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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]> + 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]> <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> +<![endif]--></head><body data-spy="scroll" data-target="#toc"> + - <body data-spy="scroll" data-target="#toc"> <div class="container template-reference-topic"> - <header> - <div class="navbar navbar-default navbar-fixed-top" role="navigation"> + <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" aria-expanded="false"> @@ -79,19 +24,12 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">chemCal</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.2.2</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> - <ul class="nav navbar-nav"> - <li> - <a href="../index.html"> - <span class="fas fa-home fa-lg"></span> - - </a> -</li> -<li> + <ul class="nav navbar-nav"><li> <a href="../articles/chemCal.html">Get started</a> </li> <li> @@ -100,25 +38,19 @@ <li> <a href="../news/index.html">Changelog</a> </li> - </ul> - <ul class="nav navbar-nav navbar-right"> - <li> - <a href="https://github.com/jranke/chemCal/"> + </ul><ul class="nav navbar-nav navbar-right"><li> + <a href="https://github.com/jranke/chemCal/" class="external-link"> <span class="fab fa-github fa-lg"></span> </a> </li> - </ul> - - </div><!--/.nav-collapse --> + </ul></div><!--/.nav-collapse --> </div><!--/.container --> </div><!--/.navbar --> - </header> - -<div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header"> <h1>Estimate a limit of detection (LOD)</h1> @@ -137,62 +69,52 @@ one-sided significance test).</p> </div> - <pre class="usage"><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></pre> + <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> - <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2> - <table class="ref-arguments"> - <colgroup><col class="name" /><col class="desc" /></colgroup> - <tr> - <th>object</th> - <td><p>A univariate model object of class <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code> or - <code><a href='https://rdrr.io/pkg/MASS/man/rlm.html'>rlm</a></code> + <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></td> - </tr> - <tr> - <th>...</th> - <td><p>Placeholder for further arguments that might be needed by - future implementations.</p></td> - </tr> - <tr> - <th>alpha</th> - <td><p>The error tolerance for the decision limit (critical value).</p></td> - </tr> - <tr> - <th>beta</th> - <td><p>The error tolerance beta for the detection limit.</p></td> - </tr> - <tr> - <th>method</th> - <td><p>The “default” method uses a prediction interval at the LOD + 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></td> - </tr> - <tr> - <th>tol</th> - <td><p>When the “default” method is used, the default tolerance + 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></td> - </tr> - </table> - - <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> - + 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> - <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2> - + </div> + <div id="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='https://rdrr.io/r/stats/predict.lm.html'>predict.lm</a></code> + 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> - <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2> - + </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> @@ -202,53 +124,55 @@ <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> - - <div class='dont-index'><p>Examples for <code><a href='din32645.html'>din32645</a></code></p></div> - - <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> - <pre class="examples"><div class='input'><span class='va'>m</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>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 class='fu'>lod</span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</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='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> -</div><div class='output co'>#> $x -#> [1] 0.0698127 -#> -#> $y -#> [1] 3155.393 -#> </div></pre> + </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 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> +</code></pre></div> + </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - <nav id="toc" data-toggle="toc" class="sticky-top"> - <h2 data-toc-skip>Contents</h2> - </nav> - </div> + <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2> + </nav></div> </div> - <footer> - <div class="copyright"> - <p>Developed by Johannes Ranke.</p> + <footer><div class="copyright"> + <p></p><p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> - <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p> + <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p> </div> - </footer> - </div> + </footer></div> - </body> -</html> + + </body></html> |