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.