[ RadSafe ] Comparison of a Measured Result to the Critical/Decision Level; new question

Arvic Harms Arvic.Harms at npl.co.uk
Tue Oct 13 08:28:22 CDT 2009

```As far as I understand the ISO 11929:2008 draft, it recommends the following:

If result < y* (decision threshold), report as 'not detected' or alternatively as 'less than y# (detection limit)', if required by a regulator.
If result >= y*, report the best estimate of the result together with its uncertainty (even if the result is less than y#, the detection limit).

Example:

Background measurement time: 10000
Background counts: 100
Gross measurement time: 10000
Gross counts: 120
Net count rate: 0.0020
Decision threshold y*: 0.0023
Detection limit y#: 0.0049
Detected: No
Report as: Not detected (or less than 0.0049)

Background measurement time: 10000
Background counts: 100
Gross measurement time: 10000
Gross counts: 124
Net count rate: 0.0024
Decision threshold y*: 0.0023
Detection limit y#: 0.0049
Detected: Yes
Best estimate: 0.0026
Best estimate standard uncertainty: 0.0013
Report as: 0.0026(13) at k=1

Background measurement time: 10000
Background counts: 100
Gross measurement time: 10000
Gross counts: 200
Net count rate: 0.0100
Decision threshold y*: 0.0023
Detection limit y#: 0.0049
Detected: Yes
Best estimate: 0.0100
Best estimate standard uncertainty: 0.0017
Report as: 0.0100(17) at k=1

Summary

For net count rates

0.0020: Report as not detected or < 0.049
0.0023: Report as 0.0026(13)
0.0100: Report as 0.0100(17)

At first sight, this may seem somewhat counterintuitive, but I believe it is correct. When you want to combine the results (as a sum or a mean) in the case of a count rate of 0.0020, dividing 0.049 by a factor of two will get you a reasonable estimate close to the value of 0.020 (although this value is 'not detected'). However, it will of course fail for count rates of 0.0001 or -0.0020.

Scanning through the literature (including US-EPA document "Guidance for Data Quality Assessment" (EPA QA/G-9)) it is clear there is several ways of analysing data with non-detects (censored data).

(i) Replace non-detects with DL/2, DL/SQRT(2), DL or (my favorite) "a very small number"
(ii) Trimmed means
(iii) Proportion tests

I guess the main problem is how the detection limit (DL) is defined (Bayesian ISO 11929 y#, LLD, MDA, Currie Ld) and how you report it. The suggestion below to publish data in different ways within a report is good one.

Kind regards,

Arvic Harms

Dr Arvic Harms
National Physical Laboratory
Teddington TW11 0LW
Middlesex
United Kingdom
E-mail: arvic.harms at npl.co.uk
Tel ++44 20 8943 8512
Fax ++44 20 8614 0488

> -----Original Message-----
> Behalf Of Brennan, Mike (DOH)
> Sent: 08 October 2009 16:56
> Subject: RE: [ RadSafe ] Comparison of a Measured
> ResulttotheCritical/Decision Level; new question
>
>
> How to report less than LLD (or MDA, or whatever) is
> something worthy of discussing within your organization every
> now and then, to make sure that new people coming in from
> other places understand what you are doing.
>
> We report results in different ways, depending on who the
> intended audience is.  Sometimes we report in different ways
> within the same document.  For example, we have one report
> that sample for Co60, Cs137, and I131, as well as any other
> isotopes that produce positive results on a gamma scan (we
> exclude isotopes in the U238 chain).  In the main report,
> aimed at the general public, we have tables with "Not
> Detected" for any result where the counted activity was not
> above the LLD.  In the appendixes we have the actual result,
> so anyone who is using the data for more involved statistical
> operations will have something to work with.
>
> This may not come up too often if you are dealing with "real"
> radioactivity, but it is pretty common in environmental monitoring.
>
> -----Original Message-----
> Sent: Wednesday, October 07, 2009 5:49 PM
> Subject: Re: [ RadSafe ] Comparison of a Measured Resultto
> theCritical/Decision Level; new question
>
>
>
> Semantics is really messy especially when dealing with
> statistics.  Ditto on Bob Shannon's references and also you
> may want to look at papers published by Mark A. Tries  of
> University of MA Lowell (sometimes et. al.) who has authored
> a number of good papers on counting statistics.
>
>
>
> If you use zero you most likely are adding a bias to your
> conclusions.  This bias may be high or low.  ISO 11929 2008
> and the below references Bob submitted are in agreement that
> zero is not an appropriate approximation of the value if less
> than the detection limit.   A bias may create problems is
> conclusions are incorrect as a result of the bias.  Unbiased
> data should be used for all calculations performed to provide
> a best estimate for reporting based on an acceptable
> percentage of false + and false - results.  Even if reporting
> a best estimate it is often useful to report or at least
> maintain a record of the actual measurements and errors on
> the measurements.
>
>
>
> I have never seen value/2, perhaps the person who started
> that was confusing the 95% MDA with the Lc (detection limit)
> and taking half of the MDA or 1/2 x 4.66sigma.
>
>
>
> Hope this helps.
>
>
>
> Barbara Reider, CHP
>
> -----Original Message-----
> From: Arvic Harms <Arvic.Harms at npl.co.uk>
> Cc: Peter Bossew <Peter.Bossew at reflex.at>
> Sent: Mon, Oct 5, 2009 7:23 am
> Subject: RE: [ RadSafe ] Comparison of a Measured Resultto
> the Critical/Decision Level; ne w question
>
>
>
>
> Dear all,
> ISO 11929 2008 draft has the following recommendations in Chapter 6:
> If result < y* (decision threshold), report as 'not detected'
> or alternatively s 'less than y# (detection limit)', if
> required by a regulator.
> f result >= y*, report the best estimate of the result
> together with its ncertainty (even if the result is less than
> y#, the detection limit).
> I have a question about combining results which contain one
> or more 'less than #' types of "results" when you want, for
> instance, to calculate a mean of everal results.
> It is common to assign a value of [y# divided by factor of 2]
> to the 'less than #' results. Is there any scientific
> justification for doing this?
> The 'less than y#' types of "results" are 'not detected' and
> are therefore 0 and ot y# / 2 in my opinion.
> Kind regards,
> Arvic Harms
>
> r Arvic Harms
> ational Physical Laboratory
> eddington TW11 0LW
> iddlesex
> nited Kingdom
> -mail: arvic.harms at npl.co.uk
> el ++44 20 8943 8512
> ax ++44 20 8614 0488
> > -----Original Message-----
>  Behalf Of Bob Shannon
>  Sent: 04 March 2009 20:38
>  Cc: 'Peter Bossew'
>  Subject: RE: [ RadSafe ] Comparison of a Measured Resultto
> the  Critical/Decision Level
>
>
>  Peter -
>
>
>
>  I very much agree with the main thrust of your comment about
> critical  levels. Thanks!
>
>
>
>  I have some concerns about censoring measurement results as
> you have  proposed, though.
>  Most standards that apply to radiochemical  measurements
> (at least in the US) specify that every measured result,
> whether positive,  negative or zero, should be reported in
> association with its  measurement  uncertainty.  While there
> are a few programs that make  exceptions, and some  entities
> fail to follow the guidance, but the guidance is presented in
>  rather unambiguous terms. Here are several examples:
>
>
>
>  ·         Multi-Agency Radiological Laboratory Analytical
>  Protocols Manual
>  (MARLAP) - EPA, NRC, DOE, DOD, DHS, FDA, USGS, NIST
> (NUREG-1576, EPA  402-B-04-001A, NTIS PB2004-105421).
>
>  o    Section 19.3.8 Reporting the Measurement Uncertainty
>
>  §  It is possible to calculate radioanalytical results that
> are less than  zero, although negative radioactivity is
> physically  impossible. Laboratories  sometimes choose not to
> report negative results or results  that are near  zero. Such
> censoring of results is not recommended. All  results,
> whether  positive, negative, or zero, should be reported as
> obtained,  together with  their uncertainties.
>
>
>
>  ·         ANSI N13.30 - Performance Criteria for
>  Physics Society N13.30-1996
>
>  o    3.5 Reporting Results [results reported shall include]
>
>  (5) quantification of the amount of radionuclide(s) (whether
> positive,  negative, or zero) of each radionuclide measured
> in each part  of the body  counted;
>
>  (6) estimates of counting uncertainty
> and the total
>  propagated uncertainty
>  [which includes counting and other random and systematic
> uncertainties at  one sigma (see Appendix D, Section D.6)];
>
>  (7) value of the decision level and a priori MDA, in units
> consistent with  the results;
>
>
>
>  ·         ANSI N42.23 American National Standard Measurement
>  and Associated
>  Instrument Quality Assurance for Radioassay Laboratories,
> (IEEE, 1996/2004)
>
>  o    A.8 Reporting results by the service laboratory
>
>  §  "Calculated concentration or activity value (whether
> negative, positive,  or zero) using the appropriate blank for
> each nuclide" [and]  "Estimates of  the counting uncertainty
> and total propagated uncertainty  (which contains  counting
> and other random and systematic uncertainties" [must  be
> included in  the analytical results reported by the service
> laboratory]
>
>
>
>
>
>  Bob Shannon
>
>
>
>  Tel: 303-432-1137
>
>
>
>  -----Original Message-----
>  Sent: Wednesday, March 04, 2009 7:44 AM
>  Subject: Re: [ RadSafe ] Comparison of a Measured Result to
> the  Critical/Decision Level
>
>
>
>  Randy,
>
>
>
>  the "error" (more accurately: uncertainty) is irrelevant for
> this. The
>
>  "result" (estimate of expectation of a rnd. variable) has to
>  be compared
>
>
>  to the decision level or threshold. If, like in your case,
> result < Lc, it
>
>  has to be reported as (quantity) < MDA (also called LLD).
>  Also the alpha
>
>  and beta values connected to Lc and MDA should be reported.
>
>  Only if the "result" > Lc, it must be reported together with
>  uncertainty
>
>  (incl. k=number of sigmas), or ideally, with a confidence
> interval (again
>
>  with k) (because the distribution is not symmetrical, which
> is relevant
>
>  for low level measurements. This can only be ignored for
> high  enough count
>
>  numbers).
>
>
>
>  The relevant document is ISO 11929: Determination of the
> detection limit
>
>  and decision threshold for ionizing radiation measurements. Geneva
>
>  2000-2001 (8 parts).
>
>  For a good review of theory, De Geer L. (2005): A decent
> Currie at the
>
>  PTS. Report CTBT/PTS/TP/2005-1, Aug. 2005; available from
> the  CTBTO. Also:
>
>  De Geer L. (2004): Currie detection limits in gamma-ray spectroscopy.
>
>  Appl. Rad Isot. 61 (2-3), 151-160.
>
>  In Bayesian reasoning:
>
>  - Weise K. and W. Wöger (1993): A Bayesian theory of measurement
>
>  uncertainty. Meas. Sci. Techn. 4(1), 1-11;
>
>  - Weise K. et al. (2006): Bayesian decision threshold,
> detection limit and
>
>
>  121(1), 52-63;
>
>  - Michel R. (2000): Quality assurance of nuclear analytical
> techniques
>
>  based on Bayesian characteristic limits. J.
>  Nucl. Chem.
>
>  245(1), 137-144.
>
>  For non-Currie decision rules: Strom and MacLellan (2001):
>  Evaluation of
>
>  eight decision rules for low-level radioactivity counting.
>  Health Physics
>
>  81 (1), 27-34. The authors show that the standard rules (ISO
>  11929) may
>
>  not perform well in extreme cases.
>
>
>
>
>
>  Peter
>
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