Estimate a limit of detection (LOD)

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).

+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).

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

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

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.; 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.; 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.; 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.

Value

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

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

Note

- 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.

* 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.

References

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

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

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

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

+Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. +Web edition.

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

Examples

m <- lm(y ~ x, data = din32645)
+    
+m <- lm(y ~ x, data = din32645)
 lod(m) 
 #> $x
 #> [1] 0.08655484
@@ -150,6 +156,7 @@
 #> $y
 #> [1] 3155.393
 #> 
+