|
|
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
<head>
<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/3.3.1/jquery.min.js" integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/css/bootstrap.min.css" integrity="sha256-916EbMg70RQy9LHiGkXzG8hSg9EdNy97GazNG/aiY1w=" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha256-U5ZEeKfGNOja007MMD3YBI0A3OSZOQbeG6z2f2Y0hu8=" crossorigin="anonymous"></script>
<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css" integrity="sha256-eZrrJcwDc/3uDhsdt61sL2oOBY362qM3lon1gyExkL0=" crossorigin="anonymous" />
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.4/clipboard.min.js" integrity="sha256-FiZwavyI2V6+EXO1U+xzLG3IKldpiTFf3153ea9zikQ=" crossorigin="anonymous"></script>
<!-- sticky kit -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" 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." />
<meta name="twitter:card" content="summary" />
<!-- 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>
<div class="container template-reference-topic">
<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">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</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>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../index.html">
<span class="fa fa-home fa-lg"></span>
</a>
</li>
<li>
<a href="../articles/chemCal.html">Get started</a>
</li>
<li>
<a href="../reference/index.html">Reference</a>
</li>
<li>
<a href="../news/index.html">Changelog</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
</header>
<div class="row">
<div class="col-md-9 contents">
<div class="page-header">
<h1>Estimate a limit of quantification (LOQ)</h1>
<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>
</div>
<pre class="usage">loq(object, …, alpha = 0.05, k = 3, n = 1, w.loq = "auto",
var.loq = "auto", tol = "default")</pre>
<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://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></code> or
<code><a href='https://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. 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
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></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
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>
<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>
<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='no'>m</span> <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex1</span>)
<span class='fu'>loq</span>(<span class='no'>m</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='no'>m</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>3</span>)</div><div class='output co'>#> $x
#> [1] 9.971963
#>
#> $y
#> [1] 22.68539
#> </div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#note">Note</a></li>
<li><a href="#see-also">See also</a></li>
<li><a href="#examples">Examples</a></li>
</ul>
</div>
</div>
<footer>
<div class="copyright">
<p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown">
<p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.</p>
</div>
</footer>
</div>
</body>
</html>
|
