Improve dimethenamid vignette

1 files changed, 64 insertions, 77 deletions

diff --git a/vignettes/web_only/dimethenamid_2018.rmd b/vignettes/web_only/dimethenamid_2018.rmd
index 08661b5a..7700fe35 100644
--- a/vignettes/web_only/dimethenamid_2018.rmd
+++ b/vignettes/web_only/dimethenamid_2018.rmd
@@ -1,7 +1,7 @@
 ---
 title: Example evaluations of the dimethenamid data from 2018
 author: Johannes Ranke
-date: Last change 11 January 2022, built on `r format(Sys.Date(), format = "%d %b %Y")`
+date: Last change 10 February 2022, built on `r format(Sys.Date(), format = "%d %b %Y")`
 output:
   html_document:
     toc: true
@@ -137,6 +137,14 @@ is reduced by using the two-component error model:
 plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
 ```
 
+However, note that in the case of using this error model, the fits to the
+Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact
+that they did not converge:
+
+```{r f_parent_mkin_dfop_tc_print}
+print(f_parent_mkin_tc["DFOP", ])
+```
+
 ## Nonlinear mixed-effects models
 
 Instead of taking a model selection decision for each of the individual fits, we fit
@@ -236,6 +244,8 @@ saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 ```
 
 The convergence plot for the SFO model using constant variance is shown below.
@@ -271,43 +281,25 @@ stable already after 200 iterations of the first phase.
 ```{r f_parent_saemix_dfop_tc, results = 'hide', dependson = "saemix_control"}
 f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
-```
-
-```{r f_parent_saemix_dfop_tc_moreiter, results = 'hide', dependson = "saemix_control"}
-# The last time I tried (2022-01-11) this gives an error in solve.default(omega.eta)
-# system is computationally singular: reciprocal condition number = 5e-17
-#f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-#  control = saemix_control_10k, transformations = "saemix")
-# Now we do not get a significant improvement by using twice the number of iterations
 f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control_moreiter, transformations = "saemix")
-#plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
 ```
 
+Doubling the number of iterations in the first phase of the algorithm
+leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values.
+With even more iterations, the algorithm stops with an error message. This is
+related to the variance of k2 approximating zero. This has been submitted
+as a [bug to the saemix package](https://github.com/saemixdevelopment/saemixextension/issues/29),
+as the algorithm does not converge in this case.
+
 An alternative way to fit DFOP in combination with the two-component error model
 is to use the model formulation with transformed parameters as used per default
-in mkin.
-
-```{r f_parent_saemix_dfop_tc_mkin, results = 'hide', dependson = "saemix_control"}
-f_parent_saemix_dfop_tc_mkin <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin$so, plot.type = "convergence")
-```
-As the convergence plots do not clearly indicate that the algorithm has converged, we
-again use four times the number of iterations, which leads to almost satisfactory
-convergence (see below).
-
-```{r f_parent_saemix_dfop_tc_mkin_moreiter, results = 'hide', dependson = "saemix_control"}
-saemix_control_muchmoreiter <- saemixControl(nbiter.saemix = c(3200, 300), nb.chains = 15,
-    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
-f_parent_saemix_dfop_tc_mkin_muchmoreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_muchmoreiter, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin_muchmoreiter$so, plot.type = "convergence")
-```
+in mkin. When using this option, convergence is slower, but eventually
+the algorithm stops as well with the same error message.
 
-The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc), including
-the variations of the DFOP/tc combination can be compared using the model
+The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and
+the version with increased iterations can be compared using the model
 comparison function of the saemix package:
 
 ```{r AIC_parent_saemix, cache = FALSE}
@@ -316,22 +308,12 @@ AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_tc$so,
   f_parent_saemix_dfop_const$so,
   f_parent_saemix_dfop_tc$so,
-  f_parent_saemix_dfop_tc_moreiter$so,
-  f_parent_saemix_dfop_tc_mkin$so,
-  f_parent_saemix_dfop_tc_mkin_muchmoreiter$so)
+  f_parent_saemix_dfop_tc_moreiter$so)
 rownames(AIC_parent_saemix) <- c(
-  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations",
-  "DFOP tc mkintrans", "DFOP tc mkintrans more iterations")
+  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
 print(AIC_parent_saemix)
 ```
 
-As in the case of nlme fits, the DFOP model fitted with two-component error
-(number 4) gives the lowest AIC. Using a much larger number of iterations
-does not significantly change the AIC. When the mkin transformations are used
-instead of the saemix transformations, we need four times the number of
-iterations to obtain a goodness of fit that almost as good as the result
-obtained with saemix transformations.
-
 In order to check the influence of the likelihood calculation algorithms
 implemented in saemix, the likelihood from Gaussian quadrature is added
 to the best fit, and the AIC values obtained from the three methods
@@ -350,7 +332,22 @@ print(AIC_parent_saemix_methods)
 
 The AIC values based on importance sampling and Gaussian quadrature are very
 similar. Using linearisation is known to be less accurate, but still gives a
-similar value.
+similar value. In order to illustrate that the comparison of the three method
+depends on the degree of convergence obtained in the fit, the same comparison
+is shown below for the fit using the defaults for the number of iterations and
+the number of MCMC chains.
+
+```{r AIC_parent_saemix_methods_defaults, cache = FALSE}
+f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
+f_parent_saemix_dfop_tc_defaults$so <-
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
+AIC_parent_saemix_methods_defaults <- c(
+  is = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc_defaults$so, method = "lin")
+)
+print(AIC_parent_saemix_methods_defaults)
+```
 
 ### nlmixr
 
@@ -363,8 +360,7 @@ results when using a refined version of the First Order Conditional Estimation
 (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation
 with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
 
-First, the focei algorithm is used for the four model combinations. A number of
-warnings are produced with unclear significance.
+First, the focei algorithm is used for the four model combinations.
 
 ```{r f_parent_nlmixr_focei, results = "hide", message = FALSE, warning = FALSE}
 library(nlmixr)
@@ -374,17 +370,17 @@ f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est =
 f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
 ```
 
-```{r AIC_parent_nlmixr_focei, cache = FALSE}
+For the SFO model with constant variance, the AIC values are the same, for the 
+DFOP model, there are significant differences between the AIC values. These
+may be caused by different solutions that are found, but also by the fact that
+the AIC values for the nlmixr fits are calculated based on Gaussian quadrature,
+not on linearisation.
+
+```{r AIC_parent_nlmixr_nlme, cache = FALSE}
 aic_nlmixr_focei <- sapply(
   list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
     f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
   AIC)
-```
-
-The AIC values are very close to the ones obtained with nlme which are repeated below
-for convenience.
-
-```{r AIC_parent_nlme_rep, cache = FALSE}
 aic_nlme <- sapply(
   list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
   function(x) if (is.na(x[1])) NA else AIC(x))
@@ -399,13 +395,13 @@ print(aic_nlme_nlmixr_focei)
 ```
 
 Secondly, we use the SAEM estimation routine and check the convergence plots. The
-control parameters also used for the saemix fits are defined beforehand.
+control parameters, which were also used for the saemix fits, are defined beforehand.
 
 ```{r nlmixr_saem_control}
 nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
   nBurn = 800, nEm = 300, nmc = 15)
-nlmixr_saem_control_1000 <- saemControl(logLik = TRUE,
-  nBurn = 1000, nEm = 300, nmc = 15)
+nlmixr_saem_control_moreiter <- saemControl(logLik = TRUE,
+  nBurn = 1600, nEm = 300, nmc = 15)
 nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
   nBurn = 10000, nEm = 1000, nmc = 15)
 ```
@@ -428,7 +424,9 @@ traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
 
 For DFOP with constant variance, the convergence plots show considerable
 instability of the fit, which indicates overparameterisation which was already
-observed above for this model combination.
+observed above for this model combination. Also note that the variance of k2
+approximates zero, which was already observed in the saemix fits of the DFOP
+model.
 
 ```{r f_parent_nlmixr_saem_dfop_const, results = "hide", warning = FALSE, message = FALSE, dependson = "nlmixr_saem_control"}
 f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
@@ -436,7 +434,8 @@ f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 ```
 
-For DFOP with two-component error, a less erratic convergence is seen.
+For DFOP with two-component error, a less erratic convergence is seen, but the
+variance of k2 again approximates zero.
 
 ```{r f_parent_nlmixr_saem_dfop_tc, results = "hide", warning = FALSE, message = FALSE, dependson = "nlmixr_saem_control"}
 f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
@@ -449,9 +448,9 @@ the fit with 1000 iterations for the burn in phase and 300 iterations for the
 second phase.
 
 ```{r f_parent_nlmixr_saem_dfop_tc_1k, results = "hide", warning = FALSE, message = FALSE, dependson = "nlmixr_saem_control"}
-f_parent_nlmixr_saem_dfop_tc_1000 <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr_saem_control_1000)
-traceplot(f_parent_nlmixr_saem_dfop_tc_1000$nm)
+f_parent_nlmixr_saem_dfop_tc_moreiter <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_moreiter)
+traceplot(f_parent_nlmixr_saem_dfop_tc_moreiter$nm)
 ```
 
 Here the fit looks very similar, but we will see below that it shows a higher AIC
@@ -465,23 +464,21 @@ f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "sa
 traceplot(f_parent_nlmixr_saem_dfop_tc_10k$nm)
 ```
 
-In the above convergence plot, the time course of 'eta.DMTA_0' and
-'log_k2' indicate a false convergence.
-
 The AIC values are internally calculated using Gaussian quadrature.
 
 ```{r AIC_parent_nlmixr_saem, cache = FALSE}
 AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm,
-  f_parent_nlmixr_saem_dfop_tc_1000$nm,
+  f_parent_nlmixr_saem_dfop_tc_moreiter$nm,
   f_parent_nlmixr_saem_dfop_tc_10k$nm)
 ```
 
 We can see that again, the DFOP/tc model shows the best goodness of fit.
-However, increasing the number of burn-in iterations from 800 to 1000 results
+However, increasing the number of burn-in iterations from 800 to 1600 results
 in a higher AIC. If we further increase the number of iterations to 10 000
 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the
-nlmixr/saem fit, supporting that the fit did not converge properly.
+nlmixr/saem fit, confirming that this fit does not converge properly with
+the SAEM algorithm.
 
 ### Comparison
 
@@ -505,16 +502,6 @@ AIC_all <- data.frame(
 kable(AIC_all)
 ```
 
-```{r parms_all, cache = FALSE}
-intervals(f_parent_saemix_dfop_tc)
-intervals(f_parent_saemix_dfop_tc)
-intervals(f_parent_saemix_dfop_tc_mkin_muchmoreiter)
-intervals(f_parent_nlmixr_saem_dfop_tc)
-intervals(f_parent_nlmixr_saem_dfop_tc_10k)
-```
-
-
-
 # References
 
 <!-- vim: set foldmethod=syntax: -->