Decision level VS MDA

[grantime]

I've studied statistics but confess that it is not my strong subject.  The way I have it in my mind is that Decision level is a value that has some probablity of being greater than background and MDA is some activity > DL that can be quantified at some confidance level.  What can be said about values that are > DL but <MDA?  There might be something but we can't quantify it? 


Is anyone using DL as a limit for smearable levels?  And does that make sense?

[Rennhack]

Thanks for asking...  Here is the "Everything you ever wanted to know about the Correct Usage of Decision Level and Minimum Detectable Amount, but were afraid to ask".  I've stated the same thing several different ways, one of them is sure to make sense to someone. 

Short answer: Measurement results are compared to the Decision Level (DL = L_C, Critical Level), not the MDA (MDA = L_D, Detection Level).

MDA is not a characteristic of the sample measured, but is a characteristic of the instrument's limit for detecting radioactivity. That is why results are expressed as "less than MDA". Such a result indicates that the radioactivity of the sample is less than the capability of the instrument for detecting radioactivity. The MDA is used to determine whether an instrument has adequate detection capability and will be greater than or equal to the DL.

Decision Level (DL = L_C):  The value of a net observation (result) at or above which a decision is made that a positive quantity of the analyte is present.  The DL depends on the acceptable probability (alpha) of incorrectly concluding that there is analyte present (a Type 1 Error); alpha is usually taken as 0.05.

Minimum detectable amount/activity (MDA = L_D): The smallest amount/activity of a radionuclide in a sample that will yield a result above the decision level with a beta probability of non-detection (Type II error) while accepting an alpha probability of erroneously detecting that radionuclide in an appropriate blank sample (Type I error). The MDA is computed using the same value of alpha as used for the DL.  The MDA depends on both alpha and beta. 

Two very important statistical concepts, the decision level (DL; a.k.a. critical level [L_C]) and the minimum detectable amount (MDA; a.k.a. detection level [L_D], lower limit of detection [LLD] ...) are based on the standard deviation of the net count rate when an appropriate blank is being counted. DL and MDA are covered mathematically later. Suffice it to say at this point that one can determine, in advance of receiving a sample, how small an amount of radioactive material is likely to be distinguishable from background with a giving counting system and choice of counting times: this amount is the MDA. The MDA is the value that one can legitimately advertise that one can measure with reasonable assurance. Once one has made a measurement on a sample, one may wish to decide whether there is indeed any activity above background in the sample. This is done by comparing the counting result to the DL, a value typically about half the MDA. Yes, it is possible and not even infrequent to be sure one has detected activity less than the MDA but more than the DL. It should be remembered that the smaller the amount of activity in the sample is compared to the MDA, the less likely it is to result in a number of counts above the DL.

Never compare a sample result to the MDA. Sample results should only be compared to a decision level. A statement that a result was "less than MDA" is statistical nonsense that originates with the poor choice of name for the MDA. The MDA is really the "if-it's-in-the-sample-you're-likely-to-detect-it" level, while the DL is the "if-you-got-a-result-above-this-it's-probably-real" level. A result above the DL is probably not a "false alarm."

One may want to evaluate the detection capability of a radioactivity measurement program. Toward this end, one may want to establish "action levels." An action level is a value of count rate (e.g., cps), concentration (e.g., Bq/m³), or concentration × time (e.g., DAC-h) at or above which one chooses to take some action and below which that action is not deemed to be necessary. The simplest "action" one can take is to state, "Activity was (or was not) detected above background."

For operational purposes, the statistical concept of "decision level" is the lowest usable action level. Results of individual or pooled measurements are compared with the decision level. The decision level is a value chosen so that results above it are unlikely to be false alarms. Thus, the one chooses the decision level to be far enough above zero so that there is an acceptably low rate of false alarms due to random statistical fluctuations in the counting process (known to statisticians as "false positives").

Another concept one needs is that of "minimum detectable activity" or "minimum detectable concentration." Unlike the decision level or action levels with which individual or pooled results are compared, the minimum detectable quantities are performance gauges of a radioactivity measurement program that can be compared with a performance goal.


Further information can be found in:

For basic statistics, a truly superb reference for its insight, clarity, examples, and problems is Chapter 11 and Appendix E in Jim Turner's second edition of Atoms, Radiation, and Radiation Protection (Turner 1995).

For slightly more applied concepts, a current consensus standard with well-thought-out statistics and examples is Performance Criteria for Radiobioassay (ANSI/HPS N13.30-1996).

Recent publications with statistics discussions include MARSSIM (Multi-Agency Radiation Survey and Site Investigation Manual) (http://www.epa.gov/radiation/marssim/) and Minimum Detectable Concentrations with Typical Radiation Survey Instruments for Various Contaminants and Field Conditions (NRC 1998)

I've "borrowed heavily" from Daniel J. Strom's HPS lecture July 15, 1998 titled "False Alarms, True Alarms, and Statistics: Correct Usage of Decision Level and Minimum Detectable Amount" also called "Statistics: Beyond Semantics to Meaning, Dan Strom, HPS CEL rev. July 15, 1998", and to that end, I've attached it.  He can say it better than I can, and in more detail than I can.