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
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html>
<head>
<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 quantification (LOQ) — loq • chemCal</title>
<!-- jquery -->
<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>
<!-- Font Awesome icons -->
<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous">
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/1.7.1/clipboard.min.js" integrity="sha384-cV+rhyOuRHc9Ub/91rihWcGmMmCXDeksTtCihMupQHSsi8GIIRDG0ThDc3HGQFJ3" crossorigin="anonymous"></script>
<!-- sticky kit -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" crossorigin="anonymous"></script>
<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>
<meta property="og:title" content="Estimate a limit of quantification (LOQ) — loq" />
<meta property="og:description" content="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
inverse.predict, and L is obtained by iteration." />
<meta name="twitter:card" content="summary" />
<!-- mathjax -->
<script src='https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></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>
<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">
<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="label label-default" data-toggle="tooltip" data-placement="bottom" title="Released package">0.2.1</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../index.html">
<span class="fa fa-home fa-lg"></span>
</a>
</li>
<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">
</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 quantification (LOQ)</h1>
<div class="hidden name"><code>loq.Rd</code></div>
</div>
<div class="ref-description">
<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>
<pre class="usage">loq(object, …, alpha = 0.05, k = 3, n = 1, w.loq = "auto",
var.loq = "auto", tol = "default")</pre>
<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>lm</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.</p></td>
</tr>
<tr>
<th>alpha</th>
<td><p>The error tolerance for the prediction of x values in the calculation.</p></td>
</tr>
<tr>
<th>…</th>
<td><p>Placeholder for further arguments that might be needed by
future implementations.</p></td>
</tr>
<tr>
<th>k</th>
<td><p>The inverse of the maximum relative error tolerated at the
desired LOQ.</p></td>
</tr>
<tr>
<th>n</th>
<td><p>The number of replicate measurements for which the LOQ should be
specified.</p></td>
</tr>
<tr>
<th>w.loq</th>
<td><p>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.</p></td>
</tr>
<tr>
<th>var.loq</th>
<td><p>The approximate variance at the LOQ. The default value is
calculated from the model.</p></td>
</tr>
<tr>
<th>tol</th>
<td><p>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.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>The estimated limit of quantification for a model used for calibration.</p>
<h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>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>
<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='no'>m</span> <span class='kw'><-</span> <span class='fu'>lm</span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex1</span>)
<span class='fu'>loq</span>(<span class='no'>m</span>)</div><div class='output co'>#> $x
#> [1] 13.97764
#>
#> $y
#> [1] 30.6235
#> </div><div class='input'>
<span class='co'># We can get better by using replicate measurements</span>
<span class='fu'>loq</span>(<span class='no'>m</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>3</span>)</div><div class='output co'>#> $x
#> [1] 9.971963
#>
#> $y
#> [1] 22.68539
#> </div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#note">Note</a></li>
<li><a href="#see-also">See also</a></li>
<li><a href="#examples">Examples</a></li>
</ul>
</div>
</div>
<footer>
<div class="copyright">
<p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown">
<p>Site built with <a href="http://pkgdown.r-lib.org/">pkgdown</a>.</p>
</div>
</footer>
</div>
</body>
</html>
|
