COMPONENTS BEFORE AND AFTER THE ONSET OF MYOPIA
3.5.1 Exploratory analysis
In this analysis, children with persistent emmetropia and newly developed myopia who had at least three visits between the ages of 6 to 13 years were considered. For children with newly developed myopia, only those who had at least 1 visit before and after the onset of myopia were analysed.
The trajectories of AL before and after the onset of myopia and LOWESS smoothing curves for children with newly developed myopia were plotted to visualise the pattern of changes before the modelling process.
3.5.2 FP models
For children with persistent emmetropia, the best-fitting FP transformations for age were determined. Subsequently, the gender and ethnicity of the children were included in the models and these FP models of SE and ocular components were referred as emmetropia models.
49 For children with newly developed myopia, the year of onset was defined as year 0, the first year prior to the onset was –1, the second year prior to onset was –2, and so forth. Similarly, the first, second and third year after the onset of myopia was defined as year +1, +2, +3 and so forth. The growth curves before and after the onset of myopia for these children were modelled using FP methods.
3.5.3 Piecewise models for children with newly developed myopia
A piecewise model incorporates separate growth profiles according to various stages from which repeated measurements were made. In this model, the growth trajectory is broken up into several separate components which represent the periods before, during or after a critical event. This model is particularly interesting when one wants to compare growth rates during two or more periods of time.(Bryk &
Raudenbush, 1987)
In the development process of myopia, a child becomes myopic when their SE of refractive error was more negative than –0.5 D. Several rates are possible for growth during the myopia development and a single growth curve may not be adequate in reflecting this process. Therefore, a piecewise model was developed to compare to best-fitting FP model in modelling the changes in refraction and ocular components before and after the onset of myopia. The model with lowest deviance was selected.
In this analysis, the two stages were referred to the years before and after the onset of myopia. The GEE method was used to estimate the piecewise growth curves before and after the onset of myopia using the AL data of children with newly developed myopia. The coefficients in the piecewise models were estimated using the STATA xtgee function with normal distribution, identity link function and the
50 exchangeable working correlation structure. This analysis assumed that the AL data is linearly related to age over time, allows one to fit pre- and post-myopia onset simultaneously using all data points, and also can account for dependence between measurements collected over time.
3.5.4 Matched-emmetropia values
For the comparison of changes in refractive error and ocular components before and after the onset of myopia, each child with newly onset myopia has to be matched to at least 1 child with persistent emmetropia based on the child’s age, gender and ethnicity. However, a one-to-one or one-to-many matching was unachievable given the sample size of these children in this study. Therefore, a set of hypothetical age, gender and ethnicity-matched emmetropia data were generated for each data point of children with newly developed myopia. Firstly, the age for each child with newly developed myopia at each study visit, their gender and ethnicity were fitted to the emmetropia models of SE and each ocular component. These yielded the age, gender and ethnicity-matched values of SE and ocular components for each observation of children with newly developed myopia. These values estimated from the emmetropia models were referred to as matched-emmetropia values. These values were modelled by FP methods and the models were defined as matched-emmetropia models.
3.5.5 Instantaneous rate of change
In addition to the overall growth pattern before and after the onset of myopia, this analysis also aimed to examine the rate of growth during the study period. The instantaneous rate of change at each time point prior to and after myopia onset was determined by the slope of the tangent line at a specific time T and mean growth
51 curve evaluated at T. The slope of the tangent line indicates the change in refractive error and ocular components for a unit increase in the year from myopia onset evaluated at T . The general form of the tangent line for FP1 is β1 zX z−1 ,
1 2 1 1 1 1
2
1− + z −
z z X
X
z β
β for FP2 with 2 different powers (z1,z2) and
1 1 1
2 1 1 1 1
2 2
1− + z − ln + z −
z z X X X
X
z β β
β for the repeated-powers model.(Long &
Ryoo, 2009) The slope can be zero at exactly one point for a FP2 model which is concave or convex with respect to time and has a single minimum or maximum value.
The differences between observed data of children who had newly developed myopia and their corresponding matched-emmetropia values for SE and each ocular component were calculated and modelled using the FP models.
3.5.6 Illustration of modelling for changes
Figure 3 - 11 shows the trajectories of AL measured before and after the onset of myopia for 10 randomly selected children with newly developed myopia. The fitted LOWESS smoothing curve revealed that the mean AL increased slightly more rapidly before-myopia. Figure 3 - 12 shows the fitted curves of the piecewise and best-fitting FP (2, 3) models and the associated 95% CIs. In terms of the deviance, the FP (2, 3) was superior to the piecewise model (differences in deviance from null model: –3,031 vs. –2,782). The residuals for both models were randomly distributed but the fit of FP (2, 3) was better than the piecewise model (Figure 3 - 13)
The raw differences between observed and matched-emmetropia values of AL and their best-fitting FP line are showed in Figure 3 - 14. The children with newly developed myopia had slightly longer AL between 4 and 2 years before onset, but the differences became much larger over time (p < 0.001).
52 Figure 3 - 15 displays the fitted FP model for children with newly developed myopia and matched-emmetropia model. When compared to the matched- emmetropia, the children who have newly developed myopia had more rapid elongation from –3 years before onset. In contrast to the steady rate of change in matched-emmetropia, the rate of change curve for children with newly developed myopia had an inverted U-shape where the peak occurred on the year of onset (lower panel of Figure 3 - 15).