The variance attributable to measurement error, var(err
DO2), was calculated from the error variances of RBF and S
aO
2, used in the calculation of DO
2 (Eq.
11). As described by Stratton et al.,
48 these error variances need to be derived from calibration. In the absence of a gold calibration standard, the error variance of the RBF was approximated from a previous experiment in an independent population, from the residual variance of RBF fitted on in vivo Laser Speckle Flowgraphy measurements.
24 Because the physiological variation of S
aO
2 in healthy individuals is expected to be minimal, the error variance of S
aO
2 was set as equal to the observed variance of S
aO
2. The corrected slope (b
cor) for VO
2 as a function of DO
2 can then be calculated as:
\begin{equation}
{{\rm{b}}_{{\rm{cor}}}} = \frac{{{{\rm{b}}_{{\rm{obs}}}}-(1-{{\rm{r}}_{\rm{D}}}{\rm{)\;}} \times {\rm{\;}}{{\rm{b}}_{{\rm{err}}}}}}{{{{\rm{r}}_{\rm{D}}}}},
\end{equation}
where b
obs is the observed slope and b
err the slope of measurement errors, which accounts for the covariance of the error in DO
2 and VO
2. We will not demonstrate here the detailed mathematical calculations of var(err
DO2) and b
err, as they are extensively provided in the aforementioned paper by Stratton et al.
48Henceforth, all normally distributed variables are described with the mean and standard deviation. Variables with a skewed distribution are described with the median and interquartile range. All analyses were performed using R (version 3.3.3; R Foundation for Statistical Computing, Vienna, Austria) and SPSS (version 26; IBM Corp., Armonk, NY). A
P value of 0.05 or less was considered statistically significant.