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| author | Johannes Ranke <jranke@uni-bremen.de> | 2016-10-04 08:45:23 +0200 |
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| committer | Johannes Ranke <jranke@uni-bremen.de> | 2016-10-04 08:45:23 +0200 |
| commit | b31824f420c9d904ab5f46774183a59e3b86cedd (patch) | |
| tree | 87737278e9a14202a07c4110cd62684807f96062 /docs/lod.html | |
| parent | 17ef63f22008c80998cb2690a40ad1238d06a400 (diff) | |
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diff --git a/docs/lod.html b/docs/lod.html new file mode 100644 index 0000000..e5eb135 --- /dev/null +++ b/docs/lod.html @@ -0,0 +1,199 @@ +<!DOCTYPE html> +<html lang="en"> + <head> + <meta charset="utf-8"> +<title>lod. chemCal 0.1-37</title> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> +<meta name="author" content=""> + +<link href="css/bootstrap.css" rel="stylesheet"> +<link href="css/bootstrap-responsive.css" rel="stylesheet"> +<link href="css/highlight.css" rel="stylesheet"> +<link href="css/staticdocs.css" rel="stylesheet"> + +<!--[if lt IE 9]> + <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script> +<![endif]--> + +<script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + tex2jax: { + inlineMath: [ ['$','$'], ["\\(","\\)"] ], + processEscapes: true + } + }); +</script> +<script type="text/javascript" + src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> +</script> + </head> + + <body> + <div class="navbar"> + <div class="navbar-inner"> + <div class="container"> + <a class="brand" href="index.html">chemCal 0.1-37</a> + <div class="nav"> + <ul class="nav"> + <li><a href="index.html">Home</a></li> + <li><a href="reference.html">Reference</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><span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">object</span><span class="keyword">,</span> <span class="symbol">...</span><span class="keyword">,</span> <span class="argument">alpha</span> <span class="argument">=</span> <span class="number">0.05</span><span class="keyword">,</span> <span class="argument">beta</span> <span class="argument">=</span> <span class="number">0.05</span><span class="keyword">,</span> <span class="argument">method</span> <span class="argument">=</span> <span class="string">"default"</span><span class="keyword">,</span> <span class="argument">tol</span> <span class="argument">=</span> <span class="string">"default"</span><span class="keyword">)</span></pre> + + <h2>Arguments</h2> + <dl> + <dt>object</dt> + <dd> + A univariate model object of class <code><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></code> or + <code><a href='http://www.rdocumentation.org/packages/MASS/topics/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 “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. + </dd> + <dt>tol</dt> + <dd> + 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. + </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.rdocumentation.org/packages/stats/topics/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'><span class="functioncall"><a href='http://www.rdocumentation.org/packages/utils/topics/data'>data</a></span><span class="keyword">(</span><span class="symbol">din32645</span><span class="keyword">)</span> +<span class="symbol">m</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span><span class="keyword">(</span><span class="symbol">y</span> <span class="keyword">~</span> <span class="symbol">x</span><span class="keyword">,</span> <span class="argument">data</span> <span class="argument">=</span> <span class="symbol">din32645</span><span class="keyword">)</span> +<span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">)</span></div> +<div class='output'>$x +[1] 0.08655484 + +$y + 1 +3317.154 + +</div> +<div class='input'> +<span class="comment"># The critical value (decision limit, German Nachweisgrenze) can be obtained</span> +<span class="comment"># by using beta = 0.5:</span> +<span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="argument">alpha</span> <span class="argument">=</span> <span class="number">0.01</span><span class="keyword">,</span> <span class="argument">beta</span> <span class="argument">=</span> <span class="number">0.5</span><span class="keyword">)</span></div> +<div class='output'>$x +[1] 0.0698127 + +$y + 1 +3155.393 + +</div></pre> + </div> + <div class="span4 sidebar"> + <!-- <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> + <p>Examples for <code><a href='din32645.html'>din32645</a></code></p> + + + + + </div> +</div> + + <footer> + <p class="pull-right"><a href="#">Back to top</a></p> +<p>Built by <a href="https://github.com/hadley/staticdocs">staticdocs</a>. Styled with <a href="https://getbootstrap.com/2.0.4/">bootstrap</a>.</p> + </footer> + </div> + </body> +</html>
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