Combining data from all subjects, the time variation of PLTF thickness was significantly better fit by an exponential decay plus constant
(equation 3) , than by a linear function (F-ratio test,
P < 0.001). This fit is illustrated in
Figure 1 , where the ordinates of the plotted points are given by
\[{\bar{h}}(t)\ {+}\ {[}{\bar{H}}{^\prime}({\infty})\ {-}\ {\bar{h}}{^\prime}({\infty}){]}\]
where h̄(
t) is the average for all subjects with valid measurements at time
t, h̄′(∞) is the average of
h′
i (∞) (see
equation 3 ) for those same subjects, and H̄′(∞) is the average of
h′
i (∞) for all subjects. The term [H̄′(∞)-h̄′(∞)] corrects for differences between the subjects with valid measurements compared to all subjects. Compared to the simple average, h̄′(∞), this method of plotting causes an unbiased reduction in the scatter of the data, particularly when there are many missing data points and when there is considerable variance in the individual estimates of the parameters
h′
i (∞). The fitted curve was determined from
equations 3 and 4 , averaged for all subjects; it is given by
\[{\bar{H}}{^\prime}({\infty})\ {+}\ Ce^{{-}t/t_{0}}\]
The final average thickness, H̄′(∞), was 2.47 ± 0.92 micrometers; the time constant of the exponential decay,
t 0 (equation 3) , was 7.1 minutes, and its amplitude,
C, was 2.0 micrometers; thus the initial thickness, H̄′(∞)+
C, was approximately 4.5 micrometers. Nine of 12 subjects showed a significantly better fit (F-ratio test,
P < 0.05) with an exponential decay plus constant compared to simply a constant thickness.