Download Measurement of Refractive Error in Native American

1040-5488/100/7703-0140/0 VOL. 77, NO. 3, PP. 140–149
OPTOMETRY AND VISION SCIENCE
Copyright © 2000 American Academy of Optometry
ORIGINAL ARTICLE
Measurement of Refractive Error in Native
American Preschoolers: Validity and
Reproducibility of Autorefraction
ERIN M. HARVEY, MA, JOSEPH M. MILLER, MD, VELMA DOBSON, PhD,
ROBERT TYSZKO, OD, and AMY L. DAVIS, OD
Departments of Ophthalmology (EMH, JMM, VD, RT), Optical Sciences (JMM), and Psychology (VD), The University of Arizona,
Tucson, Arizona
ABSTRACT: Purpose: To examine (1) reproducibility of cycloplegic retinoscopy (C-RNS), cycloplegic autorefraction
(C-Autoref), and noncycloplegic autorefraction (NC-Autoref), and (2) validity of C-Autoref and NC-Autoref compared
with C-RNS in preschoolers with astigmatism. Methods: Subjects were 36 Native American preschoolers. Three
measurements of right eye refractive error were obtained with each of three methods: C-RNS (by three different
retinoscopists), C-Autoref, and NC-Autoref (Nikon Retinomax Kⴙ). Vector methods (vector dioptric distance, VDD)
were used in the analyses. Results: Mean reproducibility was 0.41 D (SD ⴝ 0.18) for C-RNS, 0.25 D (SD ⴝ 0.17) for
C-Autoref, and 0.37 D (SD ⴝ 0.21) for NC-Autoref. Mean agreement between C-Autoref and C-RNS ranged from 0.51
to 0.61 VDD (SD ⴝ 0.24 to 0.35), and ranged from 1.66 to 1.74 VDD (SD ⴝ 1.11 to 1.25) for agreement between
NC-Autoref and C-RNS. Mean bias was ⴚ0.07 ⴙ0.21 ⴛ 149 and ⴚ1.33 ⴙ0.34 ⴛ 178 for C-Autoref and NC-Autoref,
respectively. Conclusions: C-Autoref provided reliable and valid measurements of refractive error in young children.
NC-Autoref measurements were reliable within subjects, but there was large variability in validity among subjects.
(Optom Vis Sci 2000;77:140–149)
Key Words: retinoscopy, autorefraction, children, astigmatism, Native Americans
T
he traditional method for measuring refractive errors in preschool-age children involves cycloplegic or noncycloplegic
retinoscopy. Although skilled retinoscopists can provide reliable and valid measures of refractive error in children, previous
research indicates that retinoscopy is subject to measurement bias
and intraobserver/interobserver variation.1–7 A means of measuring refractive error that is accurate, repeatable, and free of operator
bias would be desirable in clinical, research, and screening settings.
From a clinical perspective, such an instrument, along with a body
of research on the instrument’s measurement validity and reproducibility, could be used to detect significant change in refractive
error over time, independent of any between- and within-retinoscopist bias or variability. From a research perspective, the instrument could reduce the opportunity for experimenter bias and
would provide a means for standardization and comparability of
measures among studies and across research laboratories. In addition, a reliable automated instrument that can be used by lay
screeners and requires little cooperation from the children could
prove to be an effective means of identifying children with high
refractive error in a screening setting. The instrument would be
especially useful for screening if normative data on the relationship
between cycloplegic and noncycloplegic measurements were available and could be used to identify noncycloplegic refraction values
that would provide the greatest sensitivity and specificity for detection of significant refractive error.
Previous research has indicated that autorefractors can provide
reliable measures of refractive error that are comparable with or
better than retinoscopy.6 –10 One candidate for such an instrument
is the Nikon Retinomax K⫹ autorefractor (Nikon Inc., Melville,
NY), a hand-held instrument that measures refractive error. Several studies have indicated that the Retinomax K⫹ has good reproducibility of measurements, agrees well with retinoscopy measurements, and can be used with children.8 –13 However, evaluations of
reproducibility of Retinomax K⫹ representative measurements
compared with reproducibility of retinoscopy measurements in
young children have not been reported, and there have been no
Optometry and Vision Science, Vol. 77, No. 3, March 2000
Validity and Reproducibility of Autorefraction—Harvey et al.
evaluations of the validity of the Retinomax K⫹ in highly astigmatic children.
The aims of this study were (1) to determine if the reproducibility of cycloplegic autorefraction (C-Autoref) and noncycloplegic
autorefraction (NC-Autoref) measurements using the Retinomax
K⫹ compares favorably with reproducibility of cycloplegic retinoscopy (C-RNS) measurements in children and (2) to determine
the validity of the Retinomax K⫹ C-Autoref and NC-Autoref
measurements of a child’s refractive error, using optimal (gold
standard) retinoscopy measurements as a comparison. Subjects in
this study were Native American preschool children from the Tohono O’Odham Nation in Southern Arizona, a tribe with a previously documented high prevalence of astigmatism.14 –17 Data were
collected as part of a larger study of “Astigmatism and Amblyopia
Among Native American Children” (AANAC), which is aimed at
determining the most effective screening method for the detection
of high astigmatism in preschoolers, and evaluating the effectiveness of preschool screening and glasses intervention on vision once
the children reach grade school.18
METHODS
Subjects. Subjects were 42 preschool children (mean age, 4.6
years; range, 3.2 to 5.6 years) who were enrolled in the Tohono
O’Odham Early Childhood Head Start Program. All Head Start
enrollees received a complete eye examination as part of the
AANAC research study. None of the children included in the
study had any ocular abnormalities other than refractive error. The
children included in this study were those seen on two scheduled
eye exam dates (3/25/98 and 3/30/98) on which three retinoscopists were available to conduct eye examinations. The University of
Arizona Institutional Review Board (IRB) approved this study.
Written informed consent was obtained from parents of all children.
Procedure. Details of the complete testing procedure used in
the AANAC protocol have been published.18 In what follows, we
provide a description of only the testing procedures that are relevant to the present study.
Before dilation, the Retinomax K⫹ was used to obtain three
autorefraction measurements from the right eye of each subject.
Autorefraction was performed by one of the study’s trained vision
screeners. Each of the three Retinomax K⫹ measurements was the
“representative measurement” that the instrument calculates,
based on eight “measured values.” Measurements were obtained in
the instrument’s “normal” mode, rather than “quick” mode.
To achieve cycloplegia, each child was first given one drop of
proparacaine 0.5%, followed approximately 30 s later by a single
drop of cyclopentolate 2% in each eye instilled in the inferior cul
de sac. Five minutes later, each child was given a single drop of
cyclopentolate 1% in each eye. Drops were administered by holding the child, with the eyelid open and the pooled drop in contact
with the cornea for approximately 1 second, and then lifting the
upper eyelid, allowing the pooled drop to collect under the upper
eyelid.
At least 40 min after the first drop of cyclopentolate was
instilled, a check for residual accommodation was performed by
141
observing the retinoscopic reflex while the child was viewing a
distant television monitor displaying a cartoon, and then while
the child changed fixation to view a finger puppet held alongside the retinoscope. Evidence of inadequate cycloplegia was a
shift in the retinoscopic reflex as viewing distance changed. If
the results of this test of residual accommodation indicated that
a child’s eyes had not been adequately cyclopleged, the child
was asked to wait an additional 5 min. If the child’s eyes were
not adequately cyclopleged 45 min after the first drop of cyclopentolate, the data from the child were eliminated from analyses.
After the test for residual accommodation, each child underwent
C-RNS (right eye and left eye), conducted by a pediatric ophthalmologist (JMM). Three autorefraction measurements were then
obtained for the right eye of each child using the Retinomax K⫹.
The autorefractions were obtained by one of the study’s trained
vision screeners. Finally, two optometrists (RT and ALD) each
conducted C-RNS on the right eye of each child. All three clinicians had extensive experience conducting retinoscopy on young
children. None of the three retinoscopists were aware of the results
of the other retinoscopists or the autorefraction measurements at
the time of their examination.
Data Analysis. Analysis of variability of refractive error data
was conducted using refractive data (sphere, cylinder, and axis)
transformed according to a method described by Long19 and modified by Harris.20 A summary of this method and calculations used
in the present study is provided in the Appendix.
Reproducibility of Measurements. For each subject, each
of the three C-RNS measurements was converted into a value
representing a point in dioptric three-dimensional space. The
mean of the three values was calculated, and the vector dioptric
distance (VDD) between each retinoscopy measurement and the
mean of that subject’s retinoscopy measurements was determined.
This yielded a dioptric error value for each retinoscopy estimate of
refractive error. The mean of the dioptric errors was calculated for
each subject and the grand mean dioptric error was calculated
across subjects. This provided a measure of the average acrossretinoscopist VDD for three retinoscopy measurements in an individual child.
The same method was used to calculate the mean VDD for
the three C-Autoref measurements, and the three NC-Autoref
measurements. A repeated-measures analysis of variance was
used to compare mean VDDs across the three types of measurements (C-RNS, C-Autoref, and NC-Autoref).
Accuracy of Autorefraction Measurements. For each
subject, validity of autorefraction measurements was evaluated in
comparison with that subject’s “optimal” C-RNS measurement.
The optimal C-RNS measurement for each subject was the C-RNS
measurement that was closest to the vector dioptric mean of the
subject’s three C-RNS measurements (one from each clinician; i.e.,
the median of the three measurements). For each subject’s three
C-Autoref measurements, the VDD from the optimal C-RNS
measurement was calculated. This allowed us to determine if measurement validity tended to increase or decrease with repeated
measures. The same analysis was conducted with each subject’s
three NC-Autoref measurements.
Optometry and Vision Science, Vol. 77, No. 3, March 2000
142
Validity and Reproducibility of Autorefraction—Harvey et al.
Autorefraction Measurement Bias. VDDs are always represented in positive numbers. Therefore, they do not provide any
information regarding measurement bias (e.g., consistent underor over-estimation of cylinder components). To evaluate any measurement bias present in autorefraction measurements, additional
comparisons between autorefraction (C-Autoref, NC-Autoref)
and optimal C-RNS were conducted. Using the vector method of
Harris (see Appendix), the mean optimal C-RNS measurement
across subjects was subtracted from the mean of the first C-Autoref
measurements (C-Autoref measure 1 for each subject) across subjects. Results were then converted back to standard notation, for
evaluation of measurement bias of the sphere and cylinder components. This procedure was repeated for each subject’s first NCAutoref measurement.
RESULTS
Of the 42 subjects eligible for the study, 36 completed all of
the testing and are included in statistical analyses (mean age of
final sample, 4.7 years; range, 3.6 to 5.6 years). Of the six
subjects excluded, the eyes of one were judged to be not fully
cyclopleged after the 45-min waiting time, and the other five
did not complete the full testing procedure [one child was ill,
one was too uncooperative (the youngest child seen), and three
did not complete because of experimenter procedural errors
(e.g., missing data)]. However, it should be noted that at least
one autorefraction measurement and one retinoscopy measurement were obtained for each eye in 98% of subjects (41 of 42).
A summary of each subject’s right eye refractive error (optimal
C-RNS) is provided in Table 1.
Reproducibility of Measurements. The mean VDD (average deviation from the mean of three measurements) for C-RNS
was 0.41 D (SD ⫽ 0.18). The mean VDD for C-Autoref was 0.25
D (SD ⫽ 0.17), and the mean VDD for NC-Autoref was 0.37 D
(SD ⫽ 0.21). A repeated-measures ANOVA yielded a significant
effect of method on measurement reproducibility (mean VDD)
[F2, 70 ⫽ 7.90, p ⫽ 0.001]. Post hoc comparisons indicated that
the reproducibility of C-Autoref measurements was significantly
better than the reproducibility for NC-Autoref and C-RNS measurements. That is, there was less variability in C-Autoref measurements than in NC-Autoref and C-RNS measurements.
Results of reproducibility of measurements in standard notation
(rather than vector notation) for spherical equivalent measurements are presented in Fig. 1. All mean differences are 0, because
the reference was the mean of the measurements. The standard
deviation, calculated across 108 measurements (three measurements per subject for 36 subjects, calculated separately for each
refraction method) are 0.28 D, 0.18 D, and 0.31 D for C-RNS,
C-Autoref, and NC-Autoref, respectively.
Validity of Autorefraction Measurements. For each subject, the optimal C-RNS measurement (median of the three
C-RNS measurements) was determined. The optimal C-RNS
was the measurement from retinoscopist 1 for seven subjects
(19.4%), retinoscopist 2 for 12 subjects (33.3%), and retinoscopist 3 for 17 subjects (47.2%). Statistical analysis indicated
that the number of retinoscopies from each retinoscopist that
contributed to the optimal did not significantly differ
[␹22 ⫽ 4.17].
TABLE 1.
Right eye refractive error data (optimal C-RNS) for each
subject (plus cylinder notation).
Subject ID
Sphere
Cylinder
440
442
443
444
445
446
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
471
472
473
474
475
476
477
481
Mean
Std. Deviation
Minimum
Maximum
1.50
.25
1.00
1.50
.50
1.25
.00
.75
.50
.25
1.00
⫺.25
.75
1.25
1.00
.50
⫺3.75
1.00
.25
.75
1.00
1.00
.50
.50
.75
1.00
.75
.25
⫺1.00
.00
.75
⫺.25
.50
.00
.25
.25
.45
.89
⫺3.75
1.50
1.25
.50
.25
1.00
.75
.00
1.25
2.00
.25
.75
.50
2.50
2.25
1.00
1.25
.00
4.00
.75
.25
.50
.25
3.00
.50
.75
3.75
.75
.75
.25
2.25
.25
.50
.75
.75
.75
.25
.50
1.03
1.00
.00
4.00
Axis
90
90
90
90
90
90
95
90
90
90
85
95
90
92
93
90
90
90
90
100
95
90
80
85
92
90
90
90
95
90
90
90
90
85
90.35
3.43
80.00
100.00
The mean VDDs of autorefraction measurements from the optimal C-RNS measurements were 0.57 D (SD ⫽ 0.28), 0.51 D
(SD ⫽ 0.24), and 0.61 D(SD ⫽ 0.35) for the three (first, second,
and third) C-Autoref measurements, respectively, and 1.71 D
(SD ⫽ 1.12), 1.66 D (SD ⫽ 1.11), and 1.74 D (SD ⫽ 1.25) for
the three NC-Autoref measurements, respectively.
Results of validity for standard notation (rather than vector notation) spherical equivalent and cylinder measurements of each
subject’s first C-Autoref measurement and each subject’s first NCAutoref measurement are presented in Fig. 2. Autorefraction is
compared with optimal C-RNS. The mean difference in spherical
equivalent values (autorefraction ⫺ optimal C-RNS) was 0.02 D
Optometry and Vision Science, Vol. 77, No. 3, March 2000
Validity and Reproducibility of Autorefraction—Harvey et al.
143
FIGURE 1.
Subjects’ deviations (three measurements per subject) from mean spherical equivalent measurements for (a) C-RNS, (b) C-Autoref, and (c) NC-Autoref.
Solid reference lines indicate means; dashed lines indicate 95% confidence limits (⫾ 2 SD).
FIGURE 2.
Subject’s deviations from optimal retinoscopy values for C-Autoref (a and c) and for NC-Autoref (b and d). Spherical equivalent deviations are shown in a and
b, and refractive cylinder deviations are shown in c and d. Solid reference lines indicate means; dashed lines indicate 95% confidence limits (⫾ 2 SD).
(SD ⫽ 0.37) for C-Autoref and ⫺1.15 D (SD ⫽ 0.82) for NCAutoref. The mean difference in refractive cylinder values was
⫺0.02 D (SD ⫽ 0.37) for C-Autoref and ⫺0.21 D (SD ⫽ 0.28)
for NC-Autoref.
Autorefraction Measurement Bias. The mean bias for CAutoref (first C-Autoref ⫺ optimal C-RNS) was ⫺0.07 ⫹0.21 ⫻
149. The mean bias for NC-Autoref (first NC-Autoref ⫺ optimal
C-RNS) was ⫺1.33 ⫹ 0.34 ⫻ 178.
DISCUSSION
Autorefraction Success Rates. The results indicate that the
Nikon Retinomax K⫹ can be used successfully to measure refractive error in this population of preschoolers in which there is a high
prevalence of astigmatism. We were able to obtain autorefraction
measurements in 98% of children eligible for this study. The results are in agreement with previous reports indicating high success
Optometry and Vision Science, Vol. 77, No. 3, March 2000
144
Validity and Reproducibility of Autorefraction—Harvey et al.
rates in obtaining Retinomax measurements in children.8–13, 21
For example, Cordonnier and Dramaix used the Retinomax in a
screening of 897 children between the ages of 6 months and 5 years
and were able to obtain a measurement on 98.5% of the children.13
Reproducibility of Measurements. The analyses of measurement reproducibility indicated that variability of NC-Autoref
measurements was similar to variability of C-RNS measurements
across retinoscopists. C-Autoref measurements were less variable
than repeated C-RNS and NC-Autoref measurements. Reproducibility for all three methods was excellent, however, with an average
deviation from the mean that was 0.41 VDD or less for each
method.
Table 2 summarizes the reproducibility of measurements in the
present study in comparison to previous studies of reproducibility
of retinoscopy and autorefraction in children. Mean difference
values for sphere, spherical equivalent, and cylinder components
provide an indication of measurement bias, and standard deviations and confidence intervals provide an indication of measurement variability. Studies reporting reproducibility of retinoscopy
measurements (Hirsch,1 Saunders and Westall,5 and present
study) indicate bias of up to 0.55 D in measurements of spherical
equivalent and cylinder, with confidence intervals for the difference scores that ranged from ⫾ 0.39 D to ⫾ 1.14 D. Studies of the
reproducibility of Retinomax autorefraction measurements (Harvey et al.,8 Cordonnier and Dramaix,13 and present study) indicate
little bias in measurements of sphere, spherical equivalent, or cylinder either with or without cycloplegia. However, there is less
variability of Retinomax autorefraction measurements with cycloplegia than without cycloplegia. In addition, variability of Retino-
TABLE 2.
Comparison of studies evaluating the reproducibility of refraction in children.
Reproducibility
(Mean difference between repeated measurements)
Study
Subjects
Refraction Method
Saunders & Westall5
10 infants
(⬍2 years old)
C-RNSa
—
Present Study
36 Native American
preschoolers
(3.5 to 5 years old)
C-RNSc
Hirsh1
72 eyes, 36 children
(6 to 14-year-olds)
Spherical
Equivalent
(SD, 95% CI)
Cylinder
(SD, 95% CI)
VDD
(SD, 95% CI)
⬵⫺0.30 D
(⬵0.20, ⫾0.39)
—
—
⫺0.06 D
(0.48, ⫾0.94)
0.05 D
(0.58, ⫾1.14)
0.11 D
(0.44, ⫾0.86)
0.21 D
(0.43, ⫾0.84)
0.25 D
(0.52, ⫾1.02)
0.04 D
(0.40, ⫾0.78)
0.55 D
(0.34, ⫾0.67)
0.41 D
(0.32, ⫾0.63)
⫺0.14 D
(0.35, ⫾0.69)
0.41 VD
(0.18, ⫾0.35)
Non-C-RNS
—
0.28 Db
(0.34, ⫾0.67)
—
—
10 infants
(⬍2 years old)
Near Retinoscopya
—
⬵⫺0.48 D
(⬵0.20, ⫾0.39)
—
—
Harvey et al.8
22 children
(mean age, 6.6 years)
23 children
(mean age, 4.1 years)
Cycloplegic
Retinomaxd
(measured values)
⫺0.10 D
(0.20, ⫾0.39)
⫺0.04 D
(0.27, ⫾0.53)
⫺0.08 D
(0.16, ⫾0.31)
⫺0.03 D
(0.21, ⫾0.41)
0.03 D
(0.25, ⫾0.49)
0.03 D
(0.25, ⫾0.49)
0.37 VD
(0.52, ⫾1.02)
0.49 VD
(0.40, ⫾0.78)
Present Study
36 Native American
preschoolers
(3.5 to 5 years old)
Cycloplegic
Retinomax K⫹d
⫺0.04 D
(0.32, ⫾0.63)
⫺0.03 D
(0.22, ⫾0.43)
0.03 D
(0.31, ⫾0.61)
0.25 VD
(0.17, ⫾0.33)
Cordonnier &
Dramaix13
255
(9 to 36 months old)
Non-cycloplegic
Retinomax
0.09 D
(1.40, ⫾2.74)
—
—
—
Present Study
36 Native American
preschoolers
(3.5 to 5 years old)
Non-cycloplegic
Retinomax K⫹d
0.00 D
(0.51, ⫾1.00)
⫺0.05 D
(0.50, ⫾0.98)
⫺0.10 D
(0.25, ⫾0.49)
0.37 VD
(0.21, ⫾0.41)
Saunders & Westall5
Sphere
(SD, 95% CI)
SD, standard deviation; 95% CI, 95% confidence interval (1.96 ⫻ SD).
Two different clinicians, values estimated from graph.
b
Mean of the absolute values of the differences.
c
Three different clinicians (three rows represent pairwise comparisons of retinoscopists).
d
First two measurements used for mean differences in sphere, spherical equivalent, and cylinder. The Retinomax provides up to 8
measured values and determines one representative measurement (best estimate of refractive error) based on the measured values. In
the present study, we compared reproducibility and accuracy based on Retinomax representative measurements. In the study by
Harvey et al., we compared reproducibility and accuracy based on Retinomax measured values.
a
Optometry and Vision Science, Vol. 77, No. 3, March 2000
Validity and Reproducibility of Autorefraction—Harvey et al.
max autorefraction measurements with cycloplegia is equal to or
less than that of both cycloplegic and noncycloplegic retinoscopy.
In a recent literature review, Goss and Grosvenor22 summarized
data on reliability of refraction in adults tested with a variety of
techniques, including subjective refraction, retinoscopy, and autorefraction. They concluded that the 95% confidence interval for
repeated clinical refractions was ⫾ 0.50 D. This value represents a
standard with which to compare the data presented in Table 2 (i.e.,
studies of reliability of refraction in children). It is noteworthy that
despite the differences in subject characteristics and refraction
techniques, the 95% confidence intervals shown in Table 2 for
children tested with cycloplegic Retinomax autorefraction are similar to the overall value reported by Goss and Grosvenor22 for adult
refractions. In summary, the results of reproducibility of C-Autoref are comparable with findings reported in studies of clinical
refraction in adults22 and are comparable with or better than reports of reproducibility of retinoscopy in children.1, 5
Validity and Bias of Cycloplegic Autorefraction Measurements. The average deviation of each of the three C-Autoref
measurements from the optimal C-RNS measurement was within
0.61 VDD. Agreement between retinoscopy and C-Autoref did
not seem to vary with repeated measurements, i.e., across first,
second, and third autorefractions. The mean bias for the C-Autoref
145
was ⫺0.07 ⫹0.21 ⫻ 149, indicating little bias in measurements of
sphere or cylinder, compared with C-RNS.
In Table 3, we provide a summary of several recent studies that
have examined the validity of the Retinomax in measuring cycloplegic refractive error in children. We reanalyzed our data in traditional notation (i.e., separate comparisons for sphere, cylinder,
and axis components) for direct comparisons of measurement bias
and variability with other studies.
The results presented in Table 3 indicate little bias (i.e., mean
differences close to 0) between the autorefraction and subjective
refraction, or between autorefraction and retinoscopy measurements of sphere, spherical equivalent, cylinder, and axis, with the
exception of the results of Weseman and Dick who reported a
mean difference of 0.59 D spherical equivalent.9 Confidence intervals in the various studies indicated that 95% of Retinomax
measurements of spherical equivalent were within ⫾ 0.72 D to ⫾
1.39 D of retinoscopy, but greater variability (⫾1.65 D) was reported in a study comparing the Retinomax with subjective refinement.8 For measurements of cylinder, 95% of Retinomax measurements were within ⫾ 0.20 D to ⫾ 0.94 D of either retinoscopy
or subjective refraction measurements. Kallay et al.12 reported the
least variability in measurements of sphere, cylinder, and axis in
their comparison between refractions obtained with the Retino-
TABLE 3.
Comparison of studies evaluating the accuracy of the Retinomax for use with children. All measurements were made with
cycloplegia.
Accuracy (Mean difference between methods)
Spherical
Equivalent
(SD, 95% CI)
Cylinder
(SD, 95%
CI)
0.59 D
(0.44, ⫾0.86)
0.06 D
(0.47 ⫾0.92)
Study
Subjects
Comparison
Sphere (SD,
95% CI)
Wesemann
and Dick9
25 2- to 10-yearolds (50 eyes)
RetinomaxRetinoscopy
—
Harvey et
al.8
22 children w/no
occular pathology
(mean age, 6.6
years)
RetinomaxSubjective
Refraction
0.19 D
(0.90, ⫾1.76)
0.07 D
⫺0.25 D
4.18°
(0.84, ⫾1.65) (0.31, ⫾0.61) (7.86, ⫾15.41)
1.03 VD
(0.59, ⫾1.16)
23 children w/no
ocular pathology
(mean age, 4.1
years)
RetinomaxRetinoscopy
0.27 D
(0.75, ⫾1.47)
0.26 D
(0.66, ⫾1.29)
⫺0.02 D
1.87°
(0.48 ⫾0.94) (10.78, ⫾21.13)
0.82 VD
(0.58, ⫾1.14)
102 5- to 72month-olds
RetinomaxRetinoscopy
0.03 D
(0.79, ⫾1.55)
0.09 D
0.23 D
(0.71, ⫾1.39) (0.13, ⫾0.25)
132 children &
young adults w/no
ocular pathology
(mean age, 10.9
years)
RetinomaxTopcon (RMA-6000)
0.07 D
(0.09, ⫾0.18)
36 Native American
Preschoolers (3- to
5-year-olds)
Retinomax
K⫹Retinoscopyb
0.03 D
(0.46, ⫾0.90)
El-Defrawy et
al.10
Kallay et
al.12
Present Study
—
0.02 D
(0.10, ⫾0.20)
Axis (SD, 95%
CI)
VDD (SD,
95% CI)
—
—
—
0.97 VD
(0.76, ⫾1.49)
6.49°a
(4.71, ⫾9.23)
—
0.02 D
⫺0.02 D
6.97°
(0.37, ⫾0.72) (0.38, ⫾0.74) (13.87, ⫾27.18)
SD, standard deviation; 95% CI, confidence interval (1.96 ⫻ SD).
Only measurements with cylinder power ⱖ0.50 D included in cylinder and axis data.
b
Median (“optimal”) retinoscopy measurement and first cycloplegic autorefraction used in calculations.
a
Optometry and Vision Science, Vol. 77, No. 3, March 2000
0.57 VD
(0.28, ⫾0.55)
146
Validity and Reproducibility of Autorefraction—Harvey et al.
max and refractions obtained with the Topcon RM-A-6000 autorefractor.
In the present study, there was slightly less variability in measurement validity (i.e., smaller standard deviations) of sphere and
VDDs compared with previous studies (Table 3). It is possible that
we found less variability in the present study because we compared
Retinomax K⫹ measurements with the median of three retinoscopy measurements, thus eliminating any outlier retinoscopy measurements that may have been obtained, for example, in uncooperative subjects. In contrast, other studies compared Retinomax
measurements with individual retinoscopy measurements. The
differences in variability and measurement agreement between
studies may also be attributable to age differences in the samples,
and to other differences in the populations represented in each
study (e.g., the high prevalence of astigmatism in our study population).14–17
Accuracy and Bias of Noncycloplegic Autorefraction:
Implications for Vision Screening. The results indicate that
there was good reproducibility of NC-Autoref measurements
(mean VDD ⫽ 0.37 D (SD ⫽ 0.21). However, mean differences
between NC-Autoref measurements and optimal C-RNS measurements ranged from 1.66 D to 1.74 D, with relatively large
standard deviations (1.11 to 1.25). The large standard deviations
probably reflect variations in relaxation of accommodation among
subjects. The large VDDs probably indicate that accommodation
is not sufficiently relaxed during NC-Autoref measurements, resulting in underestimation of hyperopia. Although VDDs do not
provide an indication of the direction of measurement bias, the
mean bias between NC-Autoref and optimal retinoscopy measurements support this interpretation (mean bias ⫽ ⫺1.33 ⫹0.34 ⫻
178). This interpretation is also supported by the data in Fig. 1,
which indicate a negative shift in NC-Autoref measurements of
spherical equivalent (Fig. 1C), compared to C-Autoref measurements (Fig. 1B) in the same subjects. In summary, the results
indicate that although NC-Autoref provides reliable measurements within subjects (i.e., good reproducibility), results of comparisons with optimal C-RNS measurements indicate that it underestimates hyperopia (overestimates myopia) and that
measurement validity varies considerably among subjects.
El-Defrawy and his colleagues also obtained NC-Autoref data
on their subjects.10 Statistical comparisons between NC-Autoref
and retinoscopy were not reported, but the authors did indicate
that that NC-Autoref results were “grossly inaccurate and overestimated myopia by up to ⫺8.00 D.” In an earlier study of 77
Native American preschoolers, we reported a mean bias of ⫺1.23
D spherical equivalent, and ⫺0.08 D cylinder for NC-Autoref
measurements compared with C-Autoref measurements.11 In the
present study, we also found that NC-Autoref underestimated hyperopia (overestimated myopia). However, we may not have found
as great an overestimation of myopia as did El-Defrawy and his
colleagues (maximum difference between optimal C-RNS and
NC-Autoref ⫽ 5.66 VDD in the present study), possibly because
of greater cooperation in our older subjects (36 to 60 months in the
present study vs. 5 to 72 months in the study by El-Defrawy et
al.).10
The mean bias for NC-Autoref (⫺1.33 ⫹0.34 ⫻ 178) in the
present study indicates that there was relatively little bias in measurements of cylinder. Previous studies evaluating agreement be-
tween cycloplegic and noncycloplegic refractions have also found
good agreement in measures of cylinder power.11, 23, 24 These data
suggest that noncycloplegic Retinomax measurements might serve
as a useful screening tool for detection of high astigmatism. We are
currently evaluating the sensitivity and specificity of the Retinomax K⫹ in detecting astigmatism in a large sample of preschoolers
with a high prevalence of astigmatism as part of the “Astigmatism
and Amblyopia Among Native American Children” research
study. In a preliminary analysis of data from 245 Native American
preschoolers, we found that NC-Autoref measurements of refractive astigmatism had sensitivity and specificity of 91% and 86%,
respectively, for detection of significant refractive astigmatism
(2.00 D or more for 3-year-olds and 1.50 D for 4-year-olds, based
on C-Autoref measurements).21
The Retinomax may also serve as a useful screening tool for
detection of myopia and hyperopia. Additional research on large
numbers of subjects with a wide range of spherical refractive errors
would help determine if there is an appropriate referral value,
correction constant, or regression formula that can be applied to
noncycloplegic Retinomax measurements to achieve high sensitivity and specificity for detection of significant myopia or hyperopia.
For example, Chan and Edwards compared the results of cycloplegic and noncycloplegic measurements of Chinese preschool children and reported that the cycloplegic measurement can be estimated by multiplying the spherical component of the
noncycloplegic measurement by 1.45, and adding ⫹0.39 to the
result.23 Cordonnier and Dramaix13 evaluated the Retinomax for
use in screening for high hyperopia in children from 6 months to 5
years of age. They found that a threshold of ⫹1.50 D spherical
refractive error in the most hyperopic meridian as measured by the
Retinomax without cycloplegia provided a sensitivity of 70.2%
and a specificity of 94.6% for the detection of abnormal hyperopia
(defined as ⫹3.50 D by cycloplegic refraction).13 Determination
of an accurate equation for estimation of refractive error from
noncycloplegic measurements might make the Retinomax K⫹ extremely valuable for vision screening in young children. However,
the large between-subjects variability in agreement between NCAutoref and optimal C-RNS reported in the present study make
this prospect somewhat questionable.
CONCLUSIONS
The results of the present study indicate that cycloplegic measurements made with the Nikon Retinomax K⫹ autorefractor provide highly reliable and accurate measurements of refractive error
in young children. Repeatability of the instrument’s measurements
is comparable with or superior to retinoscopy in children, indicating that the Retinomax K⫹ might be useful in clinical settings, to
reliably document change over time, and in research settings, to
reduce measurement bias and provide standardization of measurements.
The repeatability and validity of Retinomax K⫹ measurements
obtained without cycloplegia indicate that although the instrument’s measurements are reliable within subjects, there is large
variability in validity between subjects. Future research might be
directed toward further examining this finding and evaluating the
Retinomax K⫹ for use in screening of young children.
Optometry and Vision Science, Vol. 77, No. 3, March 2000
Validity and Reproducibility of Autorefraction—Harvey et al.
ACKNOWLEDGMENT
We thank Don Everett, M.A., Jonathan Holmes, M.D., Rosemary Lopez,
Maureen McGuire, Ph.D., and Karla Zadnik, O.D., Ph.D., for their support
and suggestions regarding the conduct of this study. We also thank Frances
Lopez, Christie Lopez, Jenniffer Funk-Weyant, Pat Broyles, and Angel
Palanca-Capistrano, M.D., for their help in conducting the vision screenings
and eye examinations, the parents and children who participated in the study,
and the Tohono O’Odham Nation for their support of this project.
Received July 12, 1999; revision received December 9, 1999.
This study was supported by National Institutes of Health/National Eye
Institute Grant EY11155 to JMM.
APPENDIX: CALCULATION OF VECTOR
DIOPTRIC DISTANCE
The statistical analysis of clinical refraction data has traditionally
been hampered by the fact that although sphere powers can readily
be combined and subtracted from each other, the same is not true
when cylinder power is present. This is because unless cylinder axes
coincide with each other, simple addition or subtraction cannot
combine the powers associated with each axis. In the last decade,
two very clinically relevant techniques have been developed that
break a spherocylindrical refracting surface into independent components that form an orthogonal set.
The first method, as implemented by Harris,20 decomposes the
spherocylindrical surface into two perpendicular cylindrical surfaces, and a Jackson-Cross Cylinder whose axes straddle the first
two cylinders. The second method, as implemented by Thibos,25
describes the refracting surfaces as a spherical lens (whose power is
equal to the spherical equivalent of the spherocylindrical lens) that
is combined with two Jackson-Cross cylinder lenses, one with axis
0°, and the other with axis 45°.
Either method (Harris or Thibos) greatly facilitates the comparison of refractive data, and each might be preferred for certain
calculations. Each method results in the decomposition of a
spherocylindrical lens into three independent (orthogonal) component parts that can be analyzed separately. In the examples that
follow, sp is sphere power in clinical notation, cp is cylinder power
in plus-cylinder clinical notation, and ax is axis in clinical notation
in degrees.
The Harris Method: Conversion from Clinical to
Vector Notation
147
the oblique cross cylinder; and vcp is vertical cylinder power associated with the cylinder whose axis is at 90°.
The formulas for converting sp, cp, and ax into vcp, ccp, and
hcp follow (Equations 1 to 3). Several examples of sp, cp, ax, and
vcp, ccp, and hcp are provided in Table 4.
vcp ⫽ sp ⫹ cp ⫻ sin(ax) ⫻ sin(ax)
(1)
ccp ⫽ ⫺cp ⫻ sin(ax) ⫻ cos(ax)
(2)
hcp ⫽ sp ⫹ cp ⫻ cos(ax) ⫻ cos(ax)
(3)
The Harris Method: Conversion from Vector to
Clinical Notation
Average values of refraction, differences between refractions,
and summation of refracting surfaces can be calculated by performing appropriate operations on the orthogonal components of the
vcp, ccp, and hcp of the spherocylinder lens. However, clinical
relevance demands that the resultant values of vcp, ccp, and hcp be
converted back into clinical notation. This conversion is accomplished by the operations given in Equations 4 – 6.
cp ⫽ ⫺sqrt[(vcp ⫹ hcp) ⫻ (vcp ⫹ hcp) ⫺ 4.0
⫻ ((vcp ⫻ hcp) ⫺ (ccp ⫻ ccp))]
(4)
sp ⫽ (vcp ⫹ hcp ⫺ cp)/2.0
(5)
ax ⫽ arctan[(sp ⫺ vcp)/cp]
(6)
The Thibos Method: Conversion from Clinical to
Vector Notation
Convert the spherocylindrical lens into a mean lens having
power equal to the spherical equivalent of the spherocylinder lens,
and two Jackson-Cross lenses that are oriented at 0° and 45°. In the
equations that follow, M is the mean (spherical equivalent) power,
J0 is the Jackson-cross cylinder power (axis 180°), and J45 is the
Jackson-cross cylinder power (axis 45°).
The formulas for converting sp, cp, and ax into M, J0, and J45
are given by Equations 7 to 9. Several examples of M, J0, and J45
are provided in Table 5.
Convert the sphere (sp), cylinder (cp), and axis (ax) into an
equivalent pair of cylinders oriented at 90 and 180°, and an obliquely oriented Jackson-Cross cylinder. In the equations that follow, hcp is horizontal cylinder power associated with the cylinder
whose axis is at 180°, ccp is the cross cylinder power associated with
M ⫽ sp ⫹ (cp/2)
(7)
J0 ⫽ ⫺(cp/2) ⫻ cos(2 ⫻ ax)
(8)
J45 ⫽ ⫺(cp/2) ⫻ sin(2 ⫻ ax)
(9)
TABLE 4.
Harris method clinical to vector conversion values.
sp
cp
ax
vcp
ccp
hcp
Comment
⫹2.00
Plano
Plano
⫺1.00
0
⫹1.00
⫹1.00
⫹2.00
0
090
180
135
2.00
1.00
0
0
0
0
0
1.00
2.00
0
1.00
0
Sphere
Vertical cylinder
Horizontal cylinder
Oblique Jackson Cross
Optometry and Vision Science, Vol. 77, No. 3, March 2000
148
Validity and Reproducibility of Autorefraction—Harvey et al.
TABLE 5.
Thibos method clinical to vector conversion values.
sp
cp
ax
M
J0
J45
Comment
⫹2.00
Plano
Plano
⫺1.00
0
⫹1.00
⫹1.00
⫹2.00
0
090
180
135
2.00
0.50
0.50
0
0
0.50
⫺0.50
0
0
0
0
⫺1.00
Sphere
Vertical cylinder
Horizontal cylinder
Oblique Jackson Cross
The Thibos Method: Conversion from Vector to
Clinical Notation
The conversion of derived values of M, J0, and J45 back into
plus-cylinder clinical notation are accomplished by the application
of Equations 10 to 12.
sp ⫽ M ⫺ sqrt(J0 ⫻ J0 ⫹ J45 ⫻ J45)
(10)
cp ⫽ 2 ⫻ sqrt(J0 ⫻ J0 ⫹ J45 ⫻ J45)
(11)
ax ⫽ 0.5 ⫻ arctan(J45/J0) ⫹ 90
(12)
The Vector Dioptric Distance (VDD)
The representation of a spherocylindrical lens as a point in
three-dimensional space can be seen as a vector representation of
power.25 Thus, the dioptric difference between two spherocylindrical lenses can be represented as a vector between two points in
space and the length of that vector represents the magnitude of
blur.
The magnitude of the difference vector can be calculated using
either the method of Harris20, 26 or the method of Thibos,25 and
the two methods are equivalent with the introduction of an appropriate scaling factor. After a measurement in clinical notation is
converted into vector notation, as described above, the resulting
three values (vcp, ccp, and hcp in Harris notation; M, J0, and J45
in Thibos notation) allow component parts of different refractions
to “line up” with each other and be added, subtracted, and averaged in the same way that sphere powers can be compared in the
absence of cylinder.
As the units of the three values (vcp, ccp, and hcp or M, J0, and
J45) are diopters, and as they are “orthogonal” (meaning mutually
perpendicular to each other), a given clinical measurement can be
represented as a point in three-dimensional space (with the three
values forming axes in the same manner as x, y, and z). In this way,
the “distance” between any two points in the refraction space can
be calculated, and the distance between the two points will have
units of diopters.
We have used the method described by Harris to allow a single
number (representing the dioptric distance between two vectors)
to be calculated when two refractions are compared.26 This simultaneous comparison of two pairs of sphere, cylinder, and axis is
particularly helpful when measurements of repeatability are desired or when deviations from a mean value are needed to identify
an outlier.
To calculate the Vector Dioptric Distance, or VDD, two clinical measurements (Refractions 1 and 2, or R1 and R2) are converted to (vcp1, ccp1, hcp1) and (vcp2, ccp2, hcp2). The differences
between the vcp, ccp, and hcp values for the two refractions are
calculated, squared, summed, and the square root taken, after a
3-dimensional application of the Pythagorean theorem. The cross
cylinder power is included twice in this calculation because it contains two refracting surfaces contributing dioptric power. The formula for VDD is given in Equation 13.
VDD ⫽ sqrt[(vcp1 ⫺ vcp2)2 ⫹ 2 ⫻ (ccp1 ⫺ ccp2)2
⫹ (hcp1 ⫺ hcp2)2]
(13)
If the method of Thibos is used, then the equation is slightly
modified to account for a difference in scaling.25 In the Harris
method, the unit vector is 1 D of cylinder power, whereas in the
Thibos method, the unit vector is 1 D of sphere power. Because
our use of VDD26 predates Thibos’ publication,25 we provide a
formula that scales the Thibos unit vector to match the Harris unit
vector. Again, refractions R1 and R2 are converted to [M1, J01,
J451] and [M2, J02, J452]. The Vector Dioptric Distance is then
calculated as follows:
VDD ⫽ sqrt(2) ⫻ sqrt[(M1 ⫺ M2)2 ⫹ (J01 ⫺ J02)2
⫹ (J451 ⫺ J452)2]
(14)
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Erin M. Harvey
The University of Arizona College of Medicine
Department of Ophthalmology.
655 N. Alvernon Way, Suite 108
Tucson, AZ 85711
E-mail: [email protected]
Optometry and Vision Science, Vol. 77, No. 3, March 2000