Even in the absence of censoring of the type you describe, the LOD is
always "variable" in any case (ie. some samples with a TRUE concentration
above a putative LOD will give a result below the LOD simply because of
measurement imprecision, and visa versa).
I don't understand how expression of results relative to background will
correct for extraction efficiency unless you have spiked an internal
standard of some sort (otherwise how can you be sure that your denominator
(background) is the same from one sample to another, and that it is itself
not correlated with your peak of interest).
What you have is a final "result" which is determined by a numerator that
is subject to censoring, but a denominator that is presumably not. Howver,
in terms of the statistics, I don't think that the actual design of your
experiment is really relevant to the analysis - I don't think there is
anything wrong with using rank correlation analysis for your censored data
and including your zero data (you will have a lot of ties).
In terms of your concerns about deleting some subjects with zero results
who are actually higher than subjects with non-zero results: 1) don't
delete data 2) The same problem applies to any data subject to measurement
imprecision - the ranking of measured data will not conform exactly to the
"true" underlying ranking). 3) Presumably your errors will not be
asymmetric (samples with "true" results slightly below the LOD under
average circumstances will be detectable if extraction happens to be above
average, and results that are slightly above LOD will give a below LOD
result if extraction is below average).
Aubrey Blumsohn
>We are having problems performing correlation analysis on data
>obtained from GC chromatograms. As the extraction efficiency of the
>samples is highly variable we are expressing individual peaks as a
>percentage of the total peaks area.
>The problem then is that the Limit of Detection (LOD), which we are
>defining as the smallest peak that the integrator can handle divided by
>the total peaks area, changes with the extraction efficiency for each
>sample.
>We are now trying to correlate the percentage of each compound (as
>a fraction of the total) as detected by GC with other continuous
>biochemical and anthropometric variables. Deleting the data which
>is below the LOD is going to skew the analysis and reduce power. Ranking
>all the 'below the LOD' data as equally low results is also incorrect as
>the samples that extracted very poorly could have results higher than some
>of the defined data.
>Is there a formal treatment for these sort of data? If not any ideas?
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