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st: Biomarker with lower detection limits


From   Eduardo Nunez <enunezb@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Biomarker with lower detection limits
Date   Tue, 17 Nov 2009 09:01:43 -0500

Dear statalisters:

I wonder if anyone can advise me on the best way to analyse continuous
variables with lower detection limits (or left censored).
In particular, I have data on a biomarker with 92% of values reported
"undetectable" and I am trying to run 2 models:
1) a linear regression using it as dependent variables, and
2) stcox with mortality as outcome and the biomarker as the main exposure.


. tab cpies_DNA_max, m

cpies_DNA |
       _max |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        121       91.67       91.67
       2.85 |          1        0.76       92.42
      4.721 |          1        0.76       93.18
      5.059 |          1        0.76       93.94
      5.165 |          1        0.76       94.70
      6.267 |          1        0.76       95.45
      8.009 |          1        0.76       96.21
      9.965 |          1        0.76       96.97
     30.538 |          1        0.76       97.73
     35.137 |          1        0.76       98.48
         50 |          1        0.76       99.24
     71.227 |          1        0.76      100.00
------------+-----------------------------------
      Total |        132      100.00


Censored values occur in enviromental, metabolomics, proteomics data
most commonly when the level of a biomarker in a sample is less than
the limit of quantification of the machine; these values are generally
reported as being less than detectable with the detection limit (DL)
being specified (for instances "< than 2.5").
There has been proposed several solutions like to replaces those
values with zeros, or DL, or DL/2 or a random value from a
distribution over the range from zero to DL. However, any of them have
been demonstrated to be optimal in simulation studies.
What I don't want is to eliminate those values and run the analysis on
complete cases.
Is it possible to use multiple imputation for replacing those values?
If this is an option, how can I tell the imputation method not to find
values bove the DL?
Is tobit an appropriate model for the fist analysis? because of marked
skewness, should I normalize the variable by transforming only the
values above DL?


Best regards,

Eduardo


Eduardo Nunez, MD, MPH
Epidemiology Department
Department of Cardiology. Hospital Clínico Universitario.Universitat de
València. València. Spain.

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