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authorranke <ranke@5fad18fb-23f0-0310-ab10-e59a3bee62b4>2015-08-22 09:29:17 +0000
committerranke <ranke@5fad18fb-23f0-0310-ab10-e59a3bee62b4>2015-08-22 09:29:17 +0000
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treeffd6800812fd3f5a2cfa277d5177ecfc77f14e92 /inst/web/lod.html
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git-svn-id: http://kriemhild.uft.uni-bremen.de/svn/chemCal@37 5fad18fb-23f0-0310-ab10-e59a3bee62b4
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+<!DOCTYPE html>
+<html lang="en">
+ <head>
+ <meta charset="utf-8">
+<title>lod. chemCal 0.1-35.900</title>
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="author" content="">
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+ <div class="navbar">
+ <div class="navbar-inner">
+ <div class="container">
+ <a class="brand" href="#">chemCal 0.1-35.900</a>
+ <div class="nav">
+ <ul class="nav">
+ <li><a href="index.html"><i class="icon-home icon-white"></i> Index</a></li>
+ </ul>
+ </div>
+ </div>
+ </div>
+</div>
+
+ <div class="container">
+ <header>
+
+ </header>
+
+ <h1>Estimate a limit of detection (LOD)</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><div>lod(object, ..., alpha&nbsp;=&nbsp;0.05, beta&nbsp;=&nbsp;0.05, method&nbsp;=&nbsp;"default", tol&nbsp;=&nbsp;"default")</div></pre>
+
+ <h2>Arguments</h2>
+ <dl>
+ <dt>object</dt>
+ <dd>
+ A univariate model object of class <code><a href='http://www.inside-r.org/r-doc/stats/lm'>lm</a></code> or
+ <code><a href='http://www.inside-r.org/r-doc/MASS/rlm'>rlm</a></code>
+ with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>,
+ optionally from a weighted regression.
+ </dd>
+ <dt>...</dt>
+ <dd>
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ </dd>
+ <dt>alpha</dt>
+ <dd>
+ The error tolerance for the decision limit (critical value).
+ </dd>
+ <dt>beta</dt>
+ <dd>
+ The error tolerance beta for the detection limit.
+ </dd>
+ <dt>method</dt>
+ <dd>
+ The &#147;default&#148; 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 &#147;din&#148; method uses the prediction interval at
+ x = 0 as an approximation.
+ </dd>
+ <dt>tol</dt>
+ <dd>
+ When the &#147;default&#148; 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.
+ </dd>
+ </dl>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ A list containig the corresponding x and y values of the estimated limit of
+ detection of a model used for calibration.
+</dl></p>
+
+ </div>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <p>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).</p>
+
+ </div>
+
+ <div class="Note">
+ <h2>Note</h2>
+
+ <p>- 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><a href='http://www.inside-r.org/r-doc/stats/predict.lm'>predict.lm</a></code>
+ function, which is currently not supported in R.</p>
+
+ </div>
+
+ <div class="References">
+ <h2>References</h2>
+
+ <p>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</p>
+
+ <p>J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and
+ Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
+ Web edition.</p>
+
+ <p>Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
+ detection and quantification capabilities (IUPAC Recommendations 1995).
+ Analytica Chimica Acta 391, 105 - 126.</p>
+
+ </div>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'>data(din32645)
+m &lt;- lm(y ~ x, data = din32645)
+lod(m)
+</div>
+<div class='output'>$x
+[1] 0.08655484
+
+$y
+ 1
+3317.154
+
+</div>
+<div class='input'>
+# The critical value (decision limit, German Nachweisgrenze) can be obtained
+# by using beta = 0.5:
+lod(m, alpha = 0.01, beta = 0.5)
+</div>
+<div class='output'>$x
+[1] 0.0698127
+
+$y
+ 1
+3155.393
+
+</div></pre>
+ </div>
+ <div class="span4">
+ <!-- <ul>
+ <li>lod</li><li>lod.lm</li><li>lod.rlm</li><li>lod.default</li>
+ </ul>
+ <ul>
+ <li>manip</li>
+ </ul> -->
+
+ <h2>See also</h2>
+
+ Examples for <code><a href='din32645.html'>din32645</a></code>
+
+
+ </div>
+</div>
+
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