dealing with undetectable levels (below limit of quantification values) in statistics

[pran909]

Hi all,

We are doing mixed effects model analysis for our study. We have some samples where the concentration of protein (dependent variable) cannot be detected by our quantification method. So do we need include the concentration as "zero" for those samples while performing analysis? or can we just treat them as missing data and so do not include them in the analysis? Are there any other ways to deal with this problem?

[Martha Hewett]

I can't speak in detail to SPSS for this but I can strongly recommend a terrific book on this subject because I'm dealing with similar issues.  It is Nondetects and Data Analysis by D.R. Helsel, published by Wiley.  I strongly suggest you get this book.   Definitely do not throw the data out, and do not set it to zero, and do not set it to half the LOD.  Among other options, Helsel discusses treating "left-censored" data like this much like the more common right-censored data in survival analysis, where at the end of a study some of the participants are still living so you can only say they lived >x years.  Here you only know your concentration is <x.  Helsel discusses the fact that many software packages only address left-censored data and gives a careful analysis of how to transform your data to analyze it w/software that doesn't handle left-censored datasets.

Martha Hewett  |

Director of Research | 612.335.5865

Center for Energy and Environment

212 Third Avenue North, Suite 560 | Minneapolis, MN 55401

(cell) 612.839.2358 | (fax) 612.335.5888 | www.mncee.org

From:        pran909 <[hidden email]>
To:        [hidden email]
Date:        11/08/2011 11:12 AM
Subject:        dealing with undetectable levels (below limit of quantification              values) in statistics
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

Hi all,

We are doing mixed effects model analysis for our study. We have some
samples where the concentration of protein (dependent variable) cannot be
detected by our quantification method. So do we need include the
concentration as "zero" for those samples while performing analysis? or can
we just treat them as missing data and so do not include them in the
analysis? Are there any other ways to deal with this problem?

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[Rich Ulrich]

"Below detectable" is surely not Missing, unless there is
reason to exclude zero as missing.  That might be the case
if zero is a special case in other ways, or if a zero would not
fall on the line of what you would expect from some good
linear fit.

Using the value of 1/2  the detectable limit is a convention
that is frequently used, because it still allows you to take
logarithms, which is frequently the metric you want when
analyzing concentrations.  Otherwise, zero seems apt.

--
Rich Ulrich

> Date: Tue, 8 Nov 2011 09:02:44 -0800

> From: [hidden email]
> Subject: dealing with undetectable levels (below limit of quantification values) in statistics
> To: [hidden email]
>
> Hi all,
>
> We are doing mixed effects model analysis for our study. We have some
> samples where the concentration of protein (dependent variable) cannot be
> detected by our quantification method. So do we need include the
> concentration as "zero" for those samples while performing analysis? or can
> we just treat them as missing data and so do not include them in the
> analysis? Are there any other ways to deal with this problem?
>
> --