TONG, LOUIS MBBS, FRCS; SAW, SEANG-MEI MBBS, PhD; CARKEET, ANDREW PhD; CHAN, WAI-YING BSc(Hons) Optom, GDComp Sci, FIACLE; WU, HUI-MIN MD, MSc; TAN, and DONALD MBBS, FRCS, FRCOphth, FAMS
Astigmatism as a refractive error has been investigated in many previous population studies. 1–7 Astigmatism is an important clinical and public health problem for a number reasons. First, uncorrected high astigmatism provides a challenge because of the high frequency of anisometropia and patients’ rejection of eyewear. 1 Second, unlike other refractive error states, a child with uncorrected astigmatism experiences blur on a continuous basis. 8 A myopic child has a clear retinal image when looking at a near environment, and a hyperopic child can achieve a clear retinal image through accommodation. 8 It is believed that an astigmatic child is therefore at increased risk for the development of refractive amblyopia. 9,10 Third, some researchers have suggested that optical blur imposed by astigmatism may predispose to myopia development. 11 One study 11 found an association of oblique astigmatism with higher degrees of myopia, although another study 12 showed with-the-rule astigmats having a slower myopic progression rate than subjects having no astigmatism or against-the-rule astigmatism. As far as we know, the relationship between myopia and astigmatism has not been evaluated definitively in Chinese children. If astigmatism has an effect on myopia development, then its prevalence rate is obviously important because a consequential high prevalence of myopia is not only an economic burden, 13,14 but high myopia may also lead to sight-threatening retinal complications. 14
Several epidemiological studies (Table 1) have documented the prevalence of astigmatism 2,3,4,7,13,15–20,22–27. However, a detailed risk factor evaluation for childhood astigmatism has not been done. Apart from the report on the association of astigmatism with Native American ancestry in Oklahoma 27–29 and a higher prevalence of astigmatism in Bangladeshi children relative to white children, 30 no other risk factors have been identified.
Previous reports have not been able to elicit the associated risk factors of astigmatism because of a small sample size or the confounding effect of myopia. Myopia and astigmatism often coexist, 13,31 and the effect of nearwork on myopia has been well described. 13,14,32,33 Because of the coexistence of these refractive conditions, a large sample size is required to study the possible association of physical, socioeconomic, and behavioral factors of astigmatism itself. Smaller studies have produced apparently contradictory findings, for example, the extremely high prevalence rate of astigmatism in special groups such as Chinese medical students 20 and a much lower prevalence rate of astigmatism up to 17 years of age in other Chinese students. 34 Without understanding of the associated risk factors of astigmatism, it would be difficult to account for these findings.
Some previous studies have highlighted the interest in the axis of astigmatism. In Hong Kong Chinese children, the type of astigmatism found was predominantly with-the-rule. 34 In contrast, against-the-rule astigmatism was relatively more common in American military personnel 21 and in American myopes. 31,35 The prevalence rates of each subtype of astigmatism in myopic Chinese children have not been reported. In addition, these studies have not used the vectorial analysis of astigmatism, and there are disadvantages attached to the use of mutually exclusive categories of cylinder axes. 36
Previous epidemiological studies had not reported the prevalence rates of the subtypes of astigmatism with similar or dissimilar axes in the right and left eyes. One study 7 reported that as a group, the right eyes had a greater prevalence rate of axes >90° and the left eyes had a higher prevalence rate of axes <90°. This suggests, but does not prove, that dissimilar axes in oblique astigmatism may be common. In another report, 5 the correlation between the magnitude of the total refractive astigmatic vector i2 between the right eyes and the left eyes was statistically significant (p < 0.05) with a negative correlation coefficient. This also suggests that astigmatism with dissimilar axes between the right and left eyes is not uncommon. To our knowledge, the symmetry of astigmatism axes has not been described in a predominantly Chinese population.
As the first step to understand the etiology and epidemiology of astigmatism, we report the prevalence rate of astigmatism, the lateral symmetry of astigmatism axes, as well as the associated risk factors of astigmatism in Singapore school children.
The initial cross-sectional results of an ongoing longitudinal observational study that commenced in 1999, Singapore Cohort Study of the Risk Factors of Myopia (SCORM) 37, is reported here. All school children in grades I to II in a school in eastern Singapore and grades I to III in another school in northern Singapore were recruited for this study. Cases with established eye pathology or amblyopia detected before the commencement of the study or known allergy to eyedrops were excluded. The participation rate was 62%.
A total of 1028 school children (49.6% male) with a mean (±SD) age of 7.4 ± 0.5 years were recruited. The ethnic composition of this study population was composed of 70.2% Chinese, 18.9% Malay, and 5.3% Indian children. A total of 52.0% of the children were 7 years old, 31.8% of the children were 8 years old, and 16.1% of the children were 9 years old.
This study was approved by the ethics committee of the Singapore Eye Research Institute, and all procedures adhered to the Declaration of Helsinki. Informed written consent was obtained from the parents after the study was explained to them.
A questionnaire on family history, socioeconomic factors, reading, and close-work habits was administered to the parents of all children in this study. The details of this questionnaire have been reported elsewhere. 37
After instillation of 0.5% proparacaine, cycloplegia was accomplished with three drops of topical 1% cyclopentolate in each eye, each drop at 5-min intervals. Cycloplegic measurements were performed 30 min after the last drop instillation. Autorefraction was performed using one of two Canon RK-5 autorefractors (Canon, Tochigiken, Japan). From the five refractive error readings, the magnitude of the mean refractive cylinder was ascertained by calculation using a previously reported power vector method involving Fourier transformation. 38 Cycloplegic autorefraction had been shown to be the most repeatable measurement in the context of a longitudinal study. 39
For practical reasons, we were unable to perform a definitive laboratory measurement of the AC/A ratio on the large sample size, thus a simple, quick, and relatively easy on-site screening method was used to increase the compliance of the subjects. The accommodative convergence to accommodation (AC/A) ratio was measured as described in a separate report. 40
Briefly, when the child was wearing the habitual distance correction, the Maddox Wing was placed in front of the distance correction. The child was then asked to look at the white arrow, and the position of the arrow was recorded (ΔN) after 5 to 10 s. The highest and lowest reading was recorded, and the mean was taken in cases where a range of movement of the arrow was noticed. The measurement was repeated with a +1.0 D lens in front of both eyes (Δ+1) and then with a −1.0 D lens in front of both eyes (Δ-1). The ratio was then calculated as (Δ+1 − ΔN) + (Δ−1 − ΔN) divided by +1 − (−1) D or 2 D. This ratio was classified as normal, high (>5 Δ/D), or low (<3 Δ/D).
Data Analysis and Definitions
The Pearson’s correlation coefficient of the power of the right and left eye cylinder was high (r = 0.819). Because the results from the right and left eyes were similar, only the right eye’s results were presented.
Definition of Astigmatism.
Astigmatism was defined as a cylinder magnitude of worse than or equal to 0.5, 0.75, and 1 D. The prevalence rates and 95% confidence intervals were reported. The prevalence rates of astigmatism in myopia, emmetropia, and hyperopia were also reported. This was followed by the prevalence rates of the astigmatism in terms of symmetry of axes in the right and left eyes. For obvious reasons, both eyes’ data were used in the analysis on the symmetry of the axes of astigmatism between the two eyes.
For risk factor analysis, astigmatism was defined as a cylinder of at least 1 D in magnitude. This definition has been adopted by some researchers. 2,18,22,23 For the purpose of studying associations of astigmatism, we feel it is logical to use this stricter definition of astigmatism, i.e., studying the more “severe” astigmats. In addition, one study 41 involving Chinese preschool children, albeit in a different setting, stated that the criterion for astigmatism should be set higher than 0.75 D (i.e., ≥1.0 D).
Definition of Myopia.
Myopia in this study was defined as a spherical equivalent (sphere + 0.5 × cylinder) of at least −0.5 D. Although there is also no universally agreed definition of myopia, this definition has been used in previous studies. 7,42
Definition of Severity of Astigmatism.
For severity of astigmatism, we used a vectorial method that we have described in detail in a separate report. 36 In this section, each eye does not belong exclusively to one type of astigmatism but comprises two coexisting astigmatism components. The components of astigmatism labeled as J0 (Cartesian astigmatism) and J45 (oblique astigmatism) were studied separately as continuous dependent variables.
With-the-rule astigmatism is defined by a positive J0, and against-the-rule astigmatism is defined by a negative J0. An “A” type of astigmatism refers to a negative J45 in the right eye and a positive J45 in the left eye. A “V” type of astigmatism refers to a positive J45 in the right eye and a negative J45 in the left eye.
Risk Factor and Association Analysis
The study of epidemiological risk factors was divided into: 1. The risk factors for the presence of any astigmatism (as defined above), and: 2. The risk factors for the severity or magnitude of astigmatism (vectorial analysis).
We performed multiple regression analyses using three groups of independent variables. The first group was designated as the socioeconomic factors, which comprised five variables: gender, ethnic group, type of housing, total family income, and father’s education level. The second group, which we called the physical or psychophysical factors, were age (in years), height (in centimeters), weight (in kilograms), and AC/A status (0 = normal, 1 = high). The third group, which we called behavioral or nearwork factors, comprised eight independent variables: the number of books read at the age of four, the age when reading commenced, the number of books read per week, the number of hours spent watching television a day, the number of hours playing video games (other than on the computer) per day, the number of hours spent on the computer a day, the number of hours of tuition outside school hours per week, and the family history of myopia (0 = absent, 1 = present). Tuition refers to supervised academic activity performed at reading distance.
Univariate analysis was performed using χ2 tests to identify any possible socioeconomic or behavior associations. Multiple logistic regression was then performed to examine the effect of various factors on the dependent variable (the presence or absence of astigmatism). For continuous dependent variables, e.g., J0 or J45, multiple regression was performed. In all the analyses, the level of statistical significance was set at p = 0.05.
Prevalence Rates of Astigmatism.
Fig. 1 shows the distribution of the cylinder of the eyes. This is heavily skewed because there is a preponderance of cases with a less minus cylinder magnitude. The median J0 and J45 were 0.20 D (range, −0.82 to +2.73) and 0.003 D (range, −0.70 to +1.26), respectively.
In the present study, myopia (defined as a spherical equivalent of −0.5 D) is a much more prevalent condition (32%; 95% confidence interval [CI], 29 to 35) than astigmatism. As shown in Table 2, the prevalence of astigmatism (worse than or equal to −1 D cylinder) was 19% (95% CI, 17 to 22).
Prevalence Rates of Astigmatism in Various Spherical Refractive Error Categories.
The presence of myopia (defined above) was significantly associated with astigmatism (p < 0.001). The mean (±SD) spherical equivalent of the astigmats was −1.03 ± 2.09 D, whereas that of nonastigmats was −0.16 ± 1.42 D. The difference was statistically significant (p < 0.001).
Table 4 shows the subtypes of astigmatic eyes in terms of the spherical equivalent. Most cases of astigmatism were myopic as well. There was a significant association between increasing age and reduced prevalence of astigmatism for only the emmetropic astigmats (p = 0.001). In addition, there were significantly more male than female myopic astigmats (p = 0.014).
Other Prevalence Rates.
A total of 85.2% (95% CI, 82.9 to 87.4) of children had with-the-rule astigmatism, whereas 14.7% (95% CI, 12.6 to 17.1) had against-the-rule astigmatism; 40.2% (95% CI, 37.2 to 43.2) had A-pattern symmetry, whereas 19.5% (95% CI, 17.1 to 22.1) had V-pattern symmetry; and 25.3% (95% CI 22.7 to 28.1) of the children had negative J45 in each eye, whereas only 9.94% (95% CI, 8.2 to 12.0) of the children had positive J45 in each eye.
Greater severity of with-the-rule astigmatism(J0) was associated with more severe myopia (more negative spherical equivalent). Although this is statistically significant (p < 0.01), there is a lot of scatter in this correlation (r = −0.194). Oblique astigmatism (magnitude of J45) was not correlated (r = −0.001, p = 0.98) to the severity of myopia (spherical equivalent).
Risk Factors for Presence of Any Astigmatism.
The prevalence of astigmatism (Table 1) was not different between genders, ethnic groups, or age (p > 0.05). Table 3 shows that housing, income, and father’s education level were not significantly related to astigmatic status (p > 0.05).
In terms of close-work activities, none of the factors were associated with astigmatism after accounting for myopia (p > 0.05). The mean number of books read per week was 2.7 ± 4.1 for children with astigmatism and 2.7 ± 2.3 for children without astigmatism. This was not significantly different (p = 0.20).
The presence of a high AC/A ratio was significantly (p < 0.001) associated with astigmatism. This analysis was repeated by selecting nonmyopic cases or cases with spherical equivalent above −0.5 D. There was again a statistically significant (p = 0.003) association between high AC/A ratio and astigmatism.
Analyzing the nonmyopic children (N = 692) using a linear regression model with the presence of astigmatism as the response variable, only the AC/A ratio remained in the model affecting the presence of astigmatism (p = 0.049). The type of astigmatism (emmetropic vs. hypermetropic) was not associated with AC/A ratio status (either high or not) using Fisher’s exact probability test (p = 0.14).
Risk Factors for the Severity of Cartesian and Oblique Astigmatism.
There was no difference in the J0 between genders, ages, and ethnic groups. There was no difference in the J45 between ethnic group and ages. However, there was a greater oblique astigmatism component in boys compared with girls (p = 0.0035). The actual magnitude of the difference was small, with a mean difference of J45 being 0.028 D (95% CI, 0.007 to 0.049). Socioeconomic factors were not significantly (p > 0.05) associated with the severity of J0 or J45.
For the J0 component, none of the four physical factors contributed significantly. However, for the J45 or oblique astigmatism, the AC/A status was the only significant independent variable (p = 0.045).
The following factors in the regression models related to nearwork or behavior. For the J0 component, the only independent variable (of the eight evaluated) that was statistically significant was the number of hours spent playing video games per day (p = 0.029). The positive coefficient of this term in the model showed that playing television video games for longer hours a day was associated with more severe with-the-rule astigmatism. When the absolute value of J0 was used in the analysis (studying the severity of any Cartesian astigmatism), this relationship was no longer statistically significant.
For the J45 component, three of the independent variables were statistically significant: number of hours spent playing video games a day (p = 0.026), number of hours on the computer per day (p = 0.045), and family history of myopia (p = 0.010). When the analysis was repeated with the absolute value of J45 (ignoring the direction of the oblique astigmatism), only the number of hours on the computer (p = 0.029) was significant. The positive coefficient indicated that longer use of the computer was associated with a greater severity of oblique astigmatism.
Astigmatism in Singapore school children appears less prevalent (Table 1) than in Singapore adults and Singapore teenagers (military personnel and medical students). The prevalence rates of astigmatism differ for children of other ethnic groups (Americans, Native Americans, and Swedish children), but are more prevalent than Asian Indian school children (Table 1). However, comparison of results between studies should be interpreted with caution because the definitions of astigmatism vary, methodologies differ, and the ages of the populations are not similar. A previous report showed an association of astigmatism with Native American ancestry in Oklahoma. 27 In another study (N = 71), Bangladeshi school entrants were found to have a greater incidence of astigmatism than their white counterparts. 30 In our study, we did not detect a difference in the prevalence rate of astigmatism between ethnic groups (Table 2).
We have also found that the prevalence rate of astigmatism is lower than that of myopia. This study supports previous studies 11,43–52 that have found an association between astigmatism and myopia. Our study finds a lack of association of any socioeconomic factors with astigmatism. Although astigmatism on the whole appears not to be associated with nearwork, it is intriguing that the severity of astigmatism using vectorial analysis (both J0 and J45) was associated with the number of hours spent playing video games. In addition, the oblique component of astigmatism (J45) was also associated with computer use. However, we cannot explain the exact mechanism of action.
We found that with-the-rule astigmatism is more common than against-the-rule astigmatism. More children had the A type of astigmatism than the V type of astigmatism. More children had negative J45 in each eye than positive J45 in each eye. The total number from the later two groups did not add up to the number of children with the A type of astigmatism. This seems to agree with previous studies using vector-based analysis. 5,7
This study also did not show any predisposition to a higher severity of myopia in cases with oblique astigmatism, unlike an earlier report. 11 The subjects of this previous study 11 were all myopic, which may explain the different result from the present study.
In a previous study by Grosvenor et al., 12 with-the-rule astigmatism was found to be associated with myopia progression compared with patients with no astigmatism. However, a further report 31 that also reanalyzed Grosvenor’s study showed no difference in the rate of myopia progression between subtypes of astigmatism. In our cross-sectional study, it is interesting that with-the-rule astigmatism was associated with the presence of myopia and more severe myopia compared with nonastigmats. With the availability of longitudinal data from further follow-up in our study, we should be able to better assess this association.
Our study reveals that a high AC/A ratio is associated with the presence of astigmatism in Singapore children. In addition, the oblique component of astigmatism (J45) was associated with a high AC/A ratio but not the Cartesian component (with or against-the-rule). This association cannot be easily explained and, as far as we are aware, has not been reported previously. It is interesting to note that a family history of myopia was associated with oblique (J45) and not Cartesian astigmatism (J0). It is tempting to suggest that a genetic factor may increase the predisposition to oblique astigmatism and an abnormal AC/A ratio.
The strength of the present study is its size and the inclusion of a thorough, carefully designed questionnaire and standardized refraction. Another strength of the study is the use of cycloplegia. Cycloplegic autorefraction has been shown to be more repeatable than noncycloplegic autorefraction or cycloplegic retinoscopy. 39 A limitation of this study is that it is not a randomly drawn sample from the population, and, hence, the subjects may not be representative of the population. Stimulus AC/A ratio is measured rather than response AC/A ratio. In addition, we did not use the distance heterophoria method of evaluation. We think this is justified in the presence of logistic constrains because we prefer to use a clinical measurement rather than one that is restricted to specialized research settings. Using our definitions, there is a possibility of some mixed astigmats being considered as myopes and not others. The refractive changes in mixed astigmats do not resemble the myopic astigmats. 53 In our study, only 25 children have mixed astigmatism and have also been classified as myopes using our definition.
High response AC/A ratio is known to be associated with myopia and may be predictive of myopia development. 40,54–57 Astigmats may be more likely to develop myopia than the nonastigmats. 11 It may be that the association between astigmatism and AC/A ratio may be spurious. The link between these factors may be the “potential to develop myopia” because both astigmatism and high AC/A ratio could predispose to myopia development. This can be addressed further when longitudinal results are available in our study, when we study the incident cases of myopia in those with astigmatism and different baseline AC/A ratios. In future reports, we will address the incidence of astigmatism and the risk factors of incident cases of astigmatism in the cohort study.
In summary, the prevalence rate of astigmatism (>1 D cylinder magnitude) is 19.2% (95% CI, 16.8 to 21.6). Astigmatism in this study population is associated with a high AC/A ratio. In emmetropic astigmats, the prevalence of astigmatism is reduced with age. The axis of astigmatism is primarily with-the-rule.
Supported by Singapore Eye Research Grant SERI/MG/97-04/0005.
1. Garber JM. High corneal astigmatism in Navajo school children and its effect on classroom performance. J Am Optom Assoc 1981; 52: 583–6.
2. Dandona R, Dandona L, Naduvilath TJ, Srinivas M, McCarty CA, Rao GN. Refractive errors in an urban population in Southern India: the Andhra Pradesh Eye Disease Study. Invest Ophthalmol Vis Sci 1999; 40: 2810–8.
3. Pensyl CD, Harrison RA, Simpson P, Waterbor JW. Distribution of astigmatism among Sioux Indians in South Dakota. J Am Optom Assoc 1997; 68: 425–31.
4. Dobson V, Miller JM, Harvey EM. Corneal and refractive astigmatism in a sample of 3- to 5-year-old children with a high prevalence of astigmatism. Optom Vis Sci 1999; 76: 855–60.
5. McKendrick AM, Brennan NA. Distribution of astigmatism in the adult population. J Opt Soc Am (A) 1996; 13: 206–14.
6. Keller PR, Collins MJ, Carney LG, Davis BA, van Saarloos PP. The relation between corneal and total astigmatism. Optom Vis Sci 1996; 73: 86–91.
7. Attebo K, Ivers RQ, Mitchell P. Refractive errors in an older population: the Blue Mountains Eye Study. Ophthalmology 1999; 106: 1066–72.
8. Miller JM, Harvey EM, Dobson V. Visual acuity screening versus noncycloplegic autorefraction screening for astigmatism in Native American preschool children. J AAPOS 1999; 3: 160–5.
9. Sjostrand J, Abrahamsson M. Risk factors in amblyopia. Eye 1990; 4: 787–93.
10. Abrahamsson M, Fabian G, Sjostrand J. A longitudinal study of a population based sample of astigmatic children. II: the changeability of anisometropia. Acta Ophthalmol (Copenh) 1990; 68: 435–40.
11. Fulton AB, Hansen RM, Petersen RA. The relation of myopia and astigmatism in developing eyes. Ophthalmology 1982; 89: 298–302.
12. Grosvenor T, Perrigin DM, Perrigin J, Maslovitz B. Houston Myopia Control Study: a randomized clinical trial. Part II: final report by the patient care team. Am J Optom Physiol Opt 1987; 64: 482–98.
13. Wong TY, Foster PJ, Hee J, Ng TP, Tielsch JM, Chew SJ, Johnson GJ, Seah SK. Prevalence and risk factors for refractive errors in adult Chinese in Singapore. Invest Ophthalmol Vis Sci 2000; 41: 2486–94.
14. Saw SM, Katz J, Schein OD, Chew SJ, Chan TK. Epidemiology of myopia. Epidemiol Rev 1996; 18: 175–87.
15. Wu HM, Seet B, Yap EP, Saw SM, Lim TH, Chia KS. Does education explain ethnic differences in myopia prevalence? A population-based study of young adult males in Singapore. Optom Vis Sci 2001; 78: 234–9.
16. Villarreal MG, Ohlsson J, Abrahamsson M, Sjostrom A, Sjostrand J. Myopisation: the refractive tendency in teenagers: prevalence of myopia among young teenagers in Sweden. Acta Ophthalmol Scand 2000; 78: 177–81.
17. Voo I, Lee DA, Oelrich FO. Prevalences of ocular conditions among Hispanic, white, Asian, and black immigrant students examined by the UCLA Mobile Eye Clinic. J Am Optom Assoc 1998; 69: 255–61.
18. Kalikivayi V, Naduvilath TJ, Bansal AK, Dandona L. Visual impairment in school children in southern India. Indian J Ophthalmol 1997; 45: 129–34.
19. Katz J, Tielsch JM, Sommer A. Prevalence and risk factors for refractive errors in an adult inner city population. Invest Ophthalmol Vis Sci 1997; 38: 334–40.
20. Chow YC, Dhillon B, Chew PT, Chew SJ. Refractive errors in Singapore medical students. Singapore Med J 1990; 31: 472–3.
21. Satterfield DS. Prevalence and variation of astigmatism in a military population. J Am Optom Assoc 1989; 60: 14–8.
22. Dobson V, Fulton AB, Sebris SL. Cycloplegic refractions of infants and young children: the axis of astigmatism. Invest Ophthalmol Vis Sci 1984; 25: 83–7.
23. Gwiazda J, Scheiman M, Mohindra I, Held R. Astigmatism in children: changes in axis and amount from birth to six years. Invest Ophthalmol Vis Sci 1984; 25: 88–92.
24. Bear JC, Richler A. Cylindrical refractive error: a population study in western Newfoundland. Am J Optom Physiol Opt 1983; 60: 39–45.
25. Choi TB, Lee DA, Oelrich FO, Amponash D, Bateman JB, Christensen RE. A retrospective study of eye disease among first grade children in Los Angeles. J Am Optom Assoc 1995; 66: 484–8.
26. Zadnik K, Mutti DO, Friedman NE, Adams AJ. Initial cross-sectional results from the Orinda Longitudinal Study of Myopia. Optom Vis Sci 1993; 70: 750–8.
27. Goss DA. Meridional analysis of with-the-rule astigmatism in Oklahoma Indians. Optom Vis Sci 1989; 66: 281–7.
28. Wick B, Crane S. A vision profile of American Indian children. Am J Optom Physiol Opt 1976; 53: 34–40.
29. Hamilton JE. Vision anomalies of Indian school children: the Lame Deer study. J Am Optom Assoc 1976; 47: 479–87.
30. Fuller JR, Baxter LA, Harun S, Levy IS. Astigmatism in Bangladeshi and white school entrants in East London: a prospective comparative study. Eye 1995; 9: 794–6.
31. Goss D, Shewey W. Rates of childhood myopia progression as a function of type of astigmatism. Clin Exp Optom 1990; 73: 159–63.
32. McBrien NA, Adams DW. A longitudinal investigation of adult-onset and adult-progression of myopia in an occupational group: refractive and biometric findings. Invest Ophthalmol Vis Sci 1997; 38: 321–33.
33. Goss DA. Nearwork and myopia. Lancet 2000; 356: 1456–7.
34. Chan OY, Edwards M. Refractive errors in Hong Kong Chinese pre-school children. Optom Vis Sci 1993; 70: 501–5.
35. Hirsch MJ. Predictability of refraction at age 14 on the basis of testing at age 6: interim report from the Ojai longitudinal study of refraction. Am J Optom Arch Am Acad Optom 1964; 41: 567–73.
36. Tong L, Carkeet A, Saw SM, Tan DT. Corneal and refractive error astigmatism in Singaporean schoolchildren: a vector-based Javal’s rule. Optom Vis Sci 2001; 78: 881–7.
37. Saw SM, Chua WH, Wu HM, Hong CY, Chan WM, Chia KS, Tan D. Design and initial results of the Singapore Myopia Cohort Study. In: Thorn F, Troilo D, Gwiazda J, eds. Myopia 2000: Proceedings of the VIII International Conference on Myopia, July 7–9, 2000, Boston, Massachusetts. Boston: Conference on Myopia 2000, 2000: 4–10.
38. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci 1997; 74: 367–75.
39. Zadnik K, Mutti DO, Adams AJ. The repeatability of measurement of the ocular components. Invest Ophthalmol Vis Sci 1992; 33: 2325–33.
40. Chan WY, Koh LH, Saw SM, Chua WH, Wu HM, Hong CY, Chia KS, Tan D. Accommodation and convergence among children in Singapore. In: Thorn F, Troilo D, Gwiazda J, eds. Myopia 2000: Proceedings of the VIII International Conference on Myopia, July 7–9, 2000, Boston, Massachusetts. Boston: Conference on Myopia 2000, 2000: 268.
41. Chan OY, Edwards M. Refraction referral criteria for Hong Kong Chinese preschool children. Ophthalmic Physiol Opt 1994; 14: 249–56.
42. Rosenfield M, Abraham-Cohen JA. Blur sensitivity in myopes. Optom Vis Sci 1999; 76: 303–7.
43. Robb RM. Refractive errors associated with hemangiomas of the eyelids and orbit in infancy. Am J Ophthalmol 1977; 83: 52–8.
44. Angell LK, Robb RM, Berson FG. Visual prognosis in patients with ruptures in Descemet’s membrane due to forceps injuries. Arch Ophthalmol 1981; 99: 2137–9.
45. Rabin J, Van Sluyters RC, Malach R. Emmetropization: a vision-dependent phenomenon. Invest Ophthalmol Vis Sci 1981; 20: 561–4.
46. Angle J, Wissmann DA. The epidemiology of myopia. Am J Epidemiol 1980; 111: 220–8.
47. Dunphy EB, Stoll MR, King SH. Myopia among American male graduate students. Am J Ophthalmol 1968; 65: 518–21.
48. Parnell R. Sight of undergraduates: loss of visual acuity. Br J Ophthalmol 1951; 35: 467–72.
49. Merriam WW, Ellis FD, Helveston EM. Congenital blepharoptosis, anisometropia, and amblyopia. Am J Ophthalmol 1980; 89: 401–7.
50. Sorsby A, Sheridan M, Leary GA. Vision, visual acuity, and ocular refraction of young men: findings in a sample of 1033 subjects. BMJ 1960; 1: 1394–8.
51. O’Leary DJ, Millodot M. Eyelid closure causes myopia in humans. Experientia 1979; 35: 1478–9.
52. Curtin B. Physiopathology and therapy of the myopias. Trans Am Acad Ophthalmol Otolaryngol 1966; 70: 331–9.
53. Goss DA. Refractive error changes in mixed astigmatism. Ophthalmic Physiol Opt 1999; 19: 438–40.
54. Gwiazda J, Grice K, Thorn F. Response AC/A ratios are elevated in myopic children. Ophthalmic Physiol Opt 1999; 19: 173–9.
55. Jiang BC. Parameters of accommodative and vergence systems and the development of late-onset myopia. Invest Ophthalmol Vis Sci 1995; 36: 1737–42.
56. Manas L. The inconstancy of the AC/A ratio. Am J Optom Arch Am Acad Optom 1955; 32: 304–15.
57. Mutti DO, Jones LA, Moeschberger ML, Zadnik K. AC/A ratio, age, and refractive error in children. Invest Ophthalmol Vis Sci 2000; 41: 2469–78.