aboutsummaryrefslogtreecommitdiff
path: root/docs/reference/lod.html
blob: 1fbae76a6c12e9d3f47100d4fa750bb4e21a36a5 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Estimate a limit of detection (LOD) — lod • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate a limit of detection (LOD) — lod"><meta property="og:description" content="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)."><!-- 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><body data-spy="scroll" data-target="#toc">
    

    <div class="container template-reference-topic">
      <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">
        <span class="sr-only">Toggle navigation</span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
      </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="">0.2.3</span>
      </span>
    </div>

    <div id="navbar" class="navbar-collapse collapse">
      <ul class="nav navbar-nav"><li>
  <a href="../articles/chemCal.html">Get started</a>
</li>
<li>
  <a href="../reference/index.html">Reference</a>
</li>
<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/" class="external-link">
    <span class="fab fa-github fa-lg"></span>
     
  </a>
</li>
      </ul></div><!--/.nav-collapse -->
  </div><!--/.container -->
</div><!--/.navbar -->

      

      </header><div class="row">
  <div class="col-md-9 contents">
    <div class="page-header">
    <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>
    <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" class="external-link">predict.lm</a></code>
function, which is currently not supported in R.</p>
    </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">&lt;-</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">#&gt;</span> $x</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.08655484</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $y</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 3317.154</span>
<span class="r-out co"><span class="r-pr">#&gt;</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">#&gt;</span> $x</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.0698127</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $y</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 3155.393</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-in"></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>
</div>


      <footer><div class="copyright">
  <p></p><p>Developed by Johannes Ranke.</p>
</div>

<div class="pkgdown">
  <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>

  


  

  </body></html>

Contact - Imprint