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Thus, it is the solution of the equation - $$L = k c(L)$$ - where c(L) is half of the length of the confidence interval at the limit L - (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by - inverse.predict, and L is obtained by iteration."><!-- 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]> +<!-- 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 quantification (LOQ) — loq • 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 quantification (LOQ) — loq"><meta property="og:description" content="The limit of quantification is the x value, where the relative error of the +quantification given the calibration model reaches a prespecified value 1/k. +Thus, it is the solution of the equation $$L = k c(L)$$ +where c(L) is half of the length of the confidence interval at the limit L +(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by +inverse.predict, and L is obtained by iteration."><!-- 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"> @@ -53,69 +52,75 @@ <div class="col-md-9 contents"> <div class="page-header"> <h1>Estimate a limit of quantification (LOQ)</h1> - + <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/loq.R" class="external-link"><code>R/loq.R</code></a></small> <div class="hidden name"><code>loq.Rd</code></div> </div> <div class="ref-description"> - <p>The limit of quantification is the x value, where the relative error - of the quantification given the calibration model reaches a prespecified - value 1/k. Thus, it is the solution of the equation - $$L = k c(L)$$ - where c(L) is half of the length of the confidence interval at the limit L - (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by - <code><a href="inverse.predict.html">inverse.predict</a></code>, and L is obtained by iteration.</p> + <p>The limit of quantification is the x value, where the relative error of the +quantification given the calibration model reaches a prespecified value 1/k. +Thus, it is the solution of the equation $$L = k c(L)$$ +where c(L) is half of the length of the confidence interval at the limit L +(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by +<code><a href="inverse.predict.html">inverse.predict</a></code>, and L is obtained by iteration.</p> </div> <div id="ref-usage"> - <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">loq</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>, k <span class="op">=</span> <span class="fl">3</span>, n <span class="op">=</span> <span class="fl">1</span>, w.loq <span class="op">=</span> <span class="st">"auto"</span>, - var.loq <span class="op">=</span> <span class="st">"auto"</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">loq</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>, + k <span class="op">=</span> <span class="fl">3</span>, + n <span class="op">=</span> <span class="fl">1</span>, + w.loq <span class="op">=</span> <span class="st">"auto"</span>, + var.loq <span class="op">=</span> <span class="st">"auto"</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. If weights are specified - in the model, either <code>w.loq</code> or <code>var.loq</code> have to - be specified.</p></dd> -<dt>alpha</dt> -<dd><p>The error tolerance for the prediction of x values in the calculation.</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. If weights are specified in the +model, either <code>w.loq</code> or <code>var.loq</code> have to be specified.</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 prediction of x values in the +calculation.</p></dd> <dt>k</dt> -<dd><p>The inverse of the maximum relative error tolerated at the - desired LOQ.</p></dd> +<dd><p>The inverse of the maximum relative error tolerated at the desired +LOQ.</p></dd> <dt>n</dt> <dd><p>The number of replicate measurements for which the LOQ should be - specified.</p></dd> +specified.</p></dd> <dt>w.loq</dt> -<dd><p>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><a href="massart97ex3.html">massart97ex3</a></code> for - an example how to take advantage of knowledge about the - variance function.</p></dd> +<dd><p>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><a href="massart97ex3.html">massart97ex3</a></code> for an example how to take +advantage of knowledge about the variance function.</p></dd> <dt>var.loq</dt> -<dd><p>The approximate variance at the LOQ. The default value is - calculated from the model.</p></dd> +<dd><p>The approximate variance at the LOQ. The default value is +calculated from the model.</p></dd> <dt>tol</dt> -<dd><p>The default tolerance for the LOQ 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> +<dd><p>The default tolerance for the LOQ 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>The estimated limit of quantification for a model used for calibration.</p> + <p>The estimated limit of quantification for a model used for +calibration.</p> </div> <div id="note"> <h2>Note</h2> - <p>- IUPAC recommends to base the LOQ on the standard deviation of the signal - where x = 0. - - The calculation of a LOQ based on weighted regression is non-standard - and therefore not tested. Feedback is welcome.</p> + <p>* IUPAC recommends to base the LOQ on the standard deviation of the +signal where x = 0. +* The calculation of a LOQ based on weighted regression is non-standard and +therefore not tested. Feedback is welcome.</p> </div> <div id="see-also"> <h2>See also</h2> @@ -124,7 +129,8 @@ <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">massart97ex1</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">massart97ex1</span><span class="op">)</span></span> <span class="r-in"><span class="fu">loq</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] 13.97764</span> @@ -141,6 +147,7 @@ <span class="r-out co"><span class="r-pr">#></span> $y</span> <span class="r-out co"><span class="r-pr">#></span> [1] 22.68539</span> <span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-in"></span> </code></pre></div> </div> </div> |