by Stanley N. Deming


AL


Statistics in the Laboratory: The Limit of Detection


The phrase “limit of detection” sounds so simple, yet it leads to one of the biggest, murkiest, most frustrating swamps in the statistical lit- erature. All the organizations in all the towns in all the world took it upon themselves to define, redefine, and re-re-redefine the phrase. This resulted in hundreds of definitions for “limit of detection.”


In 1968, Lloyd Currie decided enough was enough, and published his famous paper clarifying limits of detection and related topics.1 Lindstrom said it best:2


Richard


Until Lloyd Currie’s paper … was published, there was enough inconsistency in the definition of “detection limit” to conceal a great deal of disagreement. In just over seven pages, this tightly written communication established a high level of uniformity in answering these questions. The paper contains fundamental information that has made it influential far beyond its size, and it is rich enough to be discussed actively in e-mail newsgroups [now nearly 50] years later. This is surely one of the most often cited publications in analytical chemistry.


In this and the next two columns, we’ll use Currie’s approach (with slightly different symbols) to discuss the limit of detection (LD uses LC


; Currie Currie’s LD


), the minimum consistently detectable amount (MCDA, related to ), and the limit of quantitation (LQ


). Then we’ll see how John


Mandel’s definition of sensitivity allows a meaningful comparison of these three quantities for the “apples and oranges” of disparate units for different analytical methods (e.g., peak area in chromatography, ion intensity in mass spec).


Detection limits have been discussed previously in American Laboratory, most notably in the acclaimed “Statistics in Analytical Chemistry” series by David Coleman and Lynn Vanatta, installments 26 (http://www.americanlaboratory.com/913-Technical-Articles/1254- Part-26-Detection-Limits-Editorial-Comments-and-Introduction/), 28–30 (http://www.americanlaboratory.com/914-Application- Notes/1094-Part-28-Statistically-Derived-Detection-Limits/, http://www. americanlaboratory.com/914-Application-Notes/1095-Part-29-Statistically- Derived-Detection-Limits-continued/, http://www.americanlaboratory. com/914-Application-Notes/1096-Part-30-Statistically-Derived-Detection- Limits-concluded/), and 32–34 (http://www.americanlaboratory. com/914-Application-Notes/1104-Part-32-Detection-Limits-Via-3-Sigma/, http://www.americanlaboratory.com/914-Application-Notes/1105- Part-33-Detection-Limits-via-3-Sigma-Concluded/, http://www. americanlaboratory.com/914-Application-Notes/1106-Part-34-Detection- Limit-Summary/) from June 2007 through May 2009. The work of Currie has been the basis of an oft-cited paper by Hubaux and Vos.3


AMERICAN LABORATORY 41


Spoiler alert 1: Many persons think the limit of detection (often mistak- enly called the “sensitivity”) is the smallest amount of analyte that can be detected reliably—that’s going to be the MCDA, discussed in the next column. The limit of detection LD of quantitation LQ


(discussed in this column) and the limit (discussed in the column after next) have to do with


the signal strength (e.g., peak area, ion intensity). Be prepared to adjust your focus.


Spoiler alert 2: There are no universal values for these things. You (the analyst) and your client have to consider the application of your measure- ment method and use an acceptable false positive risk α, an acceptable false negative risk β, and your egos to set LD


, MCDA, and LQ Currie’s paper provides the structure for making the connections.


Figure 1 shows a realistic calibration relationship between the amount of analyte (the horizontal x-axis) and the signal obtained from the measurement method (the vertical y-axis). In this figure, each vertical line segment represents one measurement—the line begins at the


, respectively.


Figure 1 – A realistic calibration relationship with non-zero interceptμb and noise σb


. JUNE/JULY 2017


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