From 0b98c459c30a0629a728acf6b311de035c55fb64 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 18 Jul 2018 15:18:30 +0200 Subject: Correct references to the Rocke and Lorenzato model Rename 'sigma_rl' to 'sigma_twocomp' as the Rocke and Lorenzato model assumes lognormal distribution for large y. Rebuild static documentation. --- vignettes/FOCUS_Z.html | 84 ++++++++++++++++++++++++++------------------------ 1 file changed, 43 insertions(+), 41 deletions(-) (limited to 'vignettes/FOCUS_Z.html') diff --git a/vignettes/FOCUS_Z.html b/vignettes/FOCUS_Z.html index 95a67f94..ab32e936 100644 --- a/vignettes/FOCUS_Z.html +++ b/vignettes/FOCUS_Z.html @@ -11,13 +11,13 @@ - + Example evaluation of FOCUS dataset Z - + @@ -25,9 +25,9 @@ - - - + + + @@ -234,7 +236,7 @@ div.tocify {

Example evaluation of FOCUS dataset Z

Johannes Ranke

-

2018-01-16

+

2018-07-17

@@ -269,11 +271,11 @@ FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z) plot_sep(m.Z.2a) 

summary(m.Z.2a, data = FALSE)$bpar
-
##             Estimate se_notrans    t value     Pr(>t)   Lower     Upper
-## Z0_0      9.7015e+01   3.553135 2.7304e+01 1.6792e-21 91.4014 102.62838
-## k_Z0_sink 6.2135e-10   0.226894 2.7385e-09 5.0000e-01  0.0000       Inf
-## k_Z0_Z1   2.2360e+00   0.165073 1.3546e+01 7.3939e-14  1.8374   2.72107
-## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08  0.4006   0.58024
+
##             Estimate se_notrans    t value     Pr(>t) Lower Upper
+## Z0_0      9.7015e+01   3.553140 2.7304e+01 1.6793e-21    NA    NA
+## k_Z0_sink 1.2790e-11   0.226895 5.6368e-11 5.0000e-01    NA    NA
+## k_Z0_Z1   2.2360e+00   0.165073 1.3546e+01 7.3938e-14    NA    NA
+## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08    NA    NA

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.

A similar result can be obtained when formation fractions are used in the model formulation:

Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
@@ -285,10 +287,10 @@ plot_sep(m.Z.2a.ff)

summary(m.Z.2a.ff, data = FALSE)$bpar
##            Estimate se_notrans t value     Pr(>t) Lower Upper
-## Z0_0       97.01488   3.553146 27.3039 1.6793e-21    NA    NA
-## k_Z0        2.23601   0.216847 10.3114 3.6617e-11    NA    NA
+## Z0_0       97.01488   3.553145 27.3039 1.6793e-21    NA    NA
+## k_Z0        2.23601   0.216849 10.3114 3.6623e-11    NA    NA
 ## k_Z1        0.48212   0.065854  7.3211 3.5520e-08    NA    NA
-## f_Z0_to_Z1  1.00000   0.101473  9.8548 9.7071e-11    NA    NA
+## f_Z0_to_Z1 1.00000 0.101473 9.8548 9.7068e-11 NA NA

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.

A simplified model is obtained by removing the pathway to the sink.

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.

@@ -300,8 +302,8 @@ plot_sep(m.Z.3) 

summary(m.Z.3, data = FALSE)$bpar
##      Estimate se_notrans t value     Pr(>t)    Lower   Upper
-## Z0_0 97.01488   2.681771  36.176 2.3636e-25 91.52152 102.508
-## k_Z0  2.23601   0.146862  15.225 2.2470e-15  1.95453   2.558
+## Z0_0 97.01488   2.681772  36.176 2.3636e-25 91.52152 102.508
+## k_Z0  2.23601   0.146861  15.225 2.2464e-15  1.95453   2.558
 ## k_Z1  0.48212   0.042687  11.294 3.0686e-12  0.40216   0.578

As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.

@@ -314,7 +316,7 @@ plot_sep(m.Z.3) 
## Successfully compiled differential equation model from auto-generated C code.
m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
 plot_sep(m.Z.5)
-

+

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.

Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
@@ -325,22 +327,22 @@ plot_sep(m.Z.5)
m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
                      parms.ini = m.Z.5$bparms.ode,
                      quiet = TRUE)
-
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation by method Port did not converge.
-## Convergence code is 1
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation by method Port did not converge:
+## false convergence (8)
plot_sep(m.Z.FOCUS)
-

+

summary(m.Z.FOCUS, data = FALSE)$bpar
-
##            Estimate se_notrans t value     Pr(>t)     Lower      Upper
-## Z0_0       96.84024   2.058814 47.0369 5.5723e-44 92.706852 100.973637
-## k_Z0        2.21540   0.118128 18.7543 7.7369e-25  1.990504   2.465708
-## k_Z1        0.47836   0.029294 16.3298 3.3443e-22  0.423035   0.540918
-## k_Z2        0.45166   0.044186 10.2218 3.0364e-14  0.371065   0.549767
-## k_Z3        0.05869   0.014290  4.1072 7.2560e-05  0.035983   0.095725
-## f_Z2_to_Z3  0.47147   0.057027  8.2676 2.7790e-11  0.360295   0.585556
+
##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.837112   2.058861 47.0343 5.5877e-44 92.703779 100.970445
+## k_Z0        2.215368   0.118098 18.7587 7.6563e-25  1.990525   2.465609
+## k_Z1        0.478302   0.029289 16.3302 3.3408e-22  0.422977   0.540864
+## k_Z2        0.451617   0.044214 10.2144 3.1133e-14  0.371034   0.549702
+## k_Z3        0.058693   0.014296  4.1056 7.2924e-05  0.035994   0.095705
+## f_Z2_to_Z3  0.471516   0.057057  8.2639 2.8156e-11  0.360381   0.585548
endpoints(m.Z.FOCUS)
## $ff
 ##   Z2_Z3 Z2_sink 
-## 0.47147 0.52853 
+## 0.47152 0.52848 
 ## 
 ## $SFORB
 ## logical(0)
@@ -348,9 +350,9 @@ plot_sep(m.Z.5)
## $distimes ## DT50 DT90 ## Z0 0.31288 1.0394 -## Z1 1.44901 4.8135 -## Z2 1.53466 5.0980 -## Z3 11.81037 39.2332 +## Z1 1.44918 4.8141 +## Z2 1.53481 5.0985 +## Z3 11.80973 39.2311

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.

@@ -374,7 +376,7 @@ plot_sep(m.Z.mkin.1) 
## Successfully compiled differential equation model from auto-generated C code.
m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
 plot_sep(m.Z.mkin.3)
-

+

This results in a much better representation of the behaviour of the parent compound Z0.

Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.

Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
@@ -386,7 +388,7 @@ plot_sep(m.Z.mkin.3)
parms.ini = m.Z.mkin.3$bparms.ode, quiet = TRUE) plot_sep(m.Z.mkin.4) -

+

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.

Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
                     Z1 = mkinsub("SFO", "Z2", sink = FALSE),
@@ -397,7 +399,7 @@ plot_sep(m.Z.mkin.4)
parms.ini = m.Z.mkin.4$bparms.ode[1:4], quiet = TRUE) plot_sep(m.Z.mkin.5) -

+

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.

m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
                        parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
@@ -409,7 +411,7 @@ plot_sep(m.Z.mkin.5a)

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.

A graphical representation of the confidence intervals can finally be obtained.

mkinparplot(m.Z.mkin.5a)
-

+

The endpoints obtained with this model are

endpoints(m.Z.mkin.5a)
## $ff
@@ -418,11 +420,11 @@ plot_sep(m.Z.mkin.5a)
## ## $SFORB ## Z0_b1 Z0_b2 Z3_b1 Z3_b2 -## 2.4471373 0.0075126 0.0800076 0.0000000 +## 2.4471382 0.0075127 0.0800075 0.0000000 ## ## $distimes ## DT50 DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2 -## Z0 0.3043 1.1848 0.28325 92.265 NA NA +## Z0 0.3043 1.1848 0.28325 92.264 NA NA ## Z1 1.5148 5.0320 NA NA NA NA ## Z2 1.6414 5.4526 NA NA NA NA ## Z3 NA NA NA NA 8.6635 Inf -- cgit v1.2.1