diff options
Diffstat (limited to 'man')
| -rw-r--r-- | man/inverse.predict.Rd | 16 | ||||
| -rw-r--r-- | man/lod.Rd | 55 | ||||
| -rw-r--r-- | man/loq.Rd | 76 |
3 files changed, 110 insertions, 37 deletions
diff --git a/man/inverse.predict.Rd b/man/inverse.predict.Rd index 8c2be9c..5be0250 100644 --- a/man/inverse.predict.Rd +++ b/man/inverse.predict.Rd @@ -57,14 +57,14 @@ p. 200 } \examples{ -data(massart97ex3) -attach(massart97ex3) -yx <- split(y,factor(x)) -s <- round(sapply(yx,sd),digits=2) -w <- round(1/(s^2),digits=3) -weights <- w[factor(x)] -m <- lm(y ~ x,w=weights) + data(massart97ex3) + attach(massart97ex3) + yx <- split(y,factor(x)) + s <- round(sapply(yx,sd),digits=2) + w <- round(1/(s^2),digits=3) + weights <- w[factor(x)] + m <- lm(y ~ x,w=weights) -inverse.predict(m,15,ws = 1.67) + inverse.predict(m,15,ws = 1.67) } \keyword{manip} @@ -3,14 +3,9 @@ \alias{lod.lm} \alias{lod.rlm} \alias{lod.default} -\alias{loq} -\alias{loq.lm} -\alias{loq.rlm} -\alias{loq.default} -\title{Estimate a limit of detection (LOD) or quantification (LOQ)} +\title{Estimate a limit of detection (LOD)} \usage{ - lod(object, \dots, alpha = 0.05, k = 1, n = 1, w = "auto") - loq(object, \dots, alpha = 0.05, k = 3, n = 1, w = "auto") + lod(object, \dots, alpha = 0.05, beta = 0.05) } \arguments{ \item{object}{ @@ -19,40 +14,42 @@ with model formula \code{y ~ x} or \code{y ~ x - 1}, optionally from a weighted regression. } - \item{alpha}{ - The error tolerance for the prediction of x values in the calculation. - } \item{\dots}{ Placeholder for further arguments that might be needed by future implementations. } - \item{k}{ - The inverse of the maximum relative error tolerated at the - desired LOD/LOQ. - } - \item{n}{ - The number of replicate measurements for which the LOD/LOQ should be - specified. + \item{alpha}{ + The error tolerance for the decision limit (critical value). } - \item{w}{ - The weight that should be attributed to the LOD/LOQ. Defaults - to one for unweighted regression, and to the mean of the weights - for weighted regression. See \code{\link{massart97ex3}} for - an example how to take advantage of knowledge about the variance function. + \item{beta}{ + The error tolerance beta for the detection limit. } } \value{ - The estimated limit of detection for 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. } \description{ - A useful operationalisation of a lower limit L of a measurement method is - simply the solution of the equation - \deqn{L = k c(L)}{L = k * c(L)} - where c(L) is half of the lenght of the confidence interval at the limit L. + 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). +} +\references{ + J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and + Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. + Web edition. } \examples{ data(din32645) m <- lm(y ~ x, data = din32645) - lod(m) + # The decision limit (critical value) is obtained by using beta = 0.5: + lod(m, alpha = 0.01, beta = 0.5) # approx. Nachweisgrenze in Dintest 2002 + lod(m, alpha = 0.01, beta = 0.01) + # In the latter case (Erfassungsgrenze), we get a slight deviation from + # Dintest 2002 test data. } \keyword{manip} diff --git a/man/loq.Rd b/man/loq.Rd new file mode 100644 index 0000000..1030399 --- /dev/null +++ b/man/loq.Rd @@ -0,0 +1,76 @@ +\name{loq} +\alias{loq} +\alias{loq.lm} +\alias{loq.rlm} +\alias{loq.default} +\title{Estimate a limit of quantification (LOQ)} +\usage{ + loq(object, \dots, alpha = 0.05, k = 3, n = 1, w = "auto") +} +\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{alpha}{ + The error tolerance for the prediction of x values in the calculation. + } + \item{\dots}{ + Placeholder for further arguments that might be needed by + future implementations. + } + \item{k}{ + The inverse of the maximum relative error tolerated at the + desired LOQ. + } + \item{n}{ + The number of replicate measurements for which the LOQ should be + specified. + } + \item{w}{ + The weight that should be attributed to the LOQ. Defaults + to one for unweighted regression, and to the mean of the weights + for weighted regression. See \code{\link{massart97ex3}} for + an example how to take advantage of knowledge about the + variance function. + } +} +\value{ + The estimated limit of quantification for a model used for calibration. +} +\description{ + A useful operationalisation of a limit of quantification is simply the + solution of the equation + \deqn{L = k c(L)}{L = k * c(L)} + where c(L) is half of the length of the confidence interval at the limit L as + estimated by \code{\link{inverse.predict}}. By virtue of this formula, the + limit of detection is the x value, where the relative error + of the quantification with the given calibration model is 1/k. +} +\examples{ + data(massart97ex3) + attach(massart97ex3) + m0 <- lm(y ~ x) + loq(m0) + + # Now we use a weighted regression + yx <- split(y,factor(x)) + s <- round(sapply(yx,sd),digits=2) + w <- round(1/(s^2),digits=3) + weights <- w[factor(x)] + mw <- lm(y ~ x,w=weights) + loq(mw) + + # In order to define the weight at the loq, we can use + # the variance function 1/y for the model + mwy <- lm(y ~ x, w = 1/y) + + # Let's do this with one iteration only + loq(mwy, w = 1 / predict(mwy,list(x = loq(mwy)))) + + # We can get better by doing replicate measurements + loq(mwy, n = 3, w = 1 / predict(mwy,list(x = loq(mwy)))) +} +\keyword{manip} |