MARLAP Chapter 20Detection and Quantification

Limits

Keith McCroan

Bioassay, Analytical & Environmental Radiochemistry Conference 2004

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

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

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

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)

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

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, , that one considers tolerable

This error rate is called the significance level By default, is often taken to be 0.05

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

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)

The Critical Value - continued

The critical value is selected to limit the type I error probability to

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

Other Names

Critical level (Currie 1968) Decision level (ANSI N42.23, N13.30)

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, , goes down as the concentration of analyte goes up (more statistical “power”)

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 , 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

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

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

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

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  = 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

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)

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)

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

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

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

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

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

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

Questions?