Abstract
purpose. To examine the relationship between monocular and binocular visual
acuities as predictors of visual disability in a population-based
sample of individuals 65 years of age and older.
methods. Two thousand five hundred twenty community-dwelling residents of
Salisbury, Maryland, between the ages of 65 and 84 years of age were
recruited for the study. Corrected visual acuity was measured
monocularly and binocularly using ETDRS charts. Reading speed, face
discrimination, and self-reported difficulty with visual tasks were
also determined.
results. Binocular acuity is predicted with reasonable accuracy by acuity in the
better eye alone, but not by the widely used American Medical
Association (AMA) weighted-average algorithm. The AMA algorithm
significantly underestimates binocular acuity when the interocular
acuity difference exceeds one line. Monocular acuity and binocular
acuity were significantly better predictors of reading speed than the
AMA weighted score or a recently proposed Functional Vision Score
(FVS). Monocular acuity in the better eye, binocular acuity, and the
AMA and FVS algorithms were equally good predictors of self-reported
vision disability. None of the acuity measures were good predictors of
face recognition ability.
conclusions. The binocular acuities of older individuals can be inferred from
measures of monocular acuity. There is little evidence for binocular
inhibition when the monocular acuities in the two eyes are unequal, as
opposed to the widely used AMA algorithm for computing binocular visual
impairment. For tasks that are strongly associated with visual acuity,
such as reading, this association can be captured from measures of
monocular acuity and does not require separate assessment of binocular
acuity.
Sensory impairment is typically defined at the organ level,
whereas disability is defined at the level of the entire individual.
Therefore, to study the relationship between vision impairment and
physical disability, one must decide how to accommodate the
contributions of both eyes. The World Health Organization (WHO) has
written widely used manuals on the classification of diseases,
impairments, and disabilities,
1 but these offer little
help. Although these manuals acknowledge that the degree of impairment
may be different for the two eyes of an individual, they make no
recommendation for the synthesis of monocular vision losses.
Many clinical investigators, see, for example, Tinetti et
al.
2 and Mangione et al.,
3 and governmental
agencies rely on an algorithm developed in 1955 for the American
Academy of Ophthalmology
4 and subsequently adopted in 1958
by the Committee on Medical Rating of Physical Impairment of the
American Medical Association.
5 According to this
algorithm, visual impairment of the individual is derived from vision
impairment measured separately for the two eyes by the following
formula:
\[\mathrm{Impairment\ of\ visual\ system}{=}\ \frac{3{\times}\mathrm{better\ eye\ value}{+}\mathrm{worse\ eye\ value}}{\mathrm{4}}\]
The terms “better eye value” and “worse eye value” are
specified in tables based on combinations of near and distance visual
acuity, visual fields, and ocular motility. In the absence of visual
field or motility data, the basic formula has been applied to visual
acuity data alone. The algorithm for deriving “values” from acuity
is not specified, but generally follows a logMAR
(log
10[minimum angle of resolution]) scale. As
a modification of the AMA algorithm, Colenbrander developed the
Functional Acuity Score (FVS)
6 :
\[\mathrm{FVS}{=}2{\times}\mathrm{binocular\ score}{+}\mathrm{right\ eye\ score}{+}\mathrm{left\ eye\ score}\]
The score for each component is derived from a table that follows
a logMAR scale. In contrast to the two combination rules, which take
both eyes into account, the US Social Security Administration adopted
new regulations in 1997 for the determination of disability benefits
based solely on the visual function of the better-seeing
eye.
7
Neither the AMA guidelines, the FVS, nor the Social Security
regulations provide any justification for their respective algorithms.
One consequence of the AMA and better-eye rules is that binocular
vision would never be better than monocular vision in the better eye.
However, laboratory studies of binocular versus monocular visual acuity
based on small samples of young normal adults with equal acuities in
the two eyes have shown a 10% to 12% advantage for binocular viewing
under high luminance, high contrast conditions.
8 9 10 The
AMA and better-eye algorithms do not allow for this “binocular
summation.” One laboratory study demonstrated that reduced luminance
or contrast can increase the summation to as much as
50%.
10 Many older adults have reduced retinal illuminance
caused by senile miosis and nuclear sclerosis. In addition, some may
experience reduced retinal contrast due to light scatter from early
cataract. Therefore, we might expect binocular summation to be greater
in older subjects than in young normal subjects. Indeed, one study of
16 older adults (mean age, 62.5 years) showed a 30% improvement in
binocular compared with monocular acuity.
11
Conversely, numerous studies of contrast sensitivity have shown that
when the sensitivities of the two eyes differ, binocular sensitivity
may be worse than the sensitivity of the better eye. The AMA algorithm
incorporates this form of “binocular inhibition,” but its
applicability to visual acuity data is uncertain. Normal subjects show
modest binocular acuity summation even when the target to one eye is
reduced in contrast.
8 Cataract patients with unequal
cataract densities in the two eyes show neither summation nor
inhibition for high contrast letters
12 and inhibition for
low contrast letters.
11
Previous epidemiologic studies of vision impairment have generally
measured monocular acuities,
13 14 whereas studies of
physical disability have typically obtained a subjective assessment of
visual function based on reported difficulty seeing with both eyes
(e.g., the Massachusetts Health Care Panel Study
15 and
EPESE Study
16 ). The Salisbury Eye Evaluation (SEE) was
initiated in 1992 as a multidisciplinary study of eye disease, vision
impairment, and physical disability in older Americans. In the SEE
project, visual acuity was measured monocularly and binocularly. In
addition, self-report and performance-based measures were obtained for
a variety of visual tasks under natural binocular viewing conditions.
This provides an opportunity to determine how binocular acuity is
related to monocular acuity and how both are related to difficulty with
visual tasks.
A complete description of the study population and recruitment
procedures has been published previously.
17 Briefly, a
sample of individuals living in the Salisbury, Maryland, metropolitan
area 65 to 84 years of age was drawn from the Health Care Financing
Administration (HCFA) Medicare eligibility lists. This sample included
100% of the identified African-American residents and an
age-stratified random sample of 58% of identified white residents.
After informed consent was obtained (in accordance with the Declaration
of Helsinki) using forms approved by the institutional human
experimentation committee, a 2-hour in-home interview was administered
to each participant followed by a 4- to 5-hour clinic examination. To
be eligible for the study, the participant could not be
institutionalized and had to score 18 or greater on the Folstein
Mini-Mental State Examination.
18 Two thousand five hundred
twenty participants completed the home interview and clinic
examination. Testing took place between September 16, 1993 and
September 26, 1995.
The overall participation rate was 65%, excluding the ineligibles.
Approximately half of those who refused (refusals) agreed to answer a
brief subset of the home questionnaire.
19 Those refusing
were somewhat older, more likely to be female, and less likely to have
completed high school than those who participated. Refusals were also
more likely to report difficulty with activities of daily living than
participants. There were no significant differences between
participants and refusals by race or self-assessed vision status.
As part of an extensive psychophysical test battery, visual acuity
was evaluated with the Lighthouse ETDRS distance charts
transilluminated with the Lighthouse Chart Illuminator (Lighthouse
International, New York, NY) to a level of approximately 130 (candela)
cd/m2. Acuity was tested at 3 m. If the
participant was unable to read the largest letters on the chart, test
distance was reduced to 1.5 m and testing repeated. This procedure
was repeated until an acuity measure was obtained or the participant
failed at a distance of 1 m. Only five participants failed to read
any letters with either eye. A strict forced-choice testing procedure
was used: The participant was required to guess even if the letters
appeared illegible until at least four of five letters on a row were
named incorrectly.
Acuity was measured binocularly then monocularly (right eye followed by
left eye) with the participant’s habitual refractive correction. If
the acuity was worse than 20/30 with either eye, then a complete
subjective refraction was performed using autorefractor findings as the
starting point. If acuity improved more than one line (≥0.1 logMAR)
after subjective refraction, then binocular acuity was remeasured using
the new refraction worn in a trial frame. Acuity measurements for the
binocular, right eye, and left eye conditions were made with different
versions of the ETDRS chart.
Ten participants were unable to identify letters because of illiteracy
and the Lea Symbols Chart was substituted. The Lea Symbols Chart has
the same layout at the ETDRS chart but uses four pictorial optotypes
instead of letters.
20
Reading performance was tested with a computer-controlled video
display. Short passages of text were displayed for up to 15 seconds and
the participants read aloud. Four print sizes were tested ranging from
0.13° (about the size of small print on medicine bottles) to 0.53°
(about the size of a small newspaper headline). Each print size was
tested twice, in random order. Face discrimination was measured with a
four-alternative forced-choice paradigm. Sixteen faces (eight male,
eight female) were digitized in each of four poses. The faces subtended
2.5° (horizontal, ear to ear) by 3.2° (vertical, chin to forehead).
Three different poses of one individual and a fourth pose of another
individual were displayed on a monochrome monitor. The participant had
to choose the odd image. Fifteen trials were presented in random order.
Visual disability was assessed with the Activities of Daily Vision
Scale, or ADVS.
3 The ADVS is a 22-item questionnaire that
assesses difficulty performing a range of vision tasks that were judged
to be important to cataract patients. Trained interviewers administered
the ADVS as originally published, excluding one question on the use of
bus service, which is not available in Salisbury. For each item, it was
determined whether the participant had done the activity within the
past 3 months, and if not, was this because of vision problems.
Activities that were not done recently for reasons unrelated to vision
were not scored. The remaining items were scored according to level of
difficulty (1 = unable to do because of vision problems; 2 =
extreme difficulty; 3 = moderate difficulty; 4 = a little
difficulty; and 5 = no difficulty).
Visual acuity was scored as the total number of letters read
correctly and converted to logMAR (log
10 minimum
angle resolvable) according to the method recommended by Bailey et
al.
21 Briefly, each correctly identified letter reduced
the logMAR acuity by 0.02. Participants who failed to read any letters
were arbitrarily assigned an acuity of 1.7 logMAR (20/1000), 0.2 logMAR
worse than the lowest acuity measured. The relationship between
monocular and binocular acuity was evaluated with scatter plots and
regression analyses. The analyses were repeated after exclusion of the
five participants with unmeasurable acuities, and the results did not
change.
For the reading test, the number of correctly read words was counted
and converted to reading rate in words per minute. Reading data were
analyzed separately for each letter size. Participants who could not
read text of any size were excluded from the analyses of reading
performance. Reading data were missing for 211 participants (8%),
either because they could not read (87) or because of equipment
malfunction (124). Among those who could not read, 55 (62%) had
acuities of 20/40 or better and were presumed to be illiterate. The
relationships between visual acuity and reading rate were similar for
all letter sizes, and only the data for newsprint-sized text (0.26°)
will be presented here. Face recognition was scored as the number of
correct responses in 15 trials. Face recognition data were missing for
124 participants (5%) because of equipment malfunction. The ADVS score
was computed by averaging all scored items and rescaling to a range of
0 to 100, where 0 = unable to do any activities because of vision
and 100 = no difficulty with any activity.
Separate linear regression analyses were used to determine the
association between acuity and reading or face recognition. Both
analyses were adjusted for age, race, gender, years of education, and
Mini-Mental score. Residuals were evaluated for evidence of
nonlinearity, and, where appropriate, linear spline regressions were
also performed.
22
The ADVS scores were highly skewed; therefore, it was felt to be
inappropriate to use continuous linear regression. Instead, logistic
regression analyses were performed to determine the association between
acuity and dichotomized ADVS score. Regression models for each of the
binocular and monocular acuity algorithms were compared by means of
their receiver-operating characteristic (ROC). As it is used here, the
ROC provides a metric for determining each algorithm’s ability to
classify individuals with regard to their dichotomized ADVS
scores.
23 At any acuity level, the regression model
predicts whether each participant will fall above or below the cutoff.
The prediction can be compared with actual data to determine proportion
of participants correctly predicted to fall below the cutoff, or
sensitivity, and the proportion of participants incorrectly predicted
to fall below the cutoff, or false-positive rate, as a function of
acuity. Separate analyses were conducted with ADVS score dichotomized
at the median, 25th percentile, and 10th percentile. Because the
results were similar for all three dichotomization schemes we will only
present results for the case where participants were classified as
falling above or below the 10th percentile in ADVS score (70.8). Each
model was adjusted for age, race, gender, years of education, and
Mini-Mental score. All statistical analyses were performed with SAS
(SAS Institute, Cary, NC).
The median best-corrected binocular acuity of this sample of 2520
older participants is −0.02 logMAR (20/19) with 4.8% of the sample
having acuities worse than 0.3 logMAR (20/40). The median monocular
acuity in the better-seeing eye is 0.00 logMAR (20/20), and the median
worse-eye acuity is 0.12 logMAR (20/26). The prevalence of visual
impairment in this population is somewhat lower than that reported for
earlier population-based studies. For a further discussion of how
visual acuity varies according to demographic factors and how these
acuity data compare with other population-based studies see Rubin et
al.
24
Figure 1 (left) compares binocular acuity to the AMA-recommended weighted
average of monocular acuities. If the AMA weighted average accurately
predicted binocular acuity, the data would be expected to cluster along
the diagonal line. However, most of the points are below the diagonal,
indicating that the AMA weighting predicts worse binocular acuity than
what is actually measured.
Figure 1 (right) shows the discrepancy between predicted acuity, based
on the AMA algorithm, and observed binocular acuity in terms of number
of ETDRS lines. This discrepancy is plotted against the interocular
acuity difference for each participant. For participants with similar
acuities in the two eyes (i.e., interocular difference of 1.0 ETDRS
line or less), the discrepancy averages only 0.4 lines. However, for
participants with dissimilar acuities in the two eyes, the discrepancy
increases at a rate of one line of discrepancy per five lines of
interocular acuity difference. Thus, the greater the difference between
eyes, the worse the algorithm predicts actual acuity.
Figure 2 (left) compares binocular acuity to acuity in the best eye alone. The
data cluster along the diagonal line, indicating good agreement between
the best-eye prediction and the observed binocular measurement. The
discrepancy between binocular acuity and best-eye acuity, shown in
Figure 2 (right), averages less than 0.2 ETDRS lines (1 letter), well
within the test–retest variability.
25 26 27 28 For 85% of
participants (2170), the discrepancy between binocular and best-eye
acuity is less than one ETDRS line (5 letters). There is a small but
statistically significant change in the discrepancy with increasing
interocular acuity difference (0.2 lines of discrepancy per five lines
of interocular difference). This trend is examined in greater detail
below.
The distribution of the difference in monocular acuities between the
two eyes is shown in
Figure 3 . The median interocular difference is 0.09 logMAR, or 0.9 lines on the
ETDRS acuity chart. Eleven percent of the population have an
interocular acuity difference of three or more lines.
It was hypothesized that binocular summation would occur when the
monocular acuities of the two eyes were nearly equivalent but that
there would be binocular inhibition when the acuities of the two eyes
were dissimilar. In keeping with previous terminology we refer to the
difference between logMAR acuity in the better eye and binocular logMAR
acuity as “binocular gain.” Positive gains indicate summation and
negative gains indicate inhibition. Incidentally, binocular gain is the
same as the discrepancy between binocular acuity and acuity in the
better eye, as shown in the right panel of
Figure 2 . Binocular gain was
independent of the underlying monocular acuities in the better- or
worse-seeing eye, but varied with the interocular acuity difference.
Figure 4 shows the distribution of binocular gain grouped according to the
similarity of monocular acuities in the two eyes. Among participants
with similar acuities in the two eyes, 38% show one line or more
binocular summation, whereas only 10% show one line or more
inhibition. The average summation for the group is 0.03, or
approximately 1.5 letters. Although the amount of binocular gain is
statistically significant (
t = 18.5,
P < 0.0001), the gain is of little clinical significance, amounting to
less than one half of one acuity line. For the groups with dissimilar
acuities in the two eyes, 20% to 29% show summation and 19% to 23%
show inhibition. The average is less than one letter of inhibition for
each of the groups with dissimilar monocular acuities. These data are
consistent with modest binocular summation when the two eyes are nearly
equivalent, but there is no evidence of binocular inhibition when one
eye is better. It might be argued that the fixed order of the acuity
tests (binocular, right eye, left eye) could have lead to practice or
training effects that would mask some of the binocular gain. However,
in approximately 30% of participants binocular acuity was remeasured
at the end of the protocol after subjective refraction. When binocular
gains between the two groups were compared (binocular acuity measured
first versus binocular acuity measured last), practice effects were
negligible. The binocular gain in the latter group was 0.04, or 2
letters, compared with 0.03, or approximately 1.5 letters, in the
former group. The difference between groups is statistically
significant (
t = 2.3,
P < 0.05) but
too small to be of clinical significance.
Regression analyses showed a significant association between binocular
acuity and both of the visual performance measures: reading newsprint
and recognizing faces. Inspection of residuals indicated that the
relationship between acuity and reading was nonlinear. Therefore,
linear spline regressions were performed with inflections at acuities
of 0.00 logMAR (20/20) and 0.47 logMAR (20/60). The regression
coefficients are shown in
Table 1 . After adjustment for age, race, gender, cognitive status, and years of
education, a one-line loss of binocular acuity predicted an 8.9 (±1.9)
words/min decline in reading rate for acuities up to 20/20 and 32.4
(±1.5) words/min decline for acuities between 20/20 and 20/60. For
acuities worse than 20/60 there was little additional change in reading
rate. The regression model accounted for 50% of the variance in
reading rate and the independent contribution of binocular acuity to
the association (additional 18% of the variance accounted for) was
statistically significant (
P < 0.0001).
The relationship between binocular acuity and face recognition accuracy
was also nonlinear, with a single inflection at approximately 0.47
logMAR (20/60). A one-line loss of binocular acuity was associated with
0.52 (±0.04) fewer correct responses for acuities up to 20/60 and
slightly less change in performance for acuities worse than 20/60
(0.50 ± 0.11). The regression model accounted for 36% of the
variance. The independent contribution of binocular acuity to the
association, although small (additional 6% of variance accounted for),
was statistically significant (P < 0.001).
ROC analysis was used to determine the association between acuity and
ADVS score. The area under the ROC is the metric for comparing
algorithms. If the algorithm is a perfect classifier the sensitivity
will be 1, the false-positive rate will be 0, and the area under the
ROC will equal 1.0. If the algorithm performs at chance the sensitivity
will be equivalent to the false-positive rate and the area under the
ROC will equal 0.5. The ROC area was 0.78 for baseline variables plus
binocular acuity.
Table 2 compares the strength of the association between the three outcome
measures and each of the binocular and monocular acuity combination
rules. All of the combination rules are equivalent when there is no
interocular acuity difference. Because one half of the observers have
less than a one-line difference in acuities between the two eyes, one
would expect little difference among the algorithms when they are
applied to the entire data set. This was indeed the case, as shown in
the left half of
Table 2 . As a stronger test of differences between
combination rules, the regression models were refit to the subset of
data for participants with more than three lines of interocular acuity
difference (
n = 261). The summary statistics are listed
in the right half of
Table 2 . For reading speed, binocular acuity and
monocular acuity accounted for 65% and 63% of the variance, whereas
the AMA and FVS algorithms accounted for only 49% and 52%,
respectively. For face recognition and ADVS score the four models still
yield nearly equivalent results.
The results illustrated in
Figure 2 demonstrate that binocular
visual acuity can be closely predicted by the monocular acuity of the
better eye. There is no support in our data for the widely used AMA
weighted-average algorithm as a predictor of binocular acuity. When the
acuities in the two eyes are similar, the AMA algorithm is equivalent
to the better-eye acuity; however, as the acuities of the two eyes
diverge, the AMA algorithm seriously underestimates the measured
binocular acuity, as shown in
Figure 1 .
Based on previous studies with small groups of subjects it was expected
that our participants with similar acuities in the two eyes would show
binocular summation (i.e., the binocular acuity would be better than
the monocular acuity in the better eye).
Figure 4 shows that there is a
small binocular summation, 0.03 logMAR units or 1.5 letters on average
for the group with less than a one-line acuity difference between the
two eyes. Although the binocular summation is statistically significant
(
t = 18.5;
P < 0.0001), it is about
half that reported in previous studies
8 12 and of doubtful
clinical significance. All the participants in the present study were
65 years of age and older. The previous studies included younger and
older subjects. However, age itself is unlikely to explain the
discrepancy because one of the previous studies
12 compared
binocular summation for younger (21 ± 2 years) and older (66 ± 6 years) subjects and found that the summation for the older group
was somewhat greater than for the younger group.
It was hypothesized that binocular summation would be greater in the
present study than in previous studies with younger observers because
summation is enhanced under conditions of reduced retinal illuminance
or contrast,
10 both of which are common in the elderly,
even among those without frank eye disease. Weale
29 has
estimated that there is an overall two- to threefold reduction in
retinal illumination from 20 to 60 years of age, mostly caused by
increased lenticular absorption and pupillary miosis. Age-related
increases in intraocular light scatter reduce retinal image
contrast.
30 31 32 Given these ocular changes and resultant
loss in illumination and contrast at the retina, we expected to see
greater binocular summation in participants with equal vision in the
two eyes. The absence of such an effect may indicate that the
age-related loss of retinal illumination and contrast is small compared
with that required for a change in binocular summation. On the other
hand, previous studies of binocular contrast
33 and
luminance summation
34 have shown a decrease rather than an
increase in summation with advancing age.
Our results also show less than a one letter difference, on average,
between monocular and binocular acuities for participants with unequal
acuities in the two eyes. Equal numbers showed binocular inhibition and
binocular summation. Previous data on individuals with unequal
monocular acuities have been equivocal. One study of unilateral
cataract patients showed minimal binocular inhibition, averaging 0.05
logMAR (2.5 letters),
35 one study showed minimal summation
(also averaging approximately 0.05 logMAR),
36 and two
studies showed neither inhibition nor summation.
11 12 A
detailed study of four subjects with normal vision in whom the contrast
of the targets presented to one eye was reduced showed no binocular
inhibition.
8 Thus, there is little consistent evidence for
significant binocular inhibition.
This study also demonstrates that the influence of visual acuity on the
performance of everyday tasks can be accounted for by monocular acuity
in the better eye. Considering all participants in the study, monocular
acuity in the better eye was as good a predictor of performance as
binocular acuity or algorithms based on weighted sums of monocular
acuities. However, the various algorithms are differentiated only for
people with significant discrepancies between the acuities in the two
eyes. For the subset of participants with interocular acuity
differences greater than three lines, monocular acuity was equivalent
to binocular acuity and both were as good or better predictors of
performance than the weighted monocular acuity algorithms.
In comparing the various algorithms, all analyses were based on
best-corrected visual acuities. One might expect everyday visual
function to be more closely associated with habitual acuity than with
corrected acuity. However, a recently published study by Wang et al. in
this journal
37 showed that best-corrected acuity was a
better predictor of self-rated health than was habitual acuity. When we
reanalyzed the present data using habitual binocular acuity, the
variance accounted for changed by no more than 1% compared with
analyses based on habitual acuity.
One implication of this study concerns the expected benefit of
second-eye cataract surgery. If binocular acuity, self-reported visual
function, and performance are controlled by acuity in the better-seeing
eye, then second-eye surgery should have little effect on acuity,
visual function, or performance. However, results from a prospective
study of 613 patients undergoing cataract surgery showed similar
improvement in subjective visual function for first-eye and second-eye
surgeries.
38 The results of two smaller studies may help
explain the apparent paradox. The first study showed significant
changes in reading speed, face recognition, mobility performance, and
perceived visual disability after second-eye surgery.
39 In
the second study there was a marked decrease in reported symptoms, and
all patients reported that their vision had improved after
second surgery.
40 Although statistically
significant, the acuity differences in both studies were small and
comparable to the average difference between monocular and binocular
acuities reported in the present study. The authors attribute much of
the subjective improvement to gains in contrast sensitivity,
binocularity, and other visual factors that may not be captured by
tests of acuity alone. Therefore, although the gains in binocular
acuity after second-eye cataract surgery may be modest, the effect of
such surgery on overall visual ability can be substantial. It is
important to consider that visual acuity is certainly not the only or
perhaps even the best predictor of function. We
41 and others
42 have shown that contrast sensitivity is an
important predictor of self-reported difficulty with daily visual
activities among the elderly.
In summary, the widely used AMA algorithm does not provide an accurate
method for predicting binocular visual function when the acuities in
the two eyes are dissimilar. If a measure of binocular acuity is not
available, it may be inferred from acuity in the better-seeing eye. For
tasks that are strongly associated with visual acuity, such as reading,
this association can be captured by monocular acuity in the
better-seeing eye rather than the weighted average of acuities in the
two eyes.