Dear Mr Dooley,
 
Respectfully, I wanted to suggest that a calculation described here in the 
responses would perhaps lead to an incorrect assessment of uncertainty.
 
Specifically:
 
"...we used the combined QC data from all analysers which perform the test in 
question. We then calculated the SD from the combined data for each level of 
qc and used +-1.96 * SD as the 95% confidence interval."
 
This is something I have come up against here in my current lab, and is an 
incorrect assumption because of the following reasons.
 
The Mean and SD of an analyser is a description of how it generates results. 
By combining the data from individual analysers and calculating the mean and 
SD from this, we now have an analytical description that fits none of the 
analysers individually, nor the laboratory as a whole (which I think is your 
reason for combining data like this?).
 
This can be shown in the following way.
Imagine three hypothetical analysers all performing the same test. These are 
their statistics:

Analyser 1...Mean = 100, SD = 1
Analyser 2...Mean = 100, SD = 2
Analyser 3...Mean = 100, SD = 3
 
(i.e. the only difference between these analysers is their imprecision)
 
If we combined the data from these analysers for say, 3,000,000 QC results, 
that data set would have the following stats:

Combined Data...Mean = 100, SD = 2.16
 
Thus this data no longer accurately describes our Analyser 3. Calculated 95% 
confidence intervals on the combined data would only apply to analysers 1 and 
2 (in fact analyser 1 would have better confidence intervals than that 
calculated). The uncertainty in analyser 3 would be much greater than the 
calculated confidence interval. Note also, that this is before we try to begin to 
assess the differences in mean values between the analysers.
 
 
In fact, this is a topic that I have spent a lot of time on recently, as I was 
asked to calculate what our global (i.e. across the whole lab) Mean and SD 
would be. The idea being that if a specimen arrived in the lab and went on any 
of our 6 main biochemistry analysers, what would be the worst-case statistics 
for that specimen's results?, as a Total Error.
 
I went about it in this way...
 
Find the mean and sd for each of the 6 analysers (for each test, and for each 
QC level of those tests).
Work out the 'global mean' for the analysers (sum the means, divided by 6, for 
each QC level)
Work out the 95% confidence intervals for each individual analyser.
Work out the largest difference between the means +/- 2SD and the global 
mean.
Divide this difference by 2.
This is now the 'global SD' which encompasses all the analytical variability of 
the lab.
 
This data could now be put into the total error equation I explained in 
response to Paul Eaton, again taking into account the ability of the QC rule 
adopted for each test (the SDcrit).
 
I have included an attachment of a screen-shot of the program I designed to 
apply this to our lab.
 
 
 
Best regards,
 
Andy Minett
BMS 1

Hull and East Yorkshire Hospitals NHS Trust

Hull

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