Richard Dixon wrote:

>I have a quick query regarding handling assay results which are below the
>assay's limit of detection. For statistical purposes a value must be
>assigned to such samples. Does anyone have any suggestions on which is the
>most appropriate value to use. Those I most commonly see used are either
>the limit of detection itself, or 50 percent of the limit of detection
>(presumably assuming that of all such samples half will have a 'true' value
>between zero and 50 % LOD, and the other half between 50-100% of the LOD)

"For statistical purposes" can mean a lot of things. If you are using
the values in order to obtain a reference range using a parametric approach
you obviously must assigned a certain value to those measurements. If you
assign zero to all those results you will get a negative bias in the 
statistics. On the other side, if you assign the limit of detection, you
will get a positive bias.

Assigning the mean value between zero and the LOD is better than assigning
zero or LOD, but probably the "true" values within this range is
assymmetrically distributed. You should not assume anything at all in this
"blind range". Maybe you can do a pilot study using a method having a
lower LOD. Such a method is probably expensive, but you need only a limited
number of measurements in order to evaluate the distribution within this
range. If you analyze 11 samples using such a method you could assign the
median (not the mean!) of these values to the tests "less than" in your
study.

Somebody prefer simply to omit those results, but this will also cause a
(positive) bias! So, if you want to make a reference limit, follow the 
IFCC recommendations and use a non-parametric method!

Also in other statistical evaluations, a non-parametric design often is
advantageous, not only in this case, but in many cases where parametric
methods usually are applied.

Instead of using t-test the Mann-Whitney test should be preferred.
Instead of using the correlation coefficient you can use the Spearman Rank
correlation, etc.

If you look at the advertisements of "the big" statistical programs, the
abilities of handling "less than", "greater than" and "data missing" are
never emphasized. All those programs can do non-parametric statistics
but the producers of the programs seem to neglect the statistical demands
of clinical chemistry data. The same applies to popular spreadsheet programs
such as Excel, Lotus 123 etc.

As far as I have seen there exist no program for a perfect statistical handling
of real biochemical data. In the absence of such programs I have worked with
home-made programs. They are perfectly fitted for my own thinking, but not
well suited for others.

I can only recommend studying of the examples in statistical textbooks, e.g.
the classical "Snedecor & Cochran", and articles on statistics in the
literature, e.g. the Lancet. Also read the recommendations from the IFCC
in this field.

Best wishes
Sten Öhman
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From:                Mr Sten Öhman, PhD
Postal address:      p.o. Box 133, S-590 70 Ljungsbro, Sweden
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