I have been following the discussion on estimation of uncertainty with much interest. However, I am concerned that the interchangeability in the use of the terms total error (TE), total error allowable (TEa) and measurement uncertainty (U) may be confounding the understanding and application of these inter-related concepts.
The concept of measurement uncertainty is meant to reflect the actual variation of a measured result, not its potential to be in error. While it is true that any given QC procedure will allow for a certain amount of error before detection, this does not mean that the uncertainty of a measured result is impacted to the full extent of that potential error. Let me illustrate my point with the following example:
CV = 1.895%, bias = 0.1%. Suppose the QC procedure used gives an SDcrit of 2.584, then
TEa = CV(SDcrit + 1.65) + bias
TEa = 1.895(2.584 + 1.65) + 0.1 = 8.1%
Note that this is total error allowable, not total error. Total error would be:
TE = (CV x 1.96) + Bias
TE = (1.895 x 1.96) + 0.1 = 3.8%
Uncertainty (U) would be calculated (using a coverage factor of 2) as follows:
U = CV x 2
U = 1.895 x 2 = 3.8%
Other contributing sources of uncertainty (such as calibration uncertainty) can be included if known in the estimation of uncertainty (by adding in quadrature). Note that bias is not included as it is assumed that any significant bias is corrected and if so the uncertainty of this correction can be included.
Now, let us say the performance of this assay changes such that the CV increases to 3.79%, which increases the TE to (3.79 x 1.96) + 0.1 = 7.5%. The total error allowable (TEa) remains the same as it is based on a CV obtained during stable analytical performance. Measurement uncertainty changes to 3.79 x 2 = 7.58%.
One of the provisos of measurement uncertainty and TE is that the variation measured must reflect the real variation of the measurement process across all analytical influences, not just under ideal conditions. On the other hand, the variation for calculation of TEa should reflect stable analytical performance, which we want to use to determine the control procedure for the assay.
Cheers
David Parry
Winnipeg, Canada
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