METHOD VALIDATION -
THE DETECTION LIMIT EXPERIMENT

James O. Westgard, PhD

Purpose

The detection limit experiment is intended to estimate the lowest concentration of an analyte that can be measured. This low concentration limit is obviously of interest in forensic drug testing, where the presence or absence of the drug may be the critical information desired from the test. Analytical performance at low concentrations is also important for tumor markers, such as prostate specific antigen (PSA), when patient values after treatment may be useful for monitoring "biochemical relapse" [1].

US laboratory regulations require that detection limit (or analytical sensitivity) be verified only for high complexity methods, modified moderate complexity methods, and moderate complexity methods that have not been cleared by FDA as meeting the CLIA requirements for quality control. Given that FDA has not implemented a QC clearance process, the requirement to verify detection limit for moderate complexity methods has been postponed. However until such time that QC clearance has been implemented, good laboratory practice should dictate that detection limit be verified, when relevant, e.g., all forensic and therapeutic drug tests; TSH and similar immunoassay tests; PSA and other cancer markers - and not glucose, cholesterol, enzymes, and constituents where reference range is more relevant for interpretation of the test results.

Terminology in this area is a mess! In making their claims, manufacturers often use a wide variety of terms, such as sensitivity, analytical sensitivity, minimum detection limit, functional sensitivity, limit of detection, and limit of quantitation. At this time there are no accepted standard definitions of these terms, therefore, it is necessary to find out what the actual experimental procedure was, how the data were calculated, how the estimate was made from the data, and whether this estimate is useful for medical application of the test.

Factors to consider

A general description of the experimental procedure is provided in the accompanying figure. Two different kinds of samples are generally prepared. One sample is a "blank" that has a zero concentration of the analyte of interest. The second is a "spiked" sample that has a low concentration of the analyte of interest. In some situations, several spiked samples may be prepared. Both the blank and spiked samples are measured repeatedly in a replication type of experiment, then the means and SDs are usually calculated from the values observed for the samples. Different estimates of detection limit may be calculated from the data on blank and spiked samples.

Blank solution. One aliquot of the blank solution is typically used for the blank and another aliquot is used to prepare the spiked sample. Ideally the blank solution should have the same matrix as the regular patient samples. However, it is common to use the "zero standard" from a series of calibrators as the blank and the lowest standard as the "spiked" sample.

Spiked sample. In validating the performance of a method, the amount of analyte added to the blank solution should represent the detection concentration claimed by the manufacturer. In establishing a detection limit, it will often be necessary to prepare several spiked samples whose concentrations are in the analytical range of the expected detection limit. For certain tests, there may also be an interest in using samples from patients who are free of disease following treatment (i.e., PSA sera from patients treated for prostate cancer) [2].

Number of replicate measurements. There is no hard and fast guideline, but 20 replicate measurements are usually recommended in the literature. This number is reasonable given that the detection limit experiment is a special case of the replication experiment and that 20 is the minimum number of measurements recommended for a replication study. Manufacturers often recommend 10 measurements in their verification protocols to minimize cost and laboratories often adopt this lower number of measurements for practicality.

Time period of study. A within run or short term study is often carried out when the main focus is the method's performance on the blank solution. A longer time period, representing day-to-day assay performance, is recommended when the focus is on the "spiked" sample [2]. When day-to-day performance is considered, practicality may dictate using 10 measurements (and 10 days) rather than a longer time period.

Quantity to be estimated. Here's where it gets confusing. There are at least three different concepts (and terms) that are commonly used, as illustrated in the accompanying figure. The determination of these different quantities involves different calculations with the data from the blank and spiked samples.

Data Calculations

Consider an example application where the blank and the spiked samples are the zero and 10 ug/L standards. [For convenience and comparison, this example is similar to the one for PSA in Table 1 of reference 1.] Both samples were analyzed 10 times and the means and SDs calculated. For the zero standard, the mean is 1000 units and the SD is 100 units (raw measurement responses being used). For the 10 ug/L sample, the mean is 2000 units and the SD is 200 units.

Lower Limit of Detection (LLD). The manufacturer's claim makes use of a 2 SD definition of LLD (i.e., meanblk + 2sblk) based on 10 replicate measurements.

  1. Select a z-value of 2.
  2. Calculate the uncertainty in the estimate of the blank as 2SD (e.g., 2sblk is 200 units).
  3. Calculate a calibration factor to convert measurement units to concentration units (e.g., the 10 ug/L gives a response of 2000 minus 1000 or 1000 units, which gives a calibration factor of 1 ug/L per 100 measurement units).
  4. Calculate the minimum detection limit by multiplying the uncertainty in the estimate of the blank by the calibration factor (200 units times 1 ug/L per 100 units, which gives a minimum detection limit of 2 ug/L in this example).

Biological Limit of Detection (BLD). The manufacturer's claim again makes use of a 2 SD definition of BLD (i.e., LLD + 2sspk) based on 10 replicate measurements.

  1. Calculate LLD as above, which is 2 ug/L.
  2. Select a z-value of 2.
  3. Calculate the uncertainty in the spiked sample as 2SD (e.g., 2 sspk is 400 units).
  4. Multiply the uncertainty in the spiked sample by the calibration factor (400 units times 1 ug/L per 100 units, which is 4 ug/L).
  5. Calculate BLD as LLD + 2sspk, which is 2 ug/L + 4 ug/L, or 6 ug/L.

Functional sensitivity (FS). A manufacturer's claim is 10 ug/L for the functional sensitivity of a method based on 10 replicate measurements.

  1. Calculate the SD in concentration units for the 10 ug/L standard (e.g., 200 units time the calibration factor of 1 ug/L per 100 units gives an SD of 2.0 ug/L)
  2. Calculate the CV for the 10 ug/L standard (e.g., CV is 2.0 ug/L times 100 divided by 10 ug/L, or 20%).
  3. FS is 10 ug/L by definition, i.e., 10 ug/L is the concentration at which the CV of the method is 20%.

    Note that additional spiked samples would generally need to be analyzed because the initial ones won't likely provide one with the desired 20% CV. Another approach would be to determine the precision profile for the method and then estimate FS by interpolation of the line of best fit from the plot of CV versus concentration. See reference 6 for detailed examples of this approach.

Summary Comments

In validating a manufacturer's performance claim for detection limit, it is important to recognize the specific form of the claim, the data need to verify that claim, and the data calculations appropriate for that form of the claim. Many manufacturers seem to choose the LLD quantity because it is simplest to estimate and also gives the lowest number - a marketing application. For medical applications, it would generally be more useful to estimate BLD or FS.

As mentioned earlier, the terminology and experimental procedures in this area are not yet standardized and additional terms and alternate experimental procedures will likely be encountered. The National Committee for Clinical Laboratory Standards (NCCLS) is working to establish a standard of practice in this area and has a draft document under development [7]. This effort will hopefully lead to a more rational and systematic understanding of detection limit in the near future.

References

  1. Diamandis EP, Yu J, Melegos DN. Ultrasensitive prostate-specific antigen assays and their clinical application. Clin Chem 1996;42:853-857.
  2. Stamey TA. Lower limits of detection, biological detection limits, functional sensitivity, or residual cancer detection? Sensitivity reports on prostate-specific antigen assays mislead clinicians. Clin Chem 1996;42:849-852.
  3. Lawson GM. Defining limit of detection and limit of quantitation as applied to drug of abuse testing: striving for a consensus. Clin Chem 1994;40:1218-1219.
  4. Armbuster DA, Tillman MD, Hubbs LM. Limit of detection (LOD)/limit of quantitation (LOQ): Comparison of the empirical and the statistical methods exemplified with GC-MS assays of abused drugs. Clin Chem 1994;40:1233-1238.
  5. Klee GG, Dodge LA, Zincke H. Oesterling JE. Measurement of serum prostate specific antigen using Imx prostate specific antigen assay. J Urol 1994;151:94-98.
  6. Spencer CA, Takeuchi M, Kazarosyan M, MacKenzie F, Beckett GJ, Wilkinson E. Interlaboratory/intermethod differences in functional sensitivity of immunometric assays of thyrotropin (TSH) and impact on reliability of measurement of subnormal concentrations of TSH. Clin Chem 1995;41:367-374.
  7. NCCLS Document EP17-P: Protocols for demonstration, verification, and evaluation of limits of detection and quantitation. Proposed document under development. National Committee for Clinical Laboratory Standards, Wayne, PA.

 

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