Correlation between Baseline Axial Length and Myopia Progression Rate in Childhood

Article information

Abstract

Materials and Methods

The study protocol adhered to the tenets of the Declaration of Helsinki and was approved by Institutional Review Board of Kim’s Eye Hospital (No. KEH 2024-10-003). The requirement for informed consent was waived due to the use of deidentified data and the retrospective nature of the study.

We retrospectively reviewed the medical records of patients aged <20 years who underwent at least two cycloplegic refraction tests and biometry measurements at an interval of ≥2 years between January 2011 and February 2024. Patients were excluded if they had previously received myopia suppression treatments (e.g., atropine or orthokeratology) or had congenital or acquired ocular conditions, such as anterior segment dysgenesis, ocular colo-bomatous diseases, congenital cataracts affecting visual acuity, aniridia, or corneal diseases (e.g., corneal opacity or keratoconus).

Baseline clinical characteristics, such as age, sex, cycloplegic refraction data, and biometry measurements from both eyes were collected. Cycloplegic refraction was performed manually by an experienced examiner 45 minutes after administering one drop of 1% cyclopentolate hydrochloride (Cyclogyl) followed by three drops of 1% tropicamide (Mydriacyl) (Alcon Lab. Inc.) at 10-minute intervals. Spherical and cylindrical errors were obtained from cycloplegic refraction data, and spherical equivalent (SE) was calculated as spherical error + 0.5 × cylindrical error.

Ocular biometry was measured using partial interferometry (IOLMaster 500, Carl Zeiss Meditec). Biometric measurements were considered reliable based on the patients’ fixation status, a signal-to-noise ratio >100, and previous biometric data, if available. Unreliable measurements were confirmed through repeated assessments. The AL and corneal radius (K radius) were measured in millimeters on the flat and steep axes.

Three measurements were used to calculate the myopia progression speed per year: AL (mm/yr), SE (diopters [D]/yr), and AL/K radius (mm/mm per year). The myopic progression rate was calculated as follows:

All statistical analyses were performed at a significance level (p-value) <0.05. The Wilcoxon signed-rank test was used to compare baseline characteristics between both eyes. The Mann-Whitney U-test was used to compare baseline parameters between eyes with low-speed and high-speed AL elongation. The cutoff value for low and high speeds was set as the median value of the AL elongation speed for all data. Spearman correlation coefficients (Spearman rho) were calculated between AL in the first exam and three speed indicators for the right and left eye. Considering the collinearity between age and AL, partial correlation coefficients were calculated between AL in the first examination and speed indicators, with the age effect removed. Multiple linear regression analysis was conducted with speed indicators as the dependent variables and age, sex, AL, and keratometry readings as independent variables for the right and left eye. To exclude multicollinearity between the independent variables, a regression analysis with AL and sex as independent variables was also conducted. In addition to the separate analysis of each eye, a comprehensive analysis of the entire dataset including both eyes was performed to enhance the robustness of our findings. To account for the potential inter-eye correlation within each subject, generalized estimating equations (GEE) with an exchangeable working correlation structure were employed. This GEE-based approach allowed for the simultaneous evaluation of all available observations while statistically adjusting for the intra-subject dependency. The models were further adjusted for baseline age and sex to evaluate the independent effect of baseline AL on myopia progression speeds.

All statistical analyses and model development were performed using Python ver. 3.12.3 (https://www.python.org/). Data preprocessing was performed using the Pandas package ver. 2.2.2 (https://pandas.pydata.org/). The Scipy library ver. 1.14.1 (https://scipy.org/) was used for statistical analysis. The Pingouin library ver. 0.5.5 (https://pingouin-stats.org/) was used for partial correlation analysis. Multiple linear regression analysis and GEE-based approach were conducted using Statsmodels Library ver. 0.14.4 (https://www.statsmodels.org/).

Results

A total of 2,916 eyes from 1,458 patients were included in the study, with 793 women (54.4%). The median age at the first visit was 6.1 years, increasing to 10.3 years at the last visit. The median follow-up period was 3.4 years.

At the first visit, the median SE was +0.50 D for the right eye and +0.38 D for the left eye, decreasing to −1.00 D for both eyes by the last visit. The median AL increased from 22.57 mm (right eye) and 22.52 mm (left eye) at the first visit to 23.78 mm (right eye) and 23.71 mm (left eye). The median corneal curvature radius (K radius) at the first visit was 7.74 mm for both eyes. At the last visit, the median K radius was 7.75 mm for both the right and left eyes.

The median AL elongation speed was 0.28 mm/yr for both the right and left eyes. The median annual SE change speed was −0.41 D/yr for the right eye and −0.39 D/yr for the left eye. The median AL/K radius increased by 0.035 per year in both the right and left eyes (Table 1).

Table 1

Baseline characteristics of subjects

The cutoff for high and low progression was set at the median axial elongation rate of 0.28 mm/yr. This threshold is consistent with previous studies on Asian children that identified annual axial growth between 0.2 and 0.3 mm as a hallmark of active myopia progression [17]. Significant differences were found in SE and AL/K radius between the two groups for both eyes (p < 0.05) (Table 2).

Table 2

Comparison of parameters in the first exam between patients with low (<0.28 mm/yr) and high (≥0.28 mm/yr) AL elongation speed

Correlations between baseline AL and myopia progression speed indicators (AL, SE, and AL/K radius) were weak for both eyes. For AL speed, the Spearman rho was 0.224 for the right eye and 0.211 for the left eye, with partial correlation coefficients of 0.297 and 0.305, respectively. For SE speed, Spearman rho was −0.373 for the right eye and −0.375 for the left eye, while the partial correlation coefficients were −0.267 and −0.278, respectively. For AL/K radius speed, the Spearman rho was 0.192 for the right eye and 0.183 for the left eye, with partial correlation coefficients of 0.259 and 0.269, respectively (Fig. 1A–1C).

Fig. 1

Correlation between the baseline AL and three myopia progression speed indicators. Correlation between the baseline AL and three myopia progression speed indicators ([A] AL rate, [B] SE rate, and [C] AL/K radius rate) in the right and left eyes. Scatter plots show Spearman rho and partial correlation coefficients after controlling for age. The dotted line depicts the linear regression. The solid line represents the median values of myopia progression speed in relation to the baseline AL. AL = axial length; D = diopters; SE = spherical equivalent; AL/K = AL/corneal radius.

The adjusted R² values for the models with annual AL speed as the dependent variable and incorporating all variables (age, sex, baseline AL, and K radius) were 0.0970 and 0.1150 for the right and left eyes, respectively, indicating that the models explained 9.7% and 11.5% of the variance in AL speed, respectively. The regression coefficients between the baseline AL and annual AL speed were 0.0397 for the right eye and 0.0413 for the left eye (p < 0.001 for both eyes). When the model was limited to AL and sex as independent variables, the adjusted R² values decreased to 0.0240 and 0.0200 for the right and left eyes, respectively, accounting only 2.4% and 2.0% of the variance, respectively (Table 3).

Table 3

Result of multiple linear regression analyses with or without age and keratometry adjustments

For SE speed, the adjusted R² values, including all variables, were 0.1260 and 0.1290 for the right and left eyes, respectively, indicating that the models explained 12.6% and 12.9% of the variance, respectively. The regression coefficients for the baseline AL were −0.0919 for the right eye and −0.0939 for the left eye (p < 0.001 for both eyes). When only AL and sex were included as independent variables, the adjusted R² decreased to 0.1000 for the right eye and 0.1050 for the left eye, accounting for 10.0% and 10.5% of the variance, respectively.

For the AL/K radius speed, with all variables included, the adjusted R² values were 0.0780 and 0.0940 for the right and left eyes, respectively, explaining 7.8% and 9.4% of the variance, respectively. The regression coefficient for baseline AL was 0.0050 (p < 0.001) in both eyes. When only AL and sex were included as independent variables, the adjusted R² decreased to 0.0150 for the right eye and 0.0130 for the left eye, explaining only 1.5% and 1.3% of the variance, respectively.

To evaluate the independent effect of baseline AL while accounting for the inter-eye correlation of both eyes within each subject, a multivariate GEE analysis was performed adjusting for age and sex. Although baseline AL was a statistically significant predictor for all progression parameters (all p < 0.001), its clinical impact was minimal, as indicated by the very small regression coefficients: 0.0138 mm/yr for AL speed, −0.0360 D/yr for SE speed, and 0.0023 mm/mm per year for AL/K radius speed. While baseline age and female sex also showed significant associations with progression (p < 0.01), the overall results suggest that baseline AL alone has limited practical utility as a standalone clinical predictor for future myopia progression (Table 4 and Fig. 2A–2C).

Table 4

Multivariate generalized estimating equations analysis for the association between baseline AL and myopia progression parameters, including data from both eyes

Fig. 2

Scatter plots illustrating the relationship between baseline AL and myopia progression parameters ([A] AL rate, [B] SE rate, and [C] AL/K radius rate). The dotted lines represent the linear regression slopes derived from the generalized estimating equations models. AL = axial length; SE = spherical equivalent; D = diopters; AL/K = AL/corneal radius.

To further investigate the age-dependent relationship between baseline AL and myopia progression, an age-stratified analysis was performed (Supplementary Table 1). In all age groups (≤6, 6–10, and >10 years), baseline AL showed a statistically significant correlation with SE speed, AL speed, and AL/K radius speed (all p < 0.05). However, the strength of these associations was consistently weak to moderate, with Spearman rho ranging from 0.145 to 0.314. Even after adjusting for baseline age within each stratum using partial correlation, the correlation coefficients remained low (partial rho range, 0.207–0.357). Notably, the correlation tended to be even weaker in the oldest age group (>10 years) compared to the younger cohorts. These stratified results confirm that the limited predictive value of baseline AL is a consistent finding across different pediatric age ranges (Supplementary Table 1).

Discussion

This study found a weak linear correlation between baseline AL and the speed of myopia progression in children. Even after controlling for age, baseline AL alone did not strongly predict rapid progression of myopia. These findings suggest that while baseline AL is relevant, it may not be sufficient as a sole predictor for identifying children at risk of accelerated myopia progression.

AL percentile-based tools, which have been widely used in clinical practice, often emphasize baseline AL as a key determinant of progression of myopia. For example, Tideman et al. [7] demonstrated that higher baseline AL percentiles are associated with faster refractive changes and progression of myopia over time. These tools provide clinicians with a practical means of risk stratification and have been instrumental in guiding early intervention strategies.

However, AL exhibited a rapid increase at younger ages (baseline age, 6–8 years; mean, 7.41 years), followed by a gradual deceleration and eventual stabilization (13–16 years of age). In addition, older children (baseline age of over 8 years; mean, 10.06 years), an initial rapid AL elongation was observed, followed by a gradual decline. This pattern suggests that rapid AL elongation was pronounced even in the relatively older stage of childhood, followed by a deceleration of AL elongation. While age is also an important factor for AL elongation, longer AL appears to be associated with a higher likelihood of stabilization [11]. Another cohort study found that baseline AL showed weak explanatory power in survival analysis for predicting future myopia, whereas baseline refractive error was a stronger predictor [12].

Our findings, along with those of other studies, challenge the reliability of baseline AL as a predictor of disease progression without considering additional factors. For instance, Chen et al. [18] found that children with nonprogressive myopia had a longer baseline AL than children with progressive myopia, indicating that a longer baseline AL does not necessarily predict faster progression of myopia. Similarly, Jiang et al. [14] reported no consistent relationship between the baseline AL and the speed of AL or SE changes in children and adolescents with high myopia. These results are consistent with our findings and emphasize the limitations of using baseline AL levels alone to predict disease progression.

Our analysis further supports these findings by demonstrating a nonproportional relationship between the baseline AL and the speed of myopia progression. Scatterplots revealed that the progression rates did not increase uniformly as the baseline AL increased. Specifically, progression speed appeared to decrease at higher AL values, considering that progression might even be slow in cases of high myopia. In a previous study, no difference in baseline AL was observed between the groups with rapid myopia progression and those without in high myopia, and the rate of myopia progression appeared to be modest in cases of high myopia [9]. This dampening effect at higher AL values has important clinical implications. This indicates that children with a longer baseline AL may not always be at the highest risk of rapid myopic progression, challenging the common assumption that a greater AL correlates with faster progression. Furthermore, the results highlight the necessity of integrating additional factors such as age, environmental influences, and dynamic growth patterns into predictive models for myopia management.

This study had some limitations. First, its retrospective design introduced inherent biases that limited the control over confounding variables. Second, while age was statistically controlled, other influential factors, including parental myopia, near work, and outdoor activity, were not considered, which may have affected the results. Third, because we relied on retrospective data, we could not establish causality. Prospective longitudinal studies are needed to confirm these findings and improve predictive models for myopia progression. These limitations underscore the need for cautious interpretation of the results and further investigation of the role of baseline AL in predicting the progression of myopia.

In conclusion, our study highlights the limitations of relying solely on baseline AL as a predictor of myopia progression. While percentile-based curves provide useful benchmarks, it can be inferred from our results that their standalone predictive utility should be interpreted with caution, given the multifactorial nature of myopia progression. Long-term prospective studies are essential to refine the predictive models by integrating AL growth measures and additional contributing factors, ultimately improving clinical decision-making in myopia management.

Supplementary Materials

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