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authorJohannes Ranke <jranke@uni-bremen.de>2016-10-04 08:45:23 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2016-10-04 08:45:23 +0200
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+
+ <h1>Estimate a limit of quantification (LOQ)</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><span class="functioncall"><a href='loq.html'>loq</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">k</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="number">3</span><span class="keyword">,</span> <span class="argument">n</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="number">1</span><span class="keyword">,</span> <span class="argument">w.loq</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="string">"auto"</span><span class="keyword">,</span>
+ <span class="argument">var.loq</span>&nbsp;<span class="argument">=</span>&nbsp;<span class="string">"auto"</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. If weights are specified
+ in the model, either <code>w.loq</code> or <code>var.loq</code> have to
+ be specified.
+ </dd>
+ <dt>alpha</dt>
+ <dd>
+ The error tolerance for the prediction of x values in the calculation.
+ </dd>
+ <dt>...</dt>
+ <dd>
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ </dd>
+ <dt>k</dt>
+ <dd>
+ The inverse of the maximum relative error tolerated at the
+ desired LOQ.
+ </dd>
+ <dt>n</dt>
+ <dd>
+ The number of replicate measurements for which the LOQ should be
+ specified.
+ </dd>
+ <dt>w.loq</dt>
+ <dd>
+ 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.
+ </dd>
+ <dt>var.loq</dt>
+ <dd>
+ The approximate variance at the LOQ. The default value is
+ calculated from the model.
+ </dd>
+ <dt>tol</dt>
+ <dd>
+ 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.
+ </dd>
+ </dl>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ The estimated limit of quantification for a model used for calibration.
+</dl></p>
+
+ </div>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <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>
+
+ <div class="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>
+
+ </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">massart97ex3</span><span class="keyword">)</span>
+<span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/attach'>attach</a></span><span class="keyword">(</span><span class="symbol">massart97ex3</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="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">)</span></div>
+<div class='output'>$x
+[1] 13.97764
+
+$y
+ 1
+30.6235
+
+</div>
+<div class='input'>
+<span class="comment"># We can get better by using replicate measurements</span>
+<span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="argument">n</span> <span class="argument">=</span> <span class="number">3</span><span class="keyword">)</span></div>
+<div class='output'>$x
+[1] 9.971963
+
+$y
+ 1
+22.68539
+
+</div></pre>
+ </div>
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+ <!-- <ul>
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+
+ <h2>See also</h2>
+ <p>Examples for <code><a href='din32645.html'>din32645</a></code></p>
+
+
+
+
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