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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
commit73e650114af77582238abf5273e63005e0b2287e (patch)
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-<!DOCTYPE html>
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-<title>lod. chemCal 0.1-37</title>
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-
- <h1>Estimate a limit of detection (LOD)</h1>
-
-<div class="row">
- <div class="span8">
- <h2>Usage</h2>
- <pre><span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">object</span><span class="keyword">,</span> <span class="symbol">...</span><span class="keyword">,</span> <span class="argument">alpha</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="number">0.05</span><span class="keyword">,</span> <span class="argument">beta</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="number">0.05</span><span class="keyword">,</span> <span class="argument">method</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="string">"default"</span><span class="keyword">,</span> <span class="argument">tol</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="string">"default"</span><span class="keyword">)</span></pre>
-
- <h2>Arguments</h2>
- <dl>
- <dt>object</dt>
- <dd>
- A univariate model object of class <code><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></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 &#147;default&#148; 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 &#147;din&#148; method uses the prediction interval at
- x = 0 as an approximation.
- </dd>
- <dt>tol</dt>
- <dd>
- When the &#147;default&#148; 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>
-
- <div class="Value">
- <h2>Value</h2>
-
- <p><dl>
- A list containig the corresponding x and y values of the estimated limit of
- detection of a model used for calibration.
-</dl></p>
-
- </div>
-
- <div class="Description">
- <h2>Description</h2>
-
- <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>
-
- </div>
-
- <div class="Note">
- <h2>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><a href='http://www.rdocumentation.org/packages/stats/topics/predict.lm'>predict.lm</a></code>
- function, which is currently not supported in R.</p>
-
- </div>
-
- <div class="References">
- <h2>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>
-
- </div>
-
- <h2 id="examples">Examples</h2>
- <pre class="examples"><div class='input'><span class="functioncall"><a href='http://www.rdocumentation.org/packages/utils/topics/data'>data</a></span><span class="keyword">(</span><span class="symbol">din32645</span><span class="keyword">)</span>
-<span class="symbol">m</span> <span class="assignement">&lt;-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span><span class="keyword">(</span><span class="symbol">y</span> <span class="keyword">~</span> <span class="symbol">x</span><span class="keyword">,</span> <span class="argument">data</span> <span class="argument">=</span> <span class="symbol">din32645</span><span class="keyword">)</span>
-<span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">)</span></div>
-<div class='output'>$x
-[1] 0.08655484
-
-$y
- 1
-3317.154
-
-</div>
-<div class='input'>
-<span class="comment"># The critical value (decision limit, German Nachweisgrenze) can be obtained</span>
-<span class="comment"># by using beta = 0.5:</span>
-<span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="argument">alpha</span> <span class="argument">=</span> <span class="number">0.01</span><span class="keyword">,</span> <span class="argument">beta</span> <span class="argument">=</span> <span class="number">0.5</span><span class="keyword">)</span></div>
-<div class='output'>$x
-[1] 0.0698127
-
-$y
- 1
-3155.393
-
-</div></pre>
- </div>
- <div class="span4 sidebar">
- <!-- <ul>
- <li>lod</li><li>lod.lm</li><li>lod.rlm</li><li>lod.default</li>
- </ul>
- <ul>
- <li>manip</li>
- </ul> -->
-
- <h2>See also</h2>
- <p>Examples for <code><a href='din32645.html'>din32645</a></code></p>
-
-
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