At 2001-12-03 16:30 +0000, Roger Ekins wrote:
>Thanks for the compliment, but I was not trying to be
thoughful, >provocative, etc, nor trying to beat Jonathan about the head.
Roger is well-informed indeed. May I add some comments.
If we only talk about "sensitivity" etc in its meaning of method
performance we can start with the formula:
V = Vo + b + e
(Yes, b and e should be the greek letters beta and epsilon and the little
"o" should occur rised, but for typographical reasons, let it stand like this).
where:
V is the apparent reading of an analytical value
Vo is the "exact" value of this sample
b is the bias (also called systematic error and sometimes inaccurracy)
e is the random error.
b and e can be positive or negative real numbers. All terms have the same
unit, e.g. mmol/L.
An analytical procedure usually requires several steps, from sampling to
the final answer. Each of these steps are prone to introduce bias as well
as random errors, b1, b2, b3... and e1, e2, e3...
Hence:
b = b1 + b2 + b3 ...
e = e1 + e2 + e4 ...
It is possible to determine the random error by repetitive analysis of one
sample. Usually e is expressed as a standard deviation or a CV value. The
determination of e will be more accurate the higher number of measurements
you do. On the other side - beware of degradation and other temporal effects!
SD is truely Gaussian distributed and its SD is: SD*SQR(2/n) and hence you
can calculate how many measurements you need until you have the desired
precision in the determination of e. Note: this parameter is, by
definition, free from bias!
The determination of b on the other side is not that simple, because the
value Vo is seldomly known uncontroversially. Nevertheless, you must use
the best estimate available. This can be an exactly weighed amount of a
chemical of highest analytical purity (e.g. calcium carbonate for calcium
measurements), a WHO primary standard, or a value obtained using a method
certified as a reference method.
You must also consider all probable sources of bias e.g. chemical,
microbiological and enzymatic degradation, water and carbon dioxide
evaporation etc.
If you avoid such sources when the method is evaluated but then neglect
them in the clinical routine, your evaluation will be misleadingly "too good".
>Possibly my fault, but Trevor Tickner (and Sten Öhman) seem to be
>interpreting my reference to "sensitivity" in the arcane sense in which
>the word is used by chemical pathologists (which is not, incidentally,
>mentioned in the OED). "Sensitivity" and "specificity" as thus used have
>nothing to do with these words' use to describe a measuring system's
>analytical performance - though the precision (or imprecision) of an
>analytical method (used in a clinical diagnostic setting) at decision
>points on the analyte concentration range obviously has a significant
>effect on the probability that tested subjects will be correctly diagnosed.
These words are used in clinical chemistry both in evaluation of an
analytical method and its ability to confirm and/or reject certain
diseases. We should use different words for these parameters, but it may
take time until this happens.
The ANALYTICAL sensitivity is currently defined as the slope of the
calibration curve. However the ability of a method to certainly distinguish
between concentrations close to each other does not only depend on the
slope. A precise method with a low slope may be better than an imprecise
method with a high slope.
A better parameter for the analytical sensitivity should be the parameter e
above, as determined in a concentration range close to the decision
limit(s). Of course, also confidence interval (CI) in that range should be
useful. This is seldomly done probably because it too overtly displays the
imprecision of the method.
Who want to answer: "Blood glucose is estimated to 5.0 mmol/L, 95% CI = 4.0
to 6.0 mmol/L".
The word "sensitivity" is sometimes also confused with the limit of
detection. This parameter is easy to determine. It is the lowest
concentration that is significantly distinguishable from a true blank
value. Hence make repeated measurements of a true blank and determine its
one-sided 95% CI.
>The "slope" definition adopted by IUPAC and the WHO is demonstrably absurd,
As indicated above: I agree!
Mr Sten Öhman, PhD
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