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1From the Department of Statistics and Actuarial Sciences and the 2School of Optometry, University of Waterloo, Waterloo, Ontario, Canada.
| Abstract |
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METHODS. Noncycloplegic autorefractive measures were taken in 1179 children attending a preschool health fair operated by their county board of health. Spherocylinder measures were transformed into three independent components.
RESULTS. The equivalent sphere showed considerable variation between retinoscopy and autorefraction that was attributed to the variable overaccommodation induced by the autorefractor. Astigmatic components were not affected. Small discrepancies between the two techniques were similar to those in adults and were not of sufficient magnitude to affect validity. With-the-rule (WTR) astigmatism of at least 0.25 D was the most frequent form (45%) followed by against-the-rule (ATR; 40%) and oblique (15%). The 95th percentile for cylinder magnitude was found at 1.25 D. Astigmatisms beyond this value were predominately WTR. The mean (negative) cylinder magnitude was 0.08 Dx 015°.
CONCLUSIONS. When spherocylinder values are transformed into a mathematical continuum rather than WTR and ATR classifications, the true central tendency of the population is better defined and is close to zero. Astigmatisms of more than 1.25 D in the preschool child exceed the 95th percentile in this population and were more frequently WTR.
Knowledge as to what size of refractive error should be treated in a preschool child is not clear cut. One source of information was a survey of a sample of pediatric ophthalmologists in regard to the dioptric thresholds at which spectacle corrections would be prescribed for refractive errors of myopia, hyperopia, and astigmatism found in infants and children of specific age groups.16 Given that these thresholds are implicitly defining abnormally high levels of refractive error, it is important to add credence to such information by defining population norms for a given refractive error.
The development of "child-friendly" autorefractors that can be used in county-wide preschool health screenings have provided the means by which refractive measures can be determined on a county-wide population of preschool children.
Measurement of refractive errors in preschool children is bedeviled by the fact that children at this age typically have 1 to 2 D of hyperopia and readily overcome their hyperopia through accommodation, unless a cycloplegic is instilled. We have shown that the varying capacity of autorefractors to manifest refractive errors in young children appears dependent on the design of the instrument and both the viewing distance and spatial composition of the targets selected.17 Even conducting retinoscopy through "fogging lenses" does not fully manifest refractive error.17 Unfortunately, large-scale screenings do not offer the opportunity for testing with cycloplegia.
In this study, we used the Retinomax K-Plus (Nikon, Inc., Tokyo, Japan) autorefractor to provide noncycloplegic measures of refractive error. The Retinomax has been well studied in populations of adults and children.18 19 20 21 22 23 The measures in adults show good agreement where small biases on the order of 0.25 D are found between the Retinomax and conventional retinoscopy for both the equivalent sphere and cylinder values. The small Retinomax bias is toward hyperopia.23 Measurements in preschool children and younger have been performed with and without cycloplegia. It appears that the close working distance of the Retinomax (5 cm) induces considerable but variable "instrument myopia" in these children, in whom, without cycloplegia, the equivalent sphere measures are consistently inaccurate and hyperopia is underestimated. However, cylinder measures are not affected by this overaccommodation.23 24 Any differences in cylinder components were not thought to be clinically important.18 In a screening situation the Retinomax has had a 99.5% success rate in detecting refractive astigmatism8 and there is little bias.
When cycloplegia is used with preschool children, accuracy in equivalent sphere is restored to adult levels. Both cylinder and axis measures show good agreement with those of retinoscopy.20 21 23
Although it can be concluded that preschool children exhibit less astigmatism than they exhibited at birth, the exact central tendency of the preschool populations astigmatism has been difficult to define. The standard spherocylinder format (sphere/cylinder/axis) does not allow the central tendency of a population to be defined. Only the magnitude of astigmatism (cylinder) can be averaged, while the orientation (axis, varying over 180°) must be ignored. Values of orthogonally oriented astigmatisms (e.g., with [WTR] and against [ATR] the rule) do not cancel but rather add, thus rendering an absolute cylinder value. If a true measure of central tendency is to be defined, then a mathematical continuum must be defined for astigmatisms of all orientations. Recent mathematical treatments25 26 have transposed the spherocylinder values into more mathematically workable formats. In particular, a format has been designed that decomposes different forms of astigmatism (ATR, WTR, and oblique) into continuums in which astigmatisms at orthogonal orientations are given opposite signs.26 In this way, a central tendency of the astigmatism of the population can be defined. This can serve as a metric of the extent to which astigmatic errors have emmetropized. Furthermore, this format allows cylinder components to be isolated from the equivalent sphere, thus allowing variations in accommodation to be independent from astigmatic measures.
This research measures the astigmatism in a county-wide population of preschool children. Using the described analysis a central tendency of astigmatism was defined.
| Methods |
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In the spring of 1999, 1179 children participated in the screening. Their mean age was 48.1 months, (range, 3886 months). Boys constituted 52% of the population. Calculations by the Board of Health indicated that this population represented close to 87% of the eligible school entrants that year. To ensure that nonattendees were not overly represented by individuals lacking the means to attend the health fair, the public health board supplied free transportation to the health fair to those in need. Figure 1 provides a flow chart representation of the screening.
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Screening Tests
The vision-screening program tested visual and stereo acuities. Specifically, visual acuity was tested with a single letter-matching test (Cambridge Crowding Cards; Clement Clarke, London, UK), and stereoacuity was tested with the Stereo Fly (Titmus Optical Co, Petersburg, VA). Children who scored poorer than 6/6 visual acuity and/or poorer than 100 seconds of arc of stereoacuity were referred to an eye care practitioner, normally within Oxford County. Failure of either or both of the screening components or failure to complete any component of the screening resulted in referrals of 369 of the 1179 children screened to eye care practitioners. The practitioners reported examination findings back to the Oxford County Board of Health. A printed form was used that specifically required retinoscopic measures.
Autorefractive Measures
During the vision testing, noncycloplegic refractive error measures were taken in 1162 preschool children with the Retinomax K-Plus autorefractor (Nikon). This instrument has been described in detail elsewhere.29 Briefly, the child was seated and the instrument was aligned for the childs right eye. The child was asked to fixate on the instruments Christmas tree target, set along the optical axis of the instrument. During fixation, the instrument averaged eight readings for each eye and supplied a confidence value based on the consistency of the repeated readings. Both the right and left eyes were measured; however, only the right eye was used for analysis purposes. Measurements were repeated until the confidence readings reached the manufacturers recommendations of at least 8 of a possible 10. In 3% of the measurements, a reading of 7 had to be accepted. In all cases, the fogging option was used in lieu of the "quick mode" in an attempt to relax the childs accommodation as much as possible.
Validation of Measures
To ensure that the measures of astigmatism were valid using the Retinomax without cycloplegia we conducted two investigations. The first compared the Retinomax readings with clinical measures of refraction taken in a subset of children whose practitioner reports were available to us. Second, we conducted a study on an adult sample, because Retinomax-induced overaccommodation has not been found to be significant in adults.29
Clinical Measures of Preschoolers
A total of 155 of the practitioner reports were returned for this analysis. Of these, 154 had complete Retinomax measures. Refractive error measures were taken by retinoscopy. In 24% of the cases, cycloplegic drugs were used; however, in the majority, retinoscopy was conducted without cycloplegia. All clinical findings were reported to the Oxford County Health Unit. These refractive error measurements provided the means to validate the Retinomax autorefractor measurements.
Adult Study
Adult subjects (n = 144; mean age, 42 years; range, 1978) were recruited from the patient population attending the Eye Care Clinic of the School of Optometry, University of Waterloo. Refractive error measures were taken using the Retinomax and retinoscopy. All retinoscopic measures were reviewed from the clinical file and found to be within 0.50 D of the subjective along either refractive meridian. Further, measures were assessed for the presence of any confounding problems, such as media opacities. Again, ethics committee approval and informed consent were obtained before subject participation.
Refractive Error Analysis
Refractive error measurements were decomposed into three independent components using the following Fourier transformation26 :
![]() | (1) |
![]() | (2) |
![]() | (3) |
is the axis in radians. This transformation produces three well-understood optical components: M, the equivalent sphere (equation 1) and two Jackson cross cylinders (equations 2 and 3) . J0 represents cylinder powers set orthogonally approximately 90° and 180° meridians, representing WTR and ATR astigmatism, respectively. J45 represents a cross cylinder set at 45° and 135°, which represents oblique astigmatism.
Accommodation acts isotropically, where astigmatic changes with increased accommodation are small; specifically, they are rarely more than 0.1 to 0.2 D.30 Astigmatism was defined to be nonzero cylinder measures starting at 0.25 D.
| Results |
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As noted in the Methods section, 35 preschoolers underwent cycloplegia and 113 did not. Thus, the effects of cycloplegia on the components had to be determined. There were five preschoolers whose cycloplegic status was unknown and one who did not have a Retinomax measurement. Cycloplegia, which fully relaxes the childs accommodation, provides the most accurate measure of equivalent sphere. We find an even greater discrepancy between the retinoscopy and the Retinomax (Table 2) ; however, this discrepancy did not vary with the magnitude of equivalent sphere. Thus, the overaccommodation induced by the Retinomax is probably underestimated by the noncycloplegic findings. Because retinoscopy in young children may also introduce overaccommodation, the variation in equivalent sphere cannot be attributed solely to the Retinomax.17
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Post Hoc Cylinder Analysis
After completing our analysis and finding that many of the retinoscopy cylinders were zero, while the Retinomax showed small astigmatisms close to zero, we performed a post hoc analysis on this phenomenon. Small cylinder values (< 0.5 D) were removed from the preschool sample resulting in a sample size of 77. Correlations for M, J0, and J45 were found to be 0.41 (P = 0.0002), 0.72 (P < 0.0001), and 0.52 (P < 0.0001) respectively. Correlations for those preschoolers with small cylinders (< 0.5D) were low 0.19 (P = 0.09), 0.28 (P = 0.01), and 0.05 (P = 0.63), respectively.
A similar analysis was performed on the adult sample where the reduced sample size was 74. Correlations were found to be 0.97, 0.62, and 0.50 for M, J0 and J45, all of which had P < 0.0001. To find out whether the practice of setting small cylinder values to zero accounts for the differences in astigmatic components, paired t-tests on this adult sample were performed. We find that the mean differences in M, J0, and J45 are -0.31 (P = 0.003), 0.11 (P = 0.08), and -0.09 (P = 0.02), respectively. Thus small differences in each component remain.
Astigmatism in the Preschool Population
The negative cylinder axes produced by the Retinomax were broken down into WTR (030° and 151180°), ATR (61120°) and oblique (3160° and 121150°) forms, in accordance with Borish.32 There were 278 (23.9%) preschoolers who had a cylinder of 0. Figure 3A 3B 3C shows the distribution of the three types of astigmatism. Of the children with astigmatism, WTR was most dominant in this preschool population (45%), followed by ATR (40%), and then oblique (15%). Within each astigmatism type, most children had very small cylinder errors (Fig. 3) . The mean astigmatism values for WTR, ATR, and oblique are -0.33 Dx 004°, -0.41 Dx 091°, and -0.13Dx 041°, respectively. The range of WTR astigmatism spanned the interval -4, -0.25, whereas ATR and oblique spanned a smaller interval (-1.75, -0.25).
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Age Stratification
The Retinomax data set were stratified into two groups. Those children less than 48 months were deemed 3-year-olds (n = 475) and those 48 months or older were deemed 4-year-olds (n = 409). These groups were also stratified by gender. There were no significant differences found between age-groups, or between age-gender groups in the distributions of astigmatism. Specifically, the marginal distribution of astigmatism in 3-year-olds can be broken down into 47% WTR, 38% ATR, and 16% oblique. Similarly, the distribution was 42% WTR, 43% ATR, and 15% oblique in 4-year-olds.
Central Tendency
Overall mean magnitude of the cylinder components were -0.08 Dx 015° and -0.08 D x 028° for the right and left eyes respectively. These measures take into account astigmatism direction, as they come from the back transformation of the mean Fourier components and are in the direction of WTR astigmatism. This value is smaller than the average cylinder value of 0.38 D, which was determined by considering only the absolute astigmatism without reference to the position of the axis.
Figure 5 plots J45 against J0. From observation of this scatterplot a symmetrical clustering is found to orbit approximately 0 astigmatism. Part of the distinct pattern is because the Retinomax provided measurements in 0.25-D intervals, which rendered continuous data into discrete data. As the astigmatism values became larger, there was a loss of symmetry where astigmatism became clearly positive along J0 and, to a lesser degree, along J45. This would lead to astigmatism of a WTR format, with an axis between 0° and 45°, which is consistent with the overall mean axis of 15°.
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| Discussion |
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It is important to recognize that simply correcting the bias of 0.88 D of overaccommodation (Table 1) will not provide a suitable calibration of the Retinomax due to the high SD. Furthermore, calibrations based on regression analysis were thwarted by the considerable intersubject variation. It appears that when children overaccommodate in response to the Retinomax, the response is variable and cannot be easily calibrated.
Clinical retinoscopies are often taken to be the gold standard for refractive error measurements. Despite this, it appeared that many of the retinoscopy cylinder and/or axis measurements when close to zero were rounded off to zero by the practitioners. This practice of rounding off increases the measurement differences between retinoscopy and the Retinomax. The post hoc analysis showed that when small cylinders were removed, improvements in the correlations for J45 were found despite a halving of the sample size. This change in correlation supports the idea that practitioners may not be measuring small astigmatisms as closely as the Retinomax.
This pattern was also found in adult studies. The retinoscopists set cylinder values to 0 twice as often as the Retinomax did. However, the removal of small cylinders did not remove the small differences found between retinoscopy and the Retinomax. The small hyperopic bias in the equivalent sphere has been found in other adult studies23 ; this small bias (0.29 D) was confirmed by the manufacturer (Nikon). However, other studies in which children underwent cycloplegia20 showed very little bias between retinoscopy and the Retinomax. It is possible that the calibration of the Retinomax is closer to the retinoscopy results taken from the eye of a child than that of an adult.
From these findings, we conclude that the variability of noncycloplegic equivalent sphere measures of the Retinomax K-Plus preclude an accurate measure of the degree of hyperopia and myopia present. This variance in equivalent sphere (Tables 1 and 2) further precludes measurement of anisometropia. Nevertheless, the Retinomax K-Plus provided a valid measure of astigmatism in this preschool population.
Astigmatism in the Preschool Population
The Oxford County preschool populations distribution of astigmatism can be broken down into 45% WTR, 40% ATR, and 15% oblique, falling into a general pattern in which WTR astigmatism is most prevalent, especially in high astigmatisms. This pattern is consistent between 3- and 4-year-olds. When the spherocylinder data are transposed into two independent components (Fig. 5) , the mean cylinder magnitude approaches zero. It appears that most of the data points cluster symmetrically about zero (Fig. 5) . This suggests that in this population the small astigmatisms are random fluctuations about zero. It appears that a second and distinct subpopulation shows significant WTR astigmatism. It is important to note that native North American preschool populations show much higher levels of astigmatism, that WTR forms represent well over 90% of the astigmatism,6 8 and that the origin appears to be corneal.8
Prescribing guidelines have not been well established for preschool children. Consideration of emmetropization suggests caution before spectacle prescription is undertaken, whereas consideration of amblyopia suggests intervention. Understandably, clinicians vary in their thresholds at which astigmatism should be corrected.16 However, on average, pediatric eye care practitioners start to correct astigmatism in 4- to 7-year-olds, once it has reached levels of 1.50 D16 close to the 95th percentile of 1.25 D calculated from this study. Prescribing for astigmatism in clinical practice has defined critical levels that represent values falling just outside the population norms.
| Acknowledgements |
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| Footnotes |
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Submitted for publication July 18, 2002; revised December 17, 2002 and March 26, 2003; accepted April 4, 2003.
Disclosure: L. Cowen, None; W.R. Bobier, Welch Allyn (F)
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C.
1734 solely to indicate this fact.
Corresponding author: William R. Bobier, School of Optometry, University of Waterloo, Waterloo, ON N2L 3G1, Canada; wbobier{at}uwaterloo.ca.
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