Posted by Sten Westgard, MS
We got an excellent question the other day via email:
I have heard the term "Within QC" and "Across QC"
used, but what do these refer to specifically and
where can I find more information about what is
meant by those terms? I was not able to find this
information, but laboratory leadership staff said
that "Within QC" referred to assessing multi-rules
"within QC level and across QC runs", and that
"Across Qc" referred to assessing multi-rules
"looking at both QC levels, can be within same run
or back-to-back runs".
A lab has the following multi-rules; "Within QC"
1:3s, 1 QC result outside 3sd; 2:2s, 2 consecutive
QC results outside 2sd on the same side of the mean;
4s, 2 consecutive Qc results differ by more than
4sd; and 1:2s, 1 Qc result outside 2sd and within 3.
(1:2s is used as a warning rule, the others as
rejection rules). The rules for "Across Qc" are as
follows; 2:2s, 2 consecutive Qc results (1 each
multiple levels) are outside of 2sd; and 4s, 2 Qc
results (one of each multiple levels) are >4sd
apart. These are both rejection rules. These
multi-rules are used to assess all tests in a
chemistry lab; the majority of tests are assessed
with 2 levels of Qc, a few use 3 levels of Qc.
The situation arose where QC results on one day for
a cancer antigen were the following:
Day 1A:
Level 1 -Within 2sd, acceptable
Level 2 -1:2s, run was accepted as only the warning
rule 1:2s was encountered.
The next day the results were as follows:
Day 2A:
Level 1 -1:2s
Level 2 -Within 2sd
Leadership said run should not be accepted,
violating the "across" 2:2s rule.
However, leadership said the inverse situation would
have been acceptable as *consecutive* data points
did not violate the "across" 2:2s rule, i.e.
Day 1B:
Level 1 1:2s
Level 2 within 2sd
Day 2B:
Level 1 within 2sd
Level 2 1:2s
In the A group, because Level 2 is outside of 2s,
and the very next data point (Level 1 from the next
day) is also out 2s, the run is unacceptable and
should be rejected. In Group B, since consecutive
data points are okay the run is acceptable.
Is this a correct approach? Is it correct to reject
group A (Day 1A and 2A) and not reject group B (Day
1B and 2B)? Do these multi-rules as outlined and
implemented detect some unacceptable variation in
group A that does not exist in group B? Thank you
for any clarification.
So what's the answer? Are scenarios A and B fundamentally different? More after the jump.
We should begin by clarifying terminology, though. We make the following distinctions:
you can interpret "within-run" and "across-run" as well as "within-material/level" and "across-material/level"
We don't use the terminology "within QC" and "across QC," though, because the definition of "QC" is not specific enough.
The first multirule combination mentioned in the scenario would be expressed by the following notation: 1:3s/2:2s/R:4s with a 1:2s "warning rule" all implemented within-run and across-material
The "across QC" multirule combination you write about would be expressed by this notation (if we ignore the first multirule)
2:2s/R:4s across-run, within-material
If we unify the expression of the QC procedure for this laboratory, it would be this:
1:3s/2:2s/R:4s with a 1:2s "warning rule."
[with the following implementation details: 2:2s implemented within-run and across-material, and across-run and within-material. R:4s implemented within-run, across-material and no other way (that is the correct use of that rule)]
Scenarios A and B are basically identical. The interpretation discussed seems more dependent on the order of plotting or reading the data than in the occurrence of the outlier itself. We would recommend that neither scenario represents an out-of-control situation based on the rules you describe. That is, a 2:2s can be in the same run, across-material, or it could be across-run, but within-material. But the 2:2s rule is not usually interpreted as across-run and across-material. So both scenarios discussed would not be interpreted as out-of-control events.
This may seem like splitting hairs. The 2:2s is designed to pick up systematic errors. The scenario you describe is more like a random error of a size that may not be important. 2s outliers occur as often as 9% of runs when you use 2 control materials and 2s limits. That can create a lot of noise.
What would be interesting to study further: what QC is really necessary for this test? Can you define the quality required by the test? What are the estimates of method imprecision and bias? Through QC Design, we could use those numbers to determine the Sigma-metric and objectively design the right QC procedure, which may or may not include some of these rules we're discussing.
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