Variations in PLTT measurements may be due to real differences
among subjects in their PLTT levels, lability of PLTT over the short
period of repeated measurements, and measurement error. In order for
our technique to be useful for clinical research, we must be certain
that the phenomenon being measured does not vary so widely in a short
period (lability) that it cannot be measured reliably and that our
readings agree closely when taken under virtually identical conditions
on separate occasions (repeatability). After examining our within-visit
data, we calculated mean values and 95% confidence intervals for mean
PLTT at each visit, and examined difference-versus-mean plots and
calculated 95% limits of agreement (LA) as suggested by Bland and
Altman
8 to assess the repeatability.
We estimated a subject’s PLTT in each eye by taking the average of the
four repeat measurements per visit. If the tear film under the CL was
relatively stable during the two measurement periods, this approach
reduced sampling bias and allowed us to better estimate a subject’s
PLTT. We therefore explored our within-visit data to determine whether
short-term stability is a reasonable assumption for our subjects’
PLTT. The results are shown in
Figures 5 and 6 .
The differences between the two 15-minute and between the two 25-minute
postinsertion measurements were relatively small, as were the
differences between the average 15-minute and 25-minute measurements. A
plot of each subject’s mean 15- and 25-minute measurements connected
by a straight line, for both eyes at visit 1 and at visit 2
(Fig. 5) ,
displays no obvious 15- versus 25-minute trends.
Figure 6 shows the
difference between the 15- and 25-minute measurements plotted against
their mean, with horizontal dashed lines at the mean difference ±
2 standard deviations. In this figure the mean differences between 15-
and 25-minute measurements are very close to zero and there does not
appear to be any obvious dependence of the differences on the magnitude
of the mean. From this examination of the data we conclude that the
PLTT is relatively stable in the short-term and that it is a reasonable
approach to estimate a subject’s PLTT by averaging the four repeat
measurements taken on each eye within this short period after lens
insertion.
Using the approach described above, we examined the estimated
values of PLTT and assessed their repeatability across visits.
Histograms of all PLTT data were examined to verify normality
assumptions. In
Figure 7 a box plot shows the key features of the distributions of PLTT for each
eye on both visits. The horizontal line inside each box represents the
median value, and the top and bottom of the box mark the 75th and 25th
percentiles, respectively. The vertical lines extending from each box
indicate the maximum and minimum PLTT values. The mean values (95%
confidence intervals) for PLTT in the right eye for visits 1 and 2 are
11 (8, 13) and 12 (10, 15) μm, respectively, and in the left eye for
visit 1 and visit 2 are 12 (10, 15) and 11 (8, 14) μm, respectively.
These results suggest that our technique yields reasonable estimates of
the PLTT on average, which are similar across visits. The repeatability
of our technique is illustrated in more detail below.
The 95% LAs, defined as the mean difference ± 1.96 SD (assuming
normality), are −16, 13 and −12, 13 μm for OD and OS, respectively.
That is to say, PLTT measured on the second visit may be as much as 16μ
m below or 13 μm above that of the first visit. Because we are
estimating the 95% LA for both eyes simultaneously, our overall type I
error probability is actually larger than 0.05. Using Bonferroni’s
correction, we adjusted the confidence level for each set of limits
such that the overall type I error rate (i.e., for looking at both eyes
simultaneously) remains 0.05, obtaining slightly broader LA of −19, 15
and −13, 15 μm for OD and OS, respectively.
Figure 8 shows the mean PLTT at visits 1 and 2 (connected by a straight line)
for each eye of our 21 subjects. Although inspection of the plot
reveals no obvious systematic differences between the two visits, there
were three right eyes and three left eyes with differences in estimated
PLTT greater than 10 μm and three individual negative PLTT estimates.
The difference-versus-mean plots for comparing visit 1 to visit 2
(Fig. 9) show that the mean difference between the two visits is very close to
zero.
The fairly wide LA and negative PLTT estimates are due to the
many sources of measurement error (see the Discussion section) and
suggest that the technique is not sufficiently precise to reliably
monitor PLTT on individual subjects. However, the technique may be
appropriate for estimating the PLTT in group studies of sufficient
sample size. To investigate the feasibility of this application of our
technique, we estimated the sample sizes needed to detect various
differences in PLTT between two groups of lens wearers with 95%
confidence and 80% power.
Table 2 presents the estimated sample sizes required for group studies of PLTT.
Because these estimates are directly dependent on the variance of the
measurement, we examined the variances in PLTT for each eye and visit
and chose the largest variance (left eye, visit 2, variance =
43.55), which resulted in the most conservative sample size estimates.
Because the other three variances (36.14, 36.70, and 37.23) were all
similar and smaller than the one used in the above calculations, we
repeated the sample size estimates using the second-largest variance of
37.23, which may better reflect the variability typically encountered
in PLTT measurements. The more conservative sample size estimates
ranged from 6 subjects per group (to detect a 7-μm difference in
PLTT) to 38 subjects per group (to detect a 3 μm difference), showing
that this technique is sufficiently precise for use in group studies of
PLTT with moderate numbers of subjects.