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authorJohannes Ranke <jranke@uni-bremen.de>2017-03-06 17:00:48 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2017-03-06 17:00:48 +0100
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+ <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, &#8230;, 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>&#8230;</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 &#8220;default&#8221; 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 &#8220;din&#8221; method uses the prediction interval at
+ x = 0 as an approximation.
+ </dd>
+ <dt>tol</dt>
+ <dd>
+ When the &#8220;default&#8221; 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'>&lt;-</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'>#&gt; $x
+#&gt; [1] 0.08655484
+#&gt;
+#&gt; $y
+#&gt; 1
+#&gt; 3317.154
+#&gt; </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'>#&gt; $x
+#&gt; [1] 0.0698127
+#&gt;
+#&gt; $y
+#&gt; 1
+#&gt; 3155.393
+#&gt; </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>
+
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