diff options
Diffstat (limited to 'R/lod.R')
| -rw-r--r-- | R/lod.R | 61 |
1 files changed, 61 insertions, 0 deletions
@@ -1,13 +1,74 @@ +#' 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). +#' +#' @aliases lod lod.lm lod.rlm lod.default +#' @param 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. +#' @param \dots Placeholder for further arguments that might be needed by +#' future implementations. +#' @param alpha The error tolerance for the decision limit (critical value). +#' @param beta The error tolerance beta for the detection limit. +#' @param method The \dQuote{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 \dQuote{din} method +#' uses the prediction interval at x = 0 as an approximation. +#' @param tol When the \dQuote{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. +#' @return 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 \code{\link{predict.lm}} +#' function, which is currently not supported in R. +#' @seealso Examples for \code{\link{din32645}} +#' @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. +#' @importFrom stats optimize predict +#' @examples +#' +#' 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) +#' +#' @export lod <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default") { UseMethod("lod") } +#' @export lod.default <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default") { stop("lod is only implemented for univariate lm objects.") } +#' @export lod.lm <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default") { if (length(object$weights) > 0) { |