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diff --git a/docs/reference/lod.html b/docs/reference/lod.html new file mode 100644 index 0000000..7c33d47 --- /dev/null +++ b/docs/reference/lod.html @@ -0,0 +1,210 @@ +<!-- Generated by pkgdown: do not edit by hand --> +<!DOCTYPE html> +<html> + <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 detection (LOD) — lod • chemCal</title> + +<!-- jquery --> +<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script> +<!-- Bootstrap --> + +<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous"> +<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script> + +<!-- Font Awesome icons --> +<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous"> + + +<!-- pkgdown --> +<link href="../pkgdown.css" rel="stylesheet"> +<script src="../jquery.sticky-kit.min.js"></script> +<script src="../pkgdown.js"></script> + +<!-- mathjax --> +<script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></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"> + <span class="icon-bar"></span> + <span class="icon-bar"></span> + <span class="icon-bar"></span> + </button> + <a class="navbar-brand" href="../index.html">chemCal</a> + </div> + <div id="navbar" class="navbar-collapse collapse"> + <ul class="nav navbar-nav"> + <li> + <a href="../reference/index.html">Reference</a> +</li> +<li> + <a href="../articles/index.html">Articles</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 detection (LOD)</h1> + </div> + + + <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> + + + <pre>lod(object, …, alpha = 0.05, beta = 0.05, method = "default", tol = "default")</pre> + + <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a> Arguments</h2> + <dl class="dl-horizontal"> + <dt>object</dt> + <dd> + A univariate model object of class <code>lm</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> + + <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>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> + + <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>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>predict.lm</code> + function, which is currently not supported in R.</p> + + <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>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> + + <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2> + + <p>Examples for <code><a href='din32645.html'>din32645</a></code></p> + + + <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> + <pre class="examples"><div class='input'><span class='fu'>data</span>(<span class='no'>din32645</span>) +<span class='no'>m</span> <span class='kw'><-</span> <span class='fu'>lm</span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>din32645</span>) +<span class='fu'>lod</span>(<span class='no'>m</span>)</div><div class='output co'>#> $x +#> [1] 0.08655484 +#> +#> $y +#> 1 +#> 3317.154 +#> </div><div class='input'> +<span class='co'># The critical value (decision limit, German Nachweisgrenze) can be obtained</span> +<span class='co'># by using beta = 0.5:</span> +<span class='fu'>lod</span>(<span class='no'>m</span>, <span class='kw'>alpha</span> <span class='kw'>=</span> <span class='fl'>0.01</span>, <span class='kw'>beta</span> <span class='kw'>=</span> <span class='fl'>0.5</span>)</div><div class='output co'>#> $x +#> [1] 0.0698127 +#> +#> $y +#> 1 +#> 3155.393 +#> </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="#references">References</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="http://hadley.github.io/pkgdown/">pkgdown</a>.</p> +</div> + + </footer> + </div> + + </body> +</html> |