lod. chemCal 0.1-37

Usage

lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")

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Arguments

object: - A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1, - optionally from a weighted regression. -
...: - Placeholder for further arguments that might be needed by - future implementations. -
alpha: - The error tolerance for the decision limit (critical value). -
beta: - The error tolerance beta for the detection limit. -
method: - The “default” method uses a prediction interval at the LOD - for the estimation of the LOD, which obviously requires - iteration. This is described for example in Massart, p. 432 ff. - The “din” method uses the prediction interval at - x = 0 as an approximation. -
tol: - When the “default” method is used, the default tolerance - for the LOD on the x scale is the value of the smallest non-zero standard - divided by 1000. Can be set to a numeric value to override this. -

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Value

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- A list containig the corresponding x and y values of the estimated limit of - detection of a model used for calibration. -

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Description

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The decision limit (German: Nachweisgrenze) is defined as the signal or - analyte concentration that is significantly different from the blank signal - with a first order error alpha (one-sided significance test). - The detection limit, or more precise, the minimum detectable value - (German: Erfassungsgrenze), is then defined as the signal or analyte - concentration where the probability that the signal is not detected although - the analyte is present (type II or false negative error), is beta (also a - one-sided significance test).

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Note

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- The default values for alpha and beta are the ones recommended by IUPAC. - - The estimation of the LOD in terms of the analyte amount/concentration - xD from the LOD in the signal domain SD is done by simply inverting the - calibration function (i.e. assuming a known calibration function). - - The calculation of a LOD from weighted calibration models requires - a weights argument for the internally used predict.lm - function, which is currently not supported in R.

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References

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Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., - Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, - Chapter 13.7.8

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J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and - Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. - Web edition.

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Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including - detection and quantification capabilities (IUPAC Recommendations 1995). - Analytica Chimica Acta 391, 105 - 126.

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Examples

data(din32645)
-m <- lm(y ~ x, data = din32645)
-lod(m) 
-
-$x
-[1] 0.08655484
-
-$y
-       1 
-3317.154 
-
-
-
-# The critical value (decision limit, German Nachweisgrenze) can be obtained
-# by using beta = 0.5:
-lod(m, alpha = 0.01, beta = 0.5)
-
-$x
-[1] 0.0698127
-
-$y
-       1 
-3155.393 
-
-

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Estimate a limit of detection (LOD)