The problem of estimating the performance of a group of instruments is not
easily resolved but there are some points that may be brought forward.
The long established total error concept focuses on the tails of a
distribution by describing the worst case.
The alternative is the uncertainty concept that focuses on the core of the
distribution by estimating an interval within which the best estimate,
previously the "true" value would be expected with a given probability.
This is all described and exemplified in the publications I referred to a
couple of weeks ago on this mail-list.
The uncertainty concept, launched in the beginning of the 1990-ies, is
becoming more and more accepted worldwide and is required in the
accreditation standard EN/ISO 15189. That is probably the reason for the
original CPA question.
In the particular case of Mr Minett the uncertainty can be estimated by the
procedure described in the recent set of documents published on the ACB
homepage under the heading "Measurement verification in the clinical
laboratory". The approach describe there is "analysis of variance
components". It is another use than the original of the "one way ANOVA". In
principle, the within instrument variance will be estimated and the between
instrument variance "purified" from the within instrument variance. The
square root of the sum of these will be the combined uncertainty. A suitable
coverage factor (usually 2) will give the expanded uncertainty that defines
an interval within which the best estimate will be expected. This is the
quantity that should accompany each result, which is impractical in the
clinical setting but should be available for those interested and used as
limits for the IQC. If the imprecision indicates a homoscedastic mode it can
be used within the entire measuring interval.
The ACB document (Estimating precision by ANOVA) includes a simple EXCEL
spreadsheet (Spreadsheet A) that provides all the calculations and the
combined and expanded uncertainty.
In the example accompanying the spreadsheet and text, the approach is used
to estimate the within and between series uncertainty of one instrument but
the principle can be extended to the situation Mr Minett describes.
One needs to consider the number of observations in each group/instrument to
reach a suitable power. A rule of thumb is that the number of observations
in each group should not be less than a total number of observations minus
the number of groups/instruments of about 30. For six instruments this would
require at least six observations in each instrument. The more the better
and a balanced design (the same number of observations in each group) is an
advantage even if the program will handle the unbalanced as well as possible
can be. The present program will accommodate ten results from ten different
groups.
In another spreadsheet program, which can be obtained from me, for free,
information from long term IQC can be used to enhance the reliability of the
estimates.
Anders Kallner
Anders Kallner
Dept Clin Chem
Phone +46 8 5177 4943
Karolinska University Hospital
SE 171 76 Stockholm
Sweden
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