I replied to Mr Eaton via email beofre I knew about this Mailing List, and I 
thought it may be usefull to post my reply here too.

====

Dear Mr Eaton,
 
I was forwarded your email of 14/01/10 regarding the measurement of 
uncertainty. I hope you don't mind me replying to you directly, but I think you 
may be interested in some of the work I have done on this topic.
 
Perhaps I should first explain my background. I am a BMS 1 band 6 currently 
working at the Hull Royal Infirmary, and have spent the last 3 or so years 
looking closely at the statistics of QC and Total Error (as described by James 
Westgard). Being an amateur computer programmer, I have also written 
numerous statistical programs that allow me to calculate how different QC 
approaches effect analytical results.
 
The calculation of uncertainty for an analytical test should incorporate four 
variables: 
 
-the CV of the analyser
This should be calculated over as many results as possible. Westgard suggests 
20 as a bare minimum, but I regard this as drastically under-powered. the EP5-
A document suggests 80 results, and Shewhart suggested 340 as a minimum.
 
-the ability of the QC rule used to control the analyte
Each QC rule has a different ability to pick up analytical error (systematic and 
random). e.g. a QC rule of 1 result out of +/-3sd can pick up smaller amounts 
of systematic error than say 1 result out of +/-10sd. Thus it is important to 
include in our calculation just how much error we can pick up with our adopted 
QC rule.
This can be calculated through the use of Power Function analysis (as 
described by Westgard here: http://www.westgard.com/lesson4.htm).
I have written my own software to calculate power functions, and thus the 
ability of different QC rules.
The amount of error picked up by a rule is termed Critical SD (SDcrit).
Westgard determined that the most efficient 'power' to run QC at is 90%, thus 
SDcrit is the amount of error picked up 90% of the time by the QC rule.
 
-the allowable defect rate for the test 
termed 'z' and is usually set at 1.65 to allow a minimal defect rate of 5% i.e. 
5% of results could have errors above the Total Error we will calculate.
 
-the bias of the analyser 
as a % and can be from EQA or other internal bias measurements.
 
 
The equation for Total Error is:
 
Total Error (%) = CV(SDcrit + 1.65) + Bias
 
 
For example,
An analyser set up to use a QC rule of 1 result out of +/-2.5SD using 3 QC 
materials, gives an SDcrit of 2.584 
(as calculated by my Power Function computer program).
 
Given an analytical CV of 1.895% and a bias of 0.1% the Total Error for this 
test is:
 
TE = 1.895 * (2.584 + 1.65) + 0.1
TE = 8.1%
 
Thus any creatinine result generated from the analyser (assuming that the QC 
is in) has a potential amount of error (or 'uncertainty') of +/- 8.1%. Or in other 
words, the true creatinine result is no more than 8.1% away from the result 
generated on the analyser.
 
Note that for this example, the analyser meets the Total Error requirements for 
the American CLIA standards (TE should be less than 15%), and also the 
standards set by Total Error based on Biological Variation (see here: 
http://www.westgard.com/biodatabase1.htm , TE should be less than 8.2%).
So, all is well for this test.
 
Another example,
Say we changed the QC rule for the analyser to 1 result out of +/- 5SD. Still 
using 3 QC materials the SDcrit here would be 5.08.
 
Thus the Total Error in this case would be
 
TE = 1.895 * (5.08 + 1.65) + 0.1
TE = 12.9%
 
Notice, that all we have done here is change the QC Rule we are using, 
nothing else has changed. We have adopted a new rule that will allow a larger 
amount of error to occur before we detect it, thus there is a larger amount of 
uncertainty in the final result.
 
For this example we would be daft to change the QC rule in this way, as now 
we are outside of the suggested Total Error based on Biological Variation, but 
note that we are still within the CLIA standards (i.e. less than 15%). As such, 
we could happily set our QC rule at +/-5SD and still meet CLIA standards. 
 
In the UK we (ashamedly) have no such TE standards: however, I believe the 
requirement for estimation of uncertainty by the CPA is a good step towards 
generating our own standards. Also, at the recent WEQAS user group meeting 
in Cardiff, they discussed introduction of Total Error goals in their EQA reports.
 
 
I shall stop waffling on here, but please reply if you would like to discuss this 
further, or indeed want a copy of some of the QC programs I have written, 
which I would be glad to forward to you (for free, of course).
 
 
Best regards,
 
Andy Minett
BMS 1
Hull and East Yorkshire Hospitals NHS Trust
Hull
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