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diff --git a/docs/reference/lod.html b/docs/reference/lod.html index a2d66ce..1fbae76 100644 --- a/docs/reference/lod.html +++ b/docs/reference/lod.html @@ -1,12 +1,12 @@ <!DOCTYPE html> <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Estimate a limit of detection (LOD) — lod • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate a limit of detection (LOD) — lod"><meta property="og:description" content="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)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> +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)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> <![endif]--></head><body data-spy="scroll" data-target="#toc"> @@ -54,76 +54,81 @@ <div class="col-md-9 contents"> <div class="page-header"> <h1>Estimate a limit of detection (LOD)</h1> - + <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/lod.R" class="external-link"><code>R/lod.R</code></a></small> <div class="hidden name"><code>lod.Rd</code></div> </div> <div class="ref-description"> <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> +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 id="ref-usage"> - <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">lod</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span>, alpha <span class="op">=</span> <span class="fl">0.05</span>, beta <span class="op">=</span> <span class="fl">0.05</span>, method <span class="op">=</span> <span class="st">"default"</span>, tol <span class="op">=</span> <span class="st">"default"</span><span class="op">)</span></code></pre></div> + <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">lod</span><span class="op">(</span> + <span class="va">object</span>, + <span class="va">...</span>, + alpha <span class="op">=</span> <span class="fl">0.05</span>, + beta <span class="op">=</span> <span class="fl">0.05</span>, + method <span class="op">=</span> <span class="st">"default"</span>, + tol <span class="op">=</span> <span class="st">"default"</span> +<span class="op">)</span></code></pre></div> </div> <div id="arguments"> <h2>Arguments</h2> <dl><dt>object</dt> -<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or - <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> - with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>, - optionally from a weighted regression.</p></dd> +<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or +<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x - +1</code>, optionally from a weighted regression.</p></dd> <dt>...</dt> -<dd><p>Placeholder for further arguments that might be needed by - future implementations.</p></dd> +<dd><p>Placeholder for further arguments that might be needed by +future implementations.</p></dd> <dt>alpha</dt> <dd><p>The error tolerance for the decision limit (critical value).</p></dd> <dt>beta</dt> <dd><p>The error tolerance beta for the detection limit.</p></dd> <dt>method</dt> -<dd><p>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.</p></dd> +<dd><p>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.</p></dd> <dt>tol</dt> <dd><p>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.</p></dd> +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.</p></dd> </dl></div> <div id="value"> <h2>Value</h2> - <p>A list containig the corresponding x and y values of the estimated limit of - detection of a model used for calibration.</p> + <p>A list containig the corresponding x and y values of the estimated +limit of detection of a model used for calibration.</p> </div> <div id="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="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code> - function, which is currently not supported in R.</p> + <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="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code> +function, which is currently not supported in R.</p> </div> <div id="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>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> +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> <div id="see-also"> <h2>See also</h2> @@ -132,7 +137,8 @@ <div id="ref-examples"> <h2>Examples</h2> - <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="va">m</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">din32645</span><span class="op">)</span></span> + <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span> +<span class="r-in"><span class="va">m</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">din32645</span><span class="op">)</span></span> <span class="r-in"><span class="fu">lod</span><span class="op">(</span><span class="va">m</span><span class="op">)</span> </span> <span class="r-out co"><span class="r-pr">#></span> $x</span> <span class="r-out co"><span class="r-pr">#></span> [1] 0.08655484</span> @@ -150,6 +156,7 @@ <span class="r-out co"><span class="r-pr">#></span> $y</span> <span class="r-out co"><span class="r-pr">#></span> [1] 3155.393</span> <span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-in"></span> </code></pre></div> </div> </div> |