MARLAP Chapter 20 Detection and Quantification Limits

1. MARLAP Chapter 20Detection and Quantification Limits Keith McCroan Bioassay, Analytical & Environmental Radiochemistry Conference 2004

2. Overview • Chapter 20 of MARLAP deals with issues of analyte detection as well as measures of detection capability and quantification capability • It makes recommendations about the proper use of the critical value and minimum detectable value • It offers suggestions for how to calculate them in various situations

3. Overview - continued • Chapter 20 also presents a concept that has tended to be ignored by radiochemists: the minimum quantifiable value • We recommend that radiochemists become familiar with this concept and use it when it is appropriate • The chapter suggests equations to calculate it

4. Hypothesis Testing • The theory of analyte detection for radiochemistry is derived from statistical hypothesis testing • In a hypothesis test, one constructs two mutually exclusive hypotheses • The null hypothesis: There is no analyte in the sample • The alternative hypothesis: There is some analyte in the sample

5. The Null and Alternative Hypotheses • The null hypothesis is presumed to be true unless there is good evidence to the contrary (like presumption of innocence in a criminal trial) • The alternative hypothesis is accepted if the null hypothesis is rejected (like finding the defendant guilty)

6. Decision Errors • Measurements aren’t perfect — There is always uncertainty • Regardless of which hypothesis is true, there is a chance of choosing the wrong one • Choosing the wrong hypothesis is a decision error

7. Type I Errors • A type I error (false rejection, false positive) is the decision error made by rejecting the null hypothesis when it is actually true • One specifies the type I error rate, a, that one considers tolerable • This error rate is called the significance level • By default, a is often taken to be 0.05

8. The Critical Value • In hypothesis testing, the critical value is the threshold value for the test statistic that is used to choose between the null and alternative hypotheses • The term has been borrowed, with only a slight change in definition, to denote the threshold value to which a measured value is compared in the lab to make a detection decision

9. The Critical Value - continued • One may base the detection decision on the gross count, net count, gross count rate, net count rate, or even on the final calculated activity • There is an associated critical value for each of these (e.g., the critical net count rate or the critical gross count)

10. The Critical Value - continued • The critical value is selected to limit the type I error probability to a • There are many possible equations for it • Choose one that is appropriate for your situation: One size does not fit all • MARLAP does not prescribe any particular equation for the critical value

11. Other Names • Critical level (Currie 1968) • Decision level (ANSI N42.23, N13.30)

12. Type II Errors • A type II error (false acceptance, false negative) is the decision error made by failing to reject the null hypothesis when it is actually false • The probability of a type II error depends on the amount of analyte in the sample • Generally the type II error rate, b, goes down as the concentration of analyte goes up (more statistical “power”)

13. The Minimum Detectable Value • The minimum detectable value is the smallest value of the analyte that ensures the type II error probability is no more than a specified value of b, which is often 0.05 by default • MARLAP generally refers to the minimum detectable concentration (MDC), on the assumption that the measurand is usually the concentration of analyte in a sample • Some say the minimum detectable activity

14. Detection Capability • Detection capability is the term used by MARLAP to mean the ability of the measurement process to detect the analyte (i.e., to avoid type II errors) • The MDC is a measure of detection capability

15. The Method Detection Limit • Beware: MDL ≠ MDC • It is unfortunate that the abbreviations are so similar — the similarity causes confusion • The regulation (40 CFR 136, App B) says the MDL is to be used as a critical value, but it is also used as measure of detection capability

16. Misuse of the MDC • A common mistake is to make a detection decision by comparing a measured result to the MDC • Make the detection decision by comparing a result to the critical value, not the MDC • The definition of the MDC presupposes that an appropriate detection criterion (the critical value) has been chosen

17. Misuse of the MDC - continued • The type II error rate for a sample whose concentration is at the MDC is supposed to be small (usually b=0.05) • If you base your detection decision on the MDC instead of the critical value, then the type II error rate at the MDC will be about 50% • Dumb mistake, but smart people make it

18. Low-Background Poisson Counting • Attachment 20A compares several published approaches for making detection decisions based on Poisson counting (similar to Strom and MacLellan’s work) • It’s fun to explore the mathematics of Poisson counting, but beware: the actual data distribution is usually not pure Poisson • The pure Poisson model is appropriate in relatively few situations (e.g., alpha spec analysis for certain analytes)

19. Quantification Capability • Quantification capability refers to the ability of a measurement process to measure the analyte with good relative precision • It may be expressed as the minimum quantifiable value (e.g., minimum quantifiable concentration, or MQC)

20. The Minimum Quantifiable Value • The minimum quantifiable value is defined as the value of the analyte for which the relative standard deviation of the measurement has a specified value, usually 1/10 • MARLAP treats random errors and systematic errors alike when estimating this relative standard deviation – much like the ISO-GUM approach to uncertainty propagation

21. Recommendations • When a detection decision is necessary, make it by comparing the signal or measured result to its critical value • The lab should choose appropriate expressions for the critical value and MDC • The client should not specify the equations without detailed knowledge of the measurement process

22. Recommendations - continued • Use an appropriate radiochemical blank to predict the signal produced by an analyte-free sample • It might be a series of reagent blanks • It might be only a blank source • Whatever works

23. Recommendations - continued • Confirm the validity of the assumption of Poisson statistics before using expressions for the critical value and MDC that are based on the Poisson model • Consider all sources of variability in the count rate when calculating critical values and MDCs – not just counting statistics

24. Recommendations - continued • Use the MDC only as a performance characteristic of the measurement process • Never compare a result to the MDC to make a detection decision • The lab should report each result and its uncertainty even if the result is less than zero – Never report “< MDC” • However, we don’t presume to tell the lab’s clients how to present data to others

25. Recommendations - continued • Don’t use the MDC for projects where the issue is quantification of the analyte and not detection (e.g., 226Ra in soil) • For such projects, MARLAP recommends the MQC as a more relevant performance characteristic of the measurement process

26. Questions?