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
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
|
<!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>Example evaluation of FOCUS dataset Z • mkin</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="Example evaluation of FOCUS dataset Z">
<meta property="og:description" content="mkin">
<meta name="robots" content="noindex">
<!-- 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-article">
<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">mkin</a>
<span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.2.5</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../../reference/index.html">Reference</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="../../articles/mkin.html">Introduction to mkin</a>
</li>
<li class="divider">
</li>
<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li>
<li>
<a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
</li>
<li>
<a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
</li>
<li>
<a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
</li>
<li class="divider">
</li>
<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li>
<li>
<a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
</li>
<li>
<a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
</li>
<li>
<a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
</li>
<li>
<a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
</li>
<li>
<a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a>
</li>
<li class="divider">
</li>
<li class="dropdown-header">Performance</li>
<li>
<a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
</li>
<li>
<a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
</li>
<li>
<a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a>
</li>
<li class="divider">
</li>
<li class="dropdown-header">Miscellaneous</li>
<li>
<a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
</li>
<li>
<a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
</li>
</ul>
</li>
<li>
<a href="../../news/index.html">News</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/jranke/mkin/" 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 toc-ignore">
<h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
<h4 data-toc-skip class="author">Johannes
Ranke</h4>
<h4 data-toc-skip class="date">Last change 16 January 2018
(rebuilt 2023-05-19)</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
<div class="hidden name"><code>FOCUS_Z.rmd</code></div>
</div>
<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher
Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the
University of Bremen</a></p>
<div class="section level2">
<h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a>
</h2>
<p>The following code defines the example dataset from Appendix 7 to the
FOCUS kinetics report <span class="citation">(FOCUS Work Group on
Degradation Kinetics 2014, 354)</span>.</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span><span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span>
<span><span class="va">FOCUS_2006_Z</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,</span>
<span> <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span><span class="op">)</span>,</span>
<span> Z0 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,</span>
<span> <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,</span>
<span> <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,</span>
<span> <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span>
<span> Z3 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,</span>
<span> <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span><span class="op">)</span><span class="op">)</span></span>
<span></span>
<span><span class="va">FOCUS_2006_Z_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_Z</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a>
</h2>
<p>The next step is to set up the models used for the kinetic analysis.
As the simultaneous fit of parent and the first metabolite is usually
straightforward, Step 1 (SFO for parent only) is skipped here. We start
with the model 2a, with formation and decline of metabolite Z1 and the
pathway from parent directly to sink included (default in mkin).</p>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span>
<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span>
<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span>
<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span>
<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre>
<p>As obvious from the parameter summary (the component of the summary),
the kinetic rate constant from parent compound Z to sink is very small
and the t-test for this parameter suggests that it is not significantly
different from zero. This suggests, in agreement with the analysis in
the FOCUS kinetics report, to simplify the model by removing the pathway
to sink.</p>
<p>A similar result can be obtained when formation fractions are used in
the model formulation:</p>
<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a.ff</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span>
<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span>
<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span>
<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span>
<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre>
<p>Here, the ilr transformed formation fraction fitted in the model
takes a very large value, and the backtransformed formation fraction
from parent Z to Z1 is practically unity. Here, the covariance matrix
used for the calculation of confidence intervals is not returned as the
model is overparameterised.</p>
<p>A simplified model is obtained by removing the pathway to the sink.
</p>
<p>In the following, we use the parameterisation with formation
fractions in order to be able to compare with the results in the FOCUS
guidance, and as it makes it easier to use parameters obtained in a
previous fit when adding a further metabolite.</p>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span>
<span><span class="co">## Z0_0 97.01488 2.597342 37.352 2.0106e-24 91.67597 102.3538</span></span>
<span><span class="co">## k_Z0 2.23601 0.146904 15.221 9.1477e-15 1.95354 2.5593</span></span>
<span><span class="co">## k_Z1 0.48212 0.041727 11.554 4.8268e-12 0.40355 0.5760</span></span>
<span><span class="co">## sigma 4.80411 0.620208 7.746 1.6110e-08 3.52925 6.0790</span></span></code></pre>
<p>As there is only one transformation product for Z0 and no pathway to
sink, the formation fraction is internally fixed to unity.</p>
</div>
<div class="section level2">
<h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a>
</h2>
<p>As suggested in the FOCUS report, the pathway to sink was removed for
metabolite Z1 as well in the next step. While this step appears
questionable on the basis of the above results, it is followed here for
the purpose of comparison. Also, in the FOCUS report, it is assumed that
there is additional empirical evidence that Z1 quickly and exclusively
hydrolyses to Z2.</p>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p>
<p>Finally, metabolite Z3 is added to the model. We use the optimised
differential equation parameter values from the previous fit in order to
accelerate the optimization.</p>
<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
<span> Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.FOCUS</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
<span> parms.ini <span class="op">=</span> <span class="va">m.Z.5</span><span class="op">$</span><span class="va">bparms.ode</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :</span></span>
<span><span class="co">## Observations with value of zero were removed from the data</span></span></code></pre>
<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:</span></span>
<span><span class="co">## false convergence (8)</span></span></code></pre>
<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span>
<span><span class="co">## Z0_0 96.838822 1.994274 48.5584 4.0280e-42 92.826981 100.850664</span></span>
<span><span class="co">## k_Z0 2.215393 0.118458 18.7019 1.0413e-23 1.989456 2.466989</span></span>
<span><span class="co">## k_Z1 0.478305 0.028258 16.9266 6.2418e-22 0.424708 0.538666</span></span>
<span><span class="co">## k_Z2 0.451627 0.042139 10.7176 1.6314e-14 0.374339 0.544872</span></span>
<span><span class="co">## k_Z3 0.058692 0.015245 3.8499 1.7803e-04 0.034808 0.098965</span></span>
<span><span class="co">## f_Z2_to_Z3 0.471502 0.058351 8.0805 9.6608e-11 0.357769 0.588274</span></span>
<span><span class="co">## sigma 3.984431 0.383402 10.3923 4.5575e-14 3.213126 4.755736</span></span></code></pre>
<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## $ff</span></span>
<span><span class="co">## Z2_Z3 Z2_sink </span></span>
<span><span class="co">## 0.4715 0.5285 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $distimes</span></span>
<span><span class="co">## DT50 DT90</span></span>
<span><span class="co">## Z0 0.31288 1.0394</span></span>
<span><span class="co">## Z1 1.44917 4.8141</span></span>
<span><span class="co">## Z2 1.53478 5.0984</span></span>
<span><span class="co">## Z3 11.80986 39.2315</span></span></code></pre>
<p>This fit corresponds to the final result chosen in Appendix 7 of the
FOCUS report. Confidence intervals returned by mkin are based on
internally transformed parameters, however.</p>
</div>
<div class="section level2">
<h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a>
</h2>
<p>As the FOCUS report states, there is a certain tailing of the time
course of metabolite Z3. Also, the time course of the parent compound is
not fitted very well using the SFO model, as residues at a certain low
level remain.</p>
<p>Therefore, an additional model is offered here, using the single
first-order reversible binding (SFORB) model for metabolite Z3. As
expected, the <span class="math inline">\(\chi^2\)</span> error level is
lower for metabolite Z3 using this model and the graphical fit for Z3 is
improved. However, the covariance matrix is not returned.</p>
<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
<span> Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div>
<pre><code><span><span class="co">## NULL</span></span></code></pre>
<p>Therefore, a further stepwise model building is performed starting
from the stage of parent and two metabolites, starting from the
assumption that the model fit for the parent compound can be improved by
using the SFORB model.</p>
<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
<p>This results in a much better representation of the behaviour of the
parent compound Z0.</p>
<p>Finally, Z3 is added as well. These models appear overparameterised
(no covariance matrix returned) if the sink for Z1 is left in the
models.</p>
<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
<span> Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.4</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.3</span><span class="op">$</span><span class="va">bparms.ode</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =</span></span>
<span><span class="co">## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the</span></span>
<span><span class="co">## data</span></span></code></pre>
<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p>
<p>The error level of the fit, but especially of metabolite Z3, can be
improved if the SFORB model is chosen for this metabolite, as this model
is capable of representing the tailing of the metabolite decline
phase.</p>
<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
<span> Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
<span> Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.4</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span>
<span><span class="co">## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from</span></span>
<span><span class="co">## the data</span></span></code></pre>
<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
<p>The summary view of the backtransformed parameters shows that we get
no confidence intervals due to overparameterisation. As the optimized is
excessively small, it seems reasonable to fix it to zero.</p>
<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
<span> parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span>
<span> k_Z3_bound_free <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span>
<span> fixed_parms <span class="op">=</span> <span class="st">"k_Z3_bound_free"</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span>
<span><span class="co">## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed</span></span>
<span><span class="co">## from the data</span></span></code></pre>
<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p>
<p>As expected, the residual plots for Z0 and Z3 are more random than in
the case of the all SFO model for which they were shown above. In
conclusion, the model is proposed as the best-fit model for the dataset
from Appendix 7 of the FOCUS report.</p>
<p>A graphical representation of the confidence intervals can finally be
obtained.</p>
<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
<p>The endpoints obtained with this model are</p>
<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## $ff</span></span>
<span><span class="co">## Z0_free Z2_Z3 Z2_sink Z3_free </span></span>
<span><span class="co">## 1.00000 0.53656 0.46344 1.00000 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $SFORB</span></span>
<span><span class="co">## Z0_b1 Z0_b2 Z0_g Z3_b1 Z3_b2 Z3_g </span></span>
<span><span class="co">## 2.4471322 0.0075125 0.9519862 0.0800069 0.0000000 0.9347820 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $distimes</span></span>
<span><span class="co">## DT50 DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2</span></span>
<span><span class="co">## Z0 0.3043 1.1848 0.35666 0.28325 92.266 NA NA</span></span>
<span><span class="co">## Z1 1.5148 5.0320 NA NA NA NA NA</span></span>
<span><span class="co">## Z2 1.6414 5.4526 NA NA NA NA NA</span></span>
<span><span class="co">## Z3 NA NA NA NA NA 8.6636 Inf</span></span></code></pre>
<p>It is clear the degradation rate of Z3 towards the end of the
experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the
system of two differential equations representing the SFORB system for
Z3, corresponding to the slower rate constant of the DFOP model) is
reported to be infinity. However, this appears to be a feature of the
data.</p>
</div>
<div class="section level2">
<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
</h2>
<!-- vim: set foldmethod=syntax: -->
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-FOCUSkinetics2014" class="csl-entry">
FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for
Estimating Persistence and Degradation Kinetics from Environmental Fate
Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.
</div>
</div>
</div>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc"><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> 2.0.7.</p>
</div>
</footer>
</div>
</body>
</html>
|
