Example evaluation of FOCUS Example Dataset D

This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using mkin. After loading the library we look a the data. We have observed concentrations in the column named value at the times specified in column time for the two observed variables named parent and m1.

library("mkin")
+print(FOCUS_2006_D)

##      name time  value
+## 1  parent    0  99.46
+## 2  parent    0 102.04
+## 3  parent    1  93.50
+## 4  parent    1  92.50
+## 5  parent    3  63.23
+## 6  parent    3  68.99
+## 7  parent    7  52.32
+## 8  parent    7  55.13
+## 9  parent   14  27.27
+## 10 parent   14  26.64
+## 11 parent   21  11.50
+## 12 parent   21  11.64
+## 13 parent   35   2.85
+## 14 parent   35   2.91
+## 15 parent   50   0.69
+## 16 parent   50   0.63
+## 17 parent   75   0.05
+## 18 parent   75   0.06
+## 19 parent  100     NA
+## 20 parent  100     NA
+## 21 parent  120     NA
+## 22 parent  120     NA
+## 23     m1    0   0.00
+## 24     m1    0   0.00
+## 25     m1    1   4.84
+## 26     m1    1   5.64
+## 27     m1    3  12.91
+## 28     m1    3  12.96
+## 29     m1    7  22.97
+## 30     m1    7  24.47
+## 31     m1   14  41.69
+## 32     m1   14  33.21
+## 33     m1   21  44.37
+## 34     m1   21  46.44
+## 35     m1   35  41.22
+## 36     m1   35  37.95
+## 37     m1   50  41.19
+## 38     m1   50  40.01
+## 39     m1   75  40.09
+## 40     m1   75  33.85
+## 41     m1  100  31.04
+## 42     m1  100  33.13
+## 43     m1  120  25.15
+## 44     m1  120  33.31

Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.

The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector $diffs of the mkinmod object. If the ccSolve package is installed and functional, the differential equation model will be compiled from auto-generated C code.

SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))

## Compiling differential equation model from auto-generated C code...

print(SFO_SFO$diffs)

##                                                       parent 
+## "d_parent = - k_parent_sink * parent - k_parent_m1 * parent" 
+##                                                           m1 
+##             "d_m1 = + k_parent_m1 * parent - k_m1_sink * m1"

We do the fitting without progress report (quiet = TRUE).

fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)

A plot of the fit including a residual plot for both observed variables is obtained using the plot method for mkinfit objects.

plot(fit, show_residuals = TRUE)

Confidence intervals for the parameter estimates are obtained using the mkinparplot function.

mkinparplot(fit)

A comprehensive report of the results is obtained using the summary method for mkinfit objects.

summary(fit)

## mkin version:    0.9.36 
+## R version:       3.2.0 
+## Date of fit:     Fri Jun  5 13:36:25 2015 
+## Date of summary: Fri Jun  5 13:36:25 2015 
+## 
+## Equations:
+## d_parent = - k_parent_sink * parent - k_parent_m1 * parent
+## d_m1 = + k_parent_m1 * parent - k_m1_sink * m1
+## 
+## Model predictions using solution type deSolve 
+## 
+## Fitted with method Port using 153 model solutions performed in 0.576 s
+## 
+## Weighting: none
+## 
+## Starting values for parameters to be optimised:
+##                  value   type
+## parent_0      100.7500  state
+## k_parent_sink   0.1000 deparm
+## k_parent_m1     0.1001 deparm
+## k_m1_sink       0.1002 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                        value lower upper
+## parent_0          100.750000  -Inf   Inf
+## log_k_parent_sink  -2.302585  -Inf   Inf
+## log_k_parent_m1    -2.301586  -Inf   Inf
+## log_k_m1_sink      -2.300587  -Inf   Inf
+## 
+## Fixed parameter values:
+##      value  type
+## m1_0     0 state
+## 
+## Optimised, transformed parameters:
+##                   Estimate Std. Error  Lower   Upper t value  Pr(>|t|)
+## parent_0            99.600    1.61400 96.330 102.900   61.72 4.048e-38
+## log_k_parent_sink   -3.038    0.07826 -3.197  -2.879  -38.82 5.601e-31
+## log_k_parent_m1     -2.980    0.04124 -3.064  -2.897  -72.27 1.446e-40
+## log_k_m1_sink       -5.248    0.13610 -5.523  -4.972  -38.56 7.087e-31
+##                      Pr(>t)
+## parent_0          2.024e-38
+## log_k_parent_sink 2.800e-31
+## log_k_parent_m1   7.228e-41
+## log_k_m1_sink     3.543e-31
+## 
+## Parameter correlation:
+##                   parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
+## parent_0           1.00000            0.6075        -0.06625       -0.1701
+## log_k_parent_sink  0.60752            1.0000        -0.08740       -0.6253
+## log_k_parent_m1   -0.06625           -0.0874         1.00000        0.4716
+## log_k_m1_sink     -0.17006           -0.6253         0.47163        1.0000
+## 
+## Residual standard error: 3.211 on 36 degrees of freedom
+## 
+## Backtransformed parameters:
+##                Estimate     Lower     Upper
+## parent_0      99.600000 96.330000 1.029e+02
+## k_parent_sink  0.047920  0.040890 5.616e-02
+## k_parent_m1    0.050780  0.046700 5.521e-02
+## k_m1_sink      0.005261  0.003992 6.933e-03
+## 
+## Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.398       4 15
+## parent     6.827       3  6
+## m1         4.490       1  9
+## 
+## Resulting formation fractions:
+##                 ff
+## parent_sink 0.4855
+## parent_m1   0.5145
+## m1_sink     1.0000
+## 
+## Estimated disappearance times:
+##           DT50   DT90
+## parent   7.023  23.33
+## m1     131.761 437.70
+## 
+## Data:
+##  time variable observed predicted   residual
+##     0   parent    99.46 9.960e+01 -1.385e-01
+##     0   parent   102.04 9.960e+01  2.442e+00
+##     1   parent    93.50 9.024e+01  3.262e+00
+##     1   parent    92.50 9.024e+01  2.262e+00
+##     3   parent    63.23 7.407e+01 -1.084e+01
+##     3   parent    68.99 7.407e+01 -5.083e+00
+##     7   parent    52.32 4.991e+01  2.408e+00
+##     7   parent    55.13 4.991e+01  5.218e+00
+##    14   parent    27.27 2.501e+01  2.257e+00
+##    14   parent    26.64 2.501e+01  1.627e+00
+##    21   parent    11.50 1.253e+01 -1.035e+00
+##    21   parent    11.64 1.253e+01 -8.946e-01
+##    35   parent     2.85 3.148e+00 -2.979e-01
+##    35   parent     2.91 3.148e+00 -2.379e-01
+##    50   parent     0.69 7.162e-01 -2.624e-02
+##    50   parent     0.63 7.162e-01 -8.624e-02
+##    75   parent     0.05 6.074e-02 -1.074e-02
+##    75   parent     0.06 6.074e-02 -7.382e-04
+##   100   parent       NA 5.151e-03         NA
+##   100   parent       NA 5.151e-03         NA
+##   120   parent       NA 7.155e-04         NA
+##   120   parent       NA 7.155e-04         NA
+##     0       m1     0.00 0.000e+00  0.000e+00
+##     0       m1     0.00 0.000e+00  0.000e+00
+##     1       m1     4.84 4.803e+00  3.704e-02
+##     1       m1     5.64 4.803e+00  8.370e-01
+##     3       m1    12.91 1.302e+01 -1.140e-01
+##     3       m1    12.96 1.302e+01 -6.400e-02
+##     7       m1    22.97 2.504e+01 -2.075e+00
+##     7       m1    24.47 2.504e+01 -5.748e-01
+##    14       m1    41.69 3.669e+01  5.000e+00
+##    14       m1    33.21 3.669e+01 -3.480e+00
+##    21       m1    44.37 4.165e+01  2.717e+00
+##    21       m1    46.44 4.165e+01  4.787e+00
+##    35       m1    41.22 4.331e+01 -2.093e+00
+##    35       m1    37.95 4.331e+01 -5.363e+00
+##    50       m1    41.19 4.122e+01 -2.831e-02
+##    50       m1    40.01 4.122e+01 -1.208e+00
+##    75       m1    40.09 3.645e+01  3.643e+00
+##    75       m1    33.85 3.645e+01 -2.597e+00
+##   100       m1    31.04 3.198e+01 -9.416e-01
+##   100       m1    33.13 3.198e+01  1.148e+00
+##   120       m1    25.15 2.879e+01 -3.640e+00
+##   120       m1    33.31 2.879e+01  4.520e+00