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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)."><!-- 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]>
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<h1>Estimate a limit of detection (LOD)</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/lod.R" class="external-link"><code>R/lod.R</code></a></small>
<div class="hidden name"><code>lod.Rd</code></div>
</div>
<div class="ref-description">
<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 id="ref-usage">
<div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">lod</span><span class="op">(</span>
<span class="va">object</span>,
<span class="va">...</span>,
alpha <span class="op">=</span> <span class="fl">0.05</span>,
beta <span class="op">=</span> <span class="fl">0.05</span>,
method <span class="op">=</span> <span class="st">"default"</span>,
tol <span class="op">=</span> <span class="st">"default"</span>
<span class="op">)</span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x -
1</code>, optionally from a weighted regression.</p></dd>
<dt>...</dt>
<dd><p>Placeholder for further arguments that might be needed by
future implementations.</p></dd>
<dt>alpha</dt>
<dd><p>The error tolerance for the decision limit (critical value).</p></dd>
<dt>beta</dt>
<dd><p>The error tolerance beta for the detection limit.</p></dd>
<dt>method</dt>
<dd><p>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.</p></dd>
<dt>tol</dt>
<dd><p>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.</p></dd>
</dl></div>
<div id="value">
<h2>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>
</div>
<div id="note">
<h2>Note</h2>
<ul><li><p>The default values for alpha and beta are the ones recommended by IUPAC.</p></li>
<li><p>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).</p></li>
<li><p>The calculation of a LOD from weighted calibration models requires a
weights argument for the internally used <code><a href="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code>
function, which is currently not supported in R.</p></li>
</ul></div>
<div id="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>
<div id="see-also">
<h2>See also</h2>
<div class="dont-index"><p>Examples for <code><a href="din32645.html">din32645</a></code></p></div>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
<span class="r-in"><span class="va">m</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">din32645</span><span class="op">)</span></span>
<span class="r-in"><span class="fu">lod</span><span class="op">(</span><span class="va">m</span><span class="op">)</span> </span>
<span class="r-out co"><span class="r-pr">#></span> $x</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.08655484</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $y</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 3317.154</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># The critical value (decision limit, German Nachweisgrenze) can be obtained</span></span>
<span class="r-in"><span class="co"># by using beta = 0.5:</span></span>
<span class="r-in"><span class="fu">lod</span><span class="op">(</span><span class="va">m</span>, alpha <span class="op">=</span> <span class="fl">0.01</span>, beta <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> $x</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.0698127</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $y</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 3155.393</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"></span>
</code></pre></div>
</div>
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