lod. chemCal 0.1-35.900

Usage

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. +
...: + 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. +

+ +

Value

+ +

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

+ +

Description

+ +

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).

+ +

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.

+ +

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

+ +

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.

+ +

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 
+
+

+ + +

Estimate a limit of detection (LOD)