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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]> + 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> +<![endif]--></head><body data-spy="scroll" data-target="#toc"> + - <body data-spy="scroll" data-target="#toc"> <div class="container template-reference-topic"> - <header> - <div class="navbar navbar-default navbar-fixed-top" role="navigation"> + <header><div class="navbar navbar-default navbar-fixed-top" role="navigation"> <div class="container"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> @@ -78,19 +23,12 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">chemCal</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.2.2</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> - <ul class="nav navbar-nav"> - <li> - <a href="../index.html"> - <span class="fas fa-home fa-lg"></span> - - </a> -</li> -<li> + <ul class="nav navbar-nav"><li> <a href="../articles/chemCal.html">Get started</a> </li> <li> @@ -99,25 +37,19 @@ <li> <a href="../news/index.html">Changelog</a> </li> - </ul> - <ul class="nav navbar-nav navbar-right"> - <li> - <a href="https://github.com/jranke/chemCal/"> + </ul><ul class="nav navbar-nav navbar-right"><li> + <a href="https://github.com/jranke/chemCal/" class="external-link"> <span class="fab fa-github fa-lg"></span> </a> </li> - </ul> - - </div><!--/.nav-collapse --> + </ul></div><!--/.nav-collapse --> </div><!--/.container --> </div><!--/.navbar --> - </header> - -<div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header"> <h1>Estimate a limit of quantification (LOQ)</h1> @@ -132,119 +64,106 @@ $$L = k c(L)$$ 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> + <code><a href="inverse.predict.html">inverse.predict</a></code>, and L is obtained by iteration.</p> </div> - <pre class="usage"><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></pre> + <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> - <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2> - <table class="ref-arguments"> - <colgroup><col class="name" /><col class="desc" /></colgroup> - <tr> - <th>object</th> - <td><p>A univariate model object of class <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code> or - <code><a href='https://rdrr.io/pkg/MASS/man/rlm.html'>rlm</a></code> + <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></td> - </tr> - <tr> - <th>alpha</th> - <td><p>The error tolerance for the prediction of x values in the calculation.</p></td> - </tr> - <tr> - <th>...</th> - <td><p>Placeholder for further arguments that might be needed by - future implementations.</p></td> - </tr> - <tr> - <th>k</th> - <td><p>The inverse of the maximum relative error tolerated at the - desired LOQ.</p></td> - </tr> - <tr> - <th>n</th> - <td><p>The number of replicate measurements for which the LOQ should be - specified.</p></td> - </tr> - <tr> - <th>w.loq</th> - <td><p>The weight that should be attributed to the LOQ. Defaults + be specified.</p></dd> +<dt>alpha</dt> +<dd><p>The error tolerance for the prediction of x values in the calculation.</p></dd> +<dt>...</dt> +<dd><p>Placeholder for further arguments that might be needed by + future implementations.</p></dd> +<dt>k</dt> +<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> +<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 + 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></td> - </tr> - <tr> - <th>var.loq</th> - <td><p>The approximate variance at the LOQ. The default value is - calculated from the model.</p></td> - </tr> - <tr> - <th>tol</th> - <td><p>The default tolerance for the LOQ on the x scale is the value of 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> +<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></td> - </tr> - </table> - - <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> - + 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> - <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2> - + </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> - <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2> - - <div class='dont-index'><p>Examples for <code><a href='din32645.html'>din32645</a></code></p></div> - - <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> - <pre class="examples"><div class='input'><span class='va'>m</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>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 class='fu'>loq</span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span> -</div><div class='output co'>#> $x -#> [1] 13.97764 -#> -#> $y -#> [1] 30.6235 -#> </div><div class='input'> -<span class='co'># We can get better by using replicate measurements</span> -<span class='fu'>loq</span><span class='op'>(</span><span class='va'>m</span>, n <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span> -</div><div class='output co'>#> $x -#> [1] 9.971963 -#> -#> $y -#> [1] 22.68539 -#> </div></pre> + </div> + <div id="see-also"> + <h2>See also</h2> + <div class="dont-index"><p>Examples for <code><a href="din32645.html">din32645</a></code></p></div> + </div> + + <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> +<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> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> $y</span> +<span class="r-out co"><span class="r-pr">#></span> [1] 30.6235</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-in"></span> +<span class="r-in"><span class="co"># We can get better by using replicate measurements</span></span> +<span class="r-in"><span class="fu">loq</span><span class="op">(</span><span class="va">m</span>, n <span class="op">=</span> <span class="fl">3</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] 9.971963</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<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> +</code></pre></div> + </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - <nav id="toc" data-toggle="toc" class="sticky-top"> - <h2 data-toc-skip>Contents</h2> - </nav> - </div> + <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2> + </nav></div> </div> - <footer> - <div class="copyright"> - <p>Developed by Johannes Ranke.</p> + <footer><div class="copyright"> + <p></p><p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> - <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p> + <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p> </div> - </footer> - </div> + </footer></div> - </body> -</html> + + </body></html> |