statistically significant AUC estimates. In the plot, parental history of myopia was represented by number of myopic parents (i.e., no, one, or two myopic parents).
AUC Associated with Predictive Models Computed Using Univariate Logistic Regression Predicting Future Myopia
ROC curves associated with sphere, axial length, corneal power, sports and outdoor hours, reading hours, and parental myopia.
To assess how well information available in the third grade could anticipate onset of myopia, multivariate logistic models were fitted. The task was to determine the predictive ability of parental history of myopia and parental report of children’s reading hours per week and hours per week of sports and outdoor activity. The predictor set was restricted to these three variables because they were the only ones that showed statistically significant differences between myopes and nonmyopes in the univariate analyses, or, in the case of reading hours per week, had an AUC significantly greater than 0.50, as summarized in and .
The multivariate logistic analysis used all three significant variables from the univariate analyses, and reading hours per week was not statistically significant (). When reading hours per week was removed from the predictor set, the number of myopic parents and hours per week of sports and outdoor activity both continued to be significantly associated with future myopia. There was no statistically significant difference between the two AUCs (AUC ± SE: model with reading = 0.73 ± 0.03, model without reading = 0.73 ± 0.03). The logistic model including only sport and outdoor activity hours per week and parental myopia was selected as the best model because it was statistically equivalent to the alternative, but was a more parsimonious model. Models including gender and the interactions of gender and parental myopia and the interaction of gender and sports and outdoor activity hours per week were also constructed. Gender was not statistically significant in any of these models (data not shown).
Logistic Model Showing Results of Inclusion of All Significant Variables from the AUC Models Adjusted for Other Variables
The correlation between sports and outdoor activity hours per week and reading hours per week was not significant (r = 0.01, P = 0.80), indicating that sports and outdoor activity hours per week were not simply reducing the effect of reading hours per week due to correlation between the two variables. To explore further the effects of parental history of myopia and activity levels on future myopia and to assess a potential effect modification between sports and outdoor activities and reading, we performed a sequence of nine logistic regressions using the following predictors: the number of reading hours per week, the number of sports and outdoor activity hours per week, the number of myopic parents, and the pair-wise interactions among these three factors. Hours of reading per week was not significant in any models tested, nor were there any statistically significant interactions with reading hours per week and parental myopia history or reading hours per week and sports and outdoor activity hours; however, sports and outdoor activity hours per week, parental myopia history, and their interaction were statistically significant effects in all models tested.
The interaction between sports and outdoor activity hours per week and number of myopic parents was explored through trends in the observed data. For each level of parental history of myopia, presents the observed chance of becoming myopic as a function of sports and outdoor activity hours per week. For these estimates, subjects were grouped according to their level of sports and outdoor activity hours per week using the variable’s quartiles. For the middle 50% of the sports and outdoor activity range, the graph shows that the chance of future myopia in subjects with one myopic parent is between that associated with no and two myopic parents. At the lowest quartile, those children with one myopic parent appeared to have a chance of becoming myopic similar to the children with no myopic parents, with the observed chance of myopia being highest among children with two myopic parents and a low level of sports and outdoor activities. At the highest quartile, those children with two myopic parents appeared to have a chance of becoming myopic similar to those children with one myopic parent, whereas those with no myopic parents and high sports and outdoor activity levels had a very low observed chance of myopia. Which parent (mother or father) was myopic had no effect (data not shown). The average number of hours per week of sports and outdoor activity was also compared to the hours per week of reading stratified at the median hour of reading. The same effect was seen within both strata, with the odds associated with a 1-unit increase in hours per week of sports and outdoor activity, yielding an odds ratio of 0.90 in each level.
Probability of myopia by quartile of sports and outdoor activity hours per week and the number of myopic parents.
The width of the confidence interval for each estimate of the probability of myopia is shown in . shows the distribution of subjects in the sports and outdoor activity quartiles as a function of the number of myopic parents (χ2 test P = 0.05). Although there is variation in the proportion of subjects in each category, there are no categories with an extremely low percentage of subjects.
Width of the 95% CI associated with the probability of myopia among the levels of sports and outdoor activity stratified by number of myopic parents.
Distribution of Parental Myopia among the Quartiles of Sports and Outdoor Activity Participation
To integrate the results of the model of parental myopia and sports and outdoor activity with our previous work, we show in the ROC curve results of three different models: the sports and outdoor activity-by-parents interaction model described herein; a model containing cycloplegic sphere, axial length, and corneal power, which is the best model from our previous work; and a model combining the ocular components with the predictors of the sports and outdoor activity-by-parents interaction. (The results of the multiple comparison of the best [MCB] analysis [difference, lower and upper bounds] are also presented in ). In terms of predictive ability, the ocular components model is a better model than the model of sports and outdoor activity hours, parental myopia, and the interaction; however, the ocular components model was significantly improved by adding sports and outdoor activity hours per week, parental myopia, and the interaction between the two (lower bound = 0, indicating this is the preferred model). provides the ROC curve model that predicts future myopia as a function of cycloplegic sphere, axial length, corneal power, sports and outdoor activity hours per week, parental history of myopia, and the interaction of these two variables.
FIGURE 5 ROC curve for a model using sphere, axial length, corneal power, number of myopic parents, sports and outdoor activity hours, and interaction of myopic parent number and sports and outdoor activity hours compared with a model including only sphere, axial (more ...)
To assess the robustness of our model, we revisited the analysis using all subjects with a third-grade visit. We used a discrete time hazard model31
to conduct a survival analysis applying the models as presented in . The results from the survival analysis were consistent with the logistic regression models (data not shown). Because the logistic model is consistent with the optimal model from our original predictors paper, we present only the results of the logistic model.