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\name{lod}
\alias{lod}
\alias{lod.lm}
\alias{lod.rlm}
\alias{lod.default}
\title{Estimate a limit of detection (LOD)}
\usage{
lod(object, \dots, alpha = 0.05, beta = 0.05)
}
\arguments{
\item{object}{
A univariate model object of class \code{\link{lm}} or
\code{\link[MASS:rlm]{rlm}}
with model formula \code{y ~ x} or \code{y ~ x - 1},
optionally from a weighted regression.
}
\item{\dots}{
Placeholder for further arguments that might be needed by
future implementations.
}
\item{alpha}{
The error tolerance for the decision limit (critical value).
}
\item{beta}{
The error tolerance beta for the detection limit.
}
}
\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 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 \code{\link{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)
# The critical value (decision limit, German Nachweisgrenze) can be obtained
# by using beta = 0.5:
lod(m, alpha = 0.01, beta = 0.5)
# or approximated by
2 * lod(m, alpha = 0.01, beta = 0.5)$x
# for the case of known, constant variance (homoscedastic data)
}
\keyword{manip}
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