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Procedures for Detection and Quantitation

WORKING DRAFT FOR DISCUSSION

Federal Advisory Committee on Detection and Quantitation for Uses in Clean Water Act Programs

September 29-30, 2005

REVISED DEFINITION OPTIONS for DETECTION and QUANTITATION from the TWG Definitions Subgroup

LC Detection — Layperson's Definitions

  1. Critical Value (LC) — The minimum result which can be reliably discriminated from a blank** (for example, with a 99% confidence level).
  2. Critical Value (LC) — The lowest result that can be distinguished from the blank** at a chosen level, α, of statistical confidence.
    • **Note: The committee aknowledged that the use of "blank" versus "zero" needs further discussion.
  3. Critical Value (LC) — The concentration which a sample result must exceed in order to conclude (with 100α percent chance of being wrong) that the analyte is present.
  4. Critical Value (LC) — The lowest result that can be distinguished from a blank with no more than α chance of reporting a false positive. (e.g., where α = 10%)
  5. Critical Value (LC) — The Critical Value (LC) is the upper 1% limit for the distribution of measurements with a true mean of zero.

LD Detection — Layperson's Definitions

  1. Detection Limit (LD) — The lowest true concentration that will almost always be detected. (The Committee wants the term "detected" to be modified.)
  2. Detection Limit (LD) — The minimum detectable value is smallest amount or concentration of a particular substance in a sample that can be reliably detected by a specific measurement process.
  3. Detection Limit (LD) — The minimum true concentration that will return a result above the critical value given a specific measurement process and confidence level.
  4. Detection Limit (LD) — The Minimum Detectable Value (LD) is the lowest true concentration at which the probability of a measurement less than (LC) is beta (β).
  5. Detection Limit (LD) — The lowest concentration for which there is a desirably small probability, β, that the determinand will not be detected – i.e., that as a result of random errors the observed result will be less than the Critical Level.
  6. Detection Limit (LD) — The concentration of analyte which must be present in a sample in order to be 100*(1-β) percent certain of detecting its presence without a false negative as well as a 100*α percent chance of not detecting a false positive. (i.e., 100(1-β) percent certain that the result will be greater than the Critical Value).

LC Detection — Statistical Definitions

  1. Critical Value (LC) — The upper limit for a distribution of sample measurements with a true mean of zero, such that a future sample measurement that exceeds LC has a probability of a false positive of 1% or less that the true sample concentration is zero. Algebraically, this is expressed as LC = z(1-α)*σ(0) where alpha (α) is the probability of a Type I error, z(1-α) is the (1-α) percentage point of the standard normal variable, and σ(0) is the standard deviation of the population of all possible measurements of a sample with a true value of zero.
  2. Critical Value (LC) — Smallest measured amount or concentration of analyte in a sample that gives rise to a Type I error tolerance of alpha under the null hypothesis that the true amount or concentration of analyte in the sample is equal to that of a blank. (The alternative hypothesis is that the true amount or concentration of analyte is greater than that of a blank.)
  3. Critical Value (LC) — The minimum observed result such that the lower 100 (1-α)% confidence limit on the result is greater than zero.
  4. Critical Value (LC) — The minimum observed result such that the lower 100 (1-α)% confidence limit on the result is greater than the mean of the method blanks.

LD Detection — Statistical Definitions

  1. The Minimum Detectable Value (LD) — The lowest true concentration at which the odds of a future false-negative measurement that is less than the Critical Value, LC, is equal to beta (β). Algebraically, this is expressed as LD = LC + z(1-β)*σ(LD), where beta is the probability of a Type II error, z(1-β) is the (1-β) percentage point of the standard normal variable, and sigma(LD) is the standard deviation of the population of all possible measurements of a sample with a true value of LD.
  2. The Minimum Detectable Value (LD) — Once LC is established, LD is the smallest concentration or amount of analyte at which the tolerance for Type II error is equal to beta.
  3. The Minimum Detectable Value (LD) — The lowest true concentration such that the frequency that the result is greater than LC will be 100% (1-β).

LC and LD Detection — Statistical Definition

Detection (LC and LD) — Following the statistical theory of Hypothesis Testing we consider two kinds of errors (really erroneous decisions): the error of the first kind ("type I, " false positive), accepting the "alternative hypothesis" (analyte present) when that is wrong; and the error of the second kind ("type II," false negative), accepting the "null hypothesis" (analyte absent) when that is wrong. The probability of the type I error is indicated by α; the probability for the type II error, by β. Default values recommended by IUPAC for α and β are 0.05, each. The Critical Value, LC, is set at a specific value of α (0.05 default) and the Minimum Detectable Value, LD, is set at a specific value of β (0.05 default), once LC has been established.

LQ Quantitation Definitions

  1. Quantification Limit (LQ) — The smallest detectable amount or concentration of analyte greater than the detection limit where the required** accuracy (precision & bias) is achieved for the intended purpose.
    • **Note: EPA requested additional conversation around the use of the word required in the definition.
  2. Quantification Limit (LQ) — The smallest amount or concentration of analyte greater than LD where some specified tolerance for uncertainty is met.
  3. Quantification Limit (LQ) — That concentration above which a given value of ρ is achieved, where ρ is the relative percent standard deviation; ρ = 10 has been suggested as suitable. If the chosen value for ρ is denoted by ρQ, the Lower Limit of Determination, LQ, is given by:
    • LQ = 100σt/ρQ
    where σt is the total standard deviation of analytical results at a determined concentration LQ.
  4. Quantification Limit (LQ) — The smallest amount or concentration of analyte greater than LC where some specified tolerance for uncertainty is met. The uncertainty for a variable of interest X (e.g., the concentration of an analyte in a sample) refers to the range of values (a, b) containing the true value of X at the required level of confidence gamma.

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