From c41381a961263c28d60976e68923157916c78b15 Mon Sep 17 00:00:00 2001
From: Johannes Ranke <jranke@uni-bremen.de>
Date: Thu, 16 Sep 2021 15:31:13 +0200
Subject: Adapt and improve the dimethenamid vignette

Adapt to the corrected data and unify control parameters for saemix and
nlmixr with saem. Update docs
---
 vignettes/web_only/dimethenamid_2018.rmd | 248 +++++++++++++++++--------------
 1 file changed, 135 insertions(+), 113 deletions(-)

(limited to 'vignettes/web_only/dimethenamid_2018.rmd')

diff --git a/vignettes/web_only/dimethenamid_2018.rmd b/vignettes/web_only/dimethenamid_2018.rmd
index c152e578..e5c8764d 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 4 August 2021, built on `r format(Sys.Date(), format = "%d %b %Y")`
+date: Last change 16 September 2021, built on `r format(Sys.Date(), format = "%d %b %Y")`
 output:
   html_document:
     toc: true
@@ -14,8 +14,7 @@ vignette: >
   %\VignetteEncoding{UTF-8}
 ---
 
-[Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany](http://www.jrwb.de)<br />
-[Privatdozent at the University of Bremen](http://chem.uft.uni-bremen.de/ranke)
+[Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany](http://www.jrwb.de)
 
 ```{r, include = FALSE}
 require(knitr)
@@ -29,10 +28,11 @@ opts_chunk$set(
 
 # Introduction
 
-During the preparation of the journal article on nonlinear mixed-effects models in
-degradation kinetics (submitted) and the analysis of the dimethenamid degradation
-data analysed therein, a need for a more detailed analysis using not only nlme and saemix,
-but also nlmixr for fitting the mixed-effects models was identified.
+During the preparation of the journal article on nonlinear mixed-effects models
+in degradation kinetics [@ranke2021] and the analysis of the dimethenamid
+degradation data analysed therein, a need for a more detailed analysis using
+not only nlme and saemix, but also nlmixr for fitting the mixed-effects models
+was identified.
 
 This vignette is an attempt to satisfy this need.
 
@@ -42,8 +42,8 @@ Residue data forming the basis for the endpoints derived in the conclusion on
 the peer review of the pesticide risk assessment of dimethenamid-P published by
 the European Food Safety Authority (EFSA) in 2018 [@efsa_2018_dimethenamid]
 were transcribed from the risk assessment report [@dimethenamid_rar_2018_b8]
-which can be downloaded from the
-[EFSA register of questions](https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716).
+which can be downloaded from the Open EFSA repository
+[https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716](https://open.efsa.europa.eu).
 
 The data are [available in the mkin
 package](https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html). The
@@ -60,16 +60,13 @@ Also, datasets observed in the same soil are merged, resulting in dimethenamid
 
 ```{r dimethenamid_data}
 library(mkin)
-dmta_ds <- lapply(1:8, function(i) {
+dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
   ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
   ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
   ds_i
 })
 names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
-dmta_ds[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]])
-dmta_ds[["Borstel 1"]] <- NULL
-dmta_ds[["Borstel 2"]] <- NULL
 dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
 dmta_ds[["Elliot 1"]] <- NULL
 dmta_ds[["Elliot 2"]] <- NULL
@@ -150,7 +147,7 @@ packages, with different algorithms and checking control parameters.
 ### nlme
 
 The nlme package was the first R extension providing facilities to fit nonlinear
-mixed-effects models. We use would like to do model selection from all four
+mixed-effects models. We would like to do model selection from all four
 combinations of degradation models and error models based on the AIC.
 However, fitting the DFOP model with constant variance and using default
 control parameters results in an error, signalling that the maximum number
@@ -165,34 +162,20 @@ fitting these data.
 ```{r f_parent_nlme, warning = FALSE}
 library(nlme)
 f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
-#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
-# maxIter = 50 reached
+# f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
 f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
 f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
 ```
-
-Note that overparameterisation is also indicated by warnings obtained when
-fitting SFO or DFOP with the two-component error model ('false convergence' in
-the 'LME step' in some iterations). In addition to these fits, attempts
-were also made to include correlations between random effects by using the
-log Cholesky parameterisation of the matrix specifying them. The code
-used for these attempts can be made visible below.
-
-```{r f_parent_nlme_logchol, warning = FALSE, eval = FALSE}
-f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
-  random = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
-anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better
-#f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc,
-#  random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
-# using log Cholesky parameterisation for random effects (nlme default) does
-# not converge here and gives lots of warnings about the LME step not converging
-```
+Note that a certain degree of overparameterisation is also indicated by a
+warning obtained when fitting DFOP with the two-component error model ('false
+convergence' in the 'LME step' in iteration 3). However, as this warning does
+not occur in later iterations, and specifically not in the last of the
+`r f_parent_nlme_dfop_tc$numIter` iterations, we can ignore this warning.
 
 The model comparison function of the nlme package can directly be applied
-to these fits showing a similar goodness-of-fit of the SFO model, but a much
-lower AIC for the DFOP model fitted with the two-component error model.
-Also, the likelihood ratio test indicates that this difference is significant.
-as the p-value is below 0.0001.
+to these fits showing a much lower AIC for the DFOP model fitted with the
+two-component error model. Also, the likelihood ratio test indicates that this
+difference is significant. as the p-value is below 0.0001.
 
 ```{r AIC_parent_nlme}
 anova(
@@ -200,6 +183,27 @@ anova(
 )
 ```
 
+In addition to these fits, attempts were also made to include correlations
+between random effects by using the log Cholesky parameterisation of the matrix
+specifying them. The code used for these attempts can be made visible below.
+
+```{r f_parent_nlme_logchol, warning = FALSE, eval = FALSE}
+f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol)
+f_parent_nlme_sfo_tc_logchol <- nlme(f_parent_mkin_tc["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_tc, f_parent_nlme_sfo_tc_logchol)
+f_parent_nlme_dfop_tc_logchol <- nlme(f_parent_mkin_const["DFOP", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
+anova(f_parent_nlme_dfop_tc, f_parent_nlme_dfop_tc_logchol)
+```
+
+While the SFO variants converge fast, the additional parameters introduced
+by this lead to convergence warnings for the DFOP model. The model comparison
+clearly show that adding correlations between random effects does not improve
+the fits.
+
 The selected model (DFOP with two-component error) fitted to the data assuming
 no correlations between random effects is shown below.
 
@@ -211,29 +215,37 @@ plot(f_parent_nlme_dfop_tc)
 
 The saemix package provided the first Open Source implementation of the
 Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm.
-SAEM fits of degradation models can be performed using an interface to the
-saemix package available in current development versions of the mkin package.
+SAEM fits of degradation models can be conveniently performed using an
+interface to the saemix package available in current development versions of
+the mkin package.
 
 The corresponding SAEM fits of the four combinations of degradation and error
 models are fitted below. As there is no convergence criterion implemented in
 the saemix package, the convergence plots need to be manually checked for every
-fit.
+fit. As we will compare the SAEM implementation of saemix to the results
+obtained using the nlmixr package later, we define control settings that
+work well for all the parent data fits shown in this vignette.
+
+```{r saemix_control}
+library(saemix)
+saemix_control <- saemixControl(nbiter.saemix = c(800, 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.
 
-```{r f_parent_saemix_sfo_const, results = 'hide'}
-library(saemix)
+```{r f_parent_saemix_sfo_const, results = 'hide', dependson = "saemix_control"}
 f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
-  transformations = "saemix")
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
 ```
 
 Obviously the default number of iterations is sufficient to reach convergence.
 This can also be said for the SFO fit using the two-component error model.
 
-```{r f_parent_saemix_sfo_tc, results = 'hide'}
+```{r f_parent_saemix_sfo_tc, results = 'hide', dependson = "saemix_control"}
 f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
-  transformations = "saemix")
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 ```
 
@@ -243,56 +255,52 @@ iterations above). Therefore, the number of iterations in the first
 phase of the algorithm was increased, leading to visually satisfying
 convergence.
 
-```{r f_parent_saemix_dfop_const, results = 'hide'}
+```{r f_parent_saemix_dfop_const, results = 'hide', dependson = "saemix_control"}
 f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
-  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
-    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
-  transformations = "saemix")
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 ```
 
-The same applies to the case where the DFOP model is fitted with the
-two-component error model. Convergence of the variance of k2 is enhanced
-by using the two-component error, it remains more or less stable already after 200
-iterations of the first phase.
-
-```{r f_parent_saemix_dfop_tc_moreiter, results = 'hide'}
-f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
-    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
-  transformations = "saemix")
-plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
-```
-
-The four combinations can be compared using the model comparison function from the
-saemix package:
+The same applies in the case where the DFOP model is fitted with the
+two-component error model. Convergence of the variance of k2 is enhanced by
+using the two-component error, it remains more or less stable already after
+200 iterations of the first phase.
 
-```{r AIC_parent_saemix}
-compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
-  f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so)
+```{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$so, plot.type = "convergence")
+```
+The four combinations and including the variations of the DFOP/tc combination
+can be compared using the model comparison function from the saemix package:
+
+```{r AIC_parent_saemix, cache = FALSE}
+compare.saemix(
+  f_parent_saemix_sfo_const$so,
+  f_parent_saemix_sfo_tc$so,
+  f_parent_saemix_dfop_const$so,
+  f_parent_saemix_dfop_tc$so)
 ```
 
 As in the case of nlme fits, the DFOP model fitted with two-component error
-(number 4) gives the lowest AIC. The numeric values are reasonably close to
-the ones obtained using nlme, considering that the algorithms for fitting the
-model and for the likelihood calculation are quite different.
+(number 4) gives the lowest AIC. Using more iterations and/or more chains
+does not have a large influence on the final AIC (not shown).
 
 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
 are compared.
 
-```{r AIC_parent_saemix_methods}
-f_parent_saemix_dfop_tc_moreiter$so <-
-  llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so)
-AIC(f_parent_saemix_dfop_tc_moreiter$so)
-AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq")
-AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin")
+```{r AIC_parent_saemix_methods, cache = FALSE}
+f_parent_saemix_dfop_tc$so <-
+  llgq.saemix(f_parent_saemix_dfop_tc$so)
+AIC(f_parent_saemix_dfop_tc$so)
+AIC(f_parent_saemix_dfop_tc$so, method = "gq")
+AIC(f_parent_saemix_dfop_tc$so, method = "lin")
 ```
-
-The AIC values based on importance sampling and Gaussian quadrature are quite
-similar. Using linearisation is less accurate, but still gives a similar value.
-
+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.
 
 ### nlmixr
 
@@ -302,11 +310,11 @@ routinely used, but which can also be used for related data like chemical
 degradation data. A current development branch of the mkin package provides
 an interface between mkin and nlmixr. Here, we check if we get equivalent
 results when using a refined version of the First Order Conditional Estimation
-(FOCE) algorithm used in nlme, namely First Order Conditional Estimation with
-Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
+(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 and the
-goodness of fit of the results is compared.
+First, the focei algorithm is used for the four model combinations. A number of
+warnings are produced with unclear significance.
 
 ```{r f_parent_nlmixr_focei, results = "hide", message = FALSE, warning = FALSE}
 library(nlmixr)
@@ -316,78 +324,92 @@ 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}
-AIC(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)
+```{r AIC_parent_nlmixr_focei, 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}
-AIC(
-  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+```{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))
+aic_nlme_nlmixr_focei <- data.frame(
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = rep(c("constant variance", "two-component"), 2),
+  "AIC (nlme)" = aic_nlme,
+  "AIC (nlmixr with FOCEI)" = aic_nlmixr_focei,
+  check.names = FALSE
 )
 ```
 
-Secondly, we use the SAEM estimation routine and check the convergence plots for
-SFO with constant variance
+Secondly, we use the SAEM estimation routine and check the convergence plots. The
+control parameters also used for the saemix fits are defined beforehand.
+
+```{r nlmixr_saem_control}
+nlmixr_saem_control <- saemControl(logLik = TRUE,
+  nBurn = 1000, nEm = 300, nmc = 15)
+```
+
+The we fit SFO with constant variance
 
-```{r f_parent_nlmixr_saem_sfo_const, results = "hide", warning = FALSE, message = FALSE}
+```{r f_parent_nlmixr_saem_sfo_const, results = "hide", warning = FALSE, message = FALSE, dependson = "nlmixr_saem_control"}
 f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 ```
 
-for SFO with two-component error
+and SFO with two-component error.
 
-```{r f_parent_nlmixr_saem_sfo_tc, results = "hide", warning = FALSE, message = FALSE}
+```{r f_parent_nlmixr_saem_sfo_tc, results = "hide", warning = FALSE, message = FALSE, dependson = "nlmixr_saem_control"}
 f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
 ```
 
-For DFOP with constant variance, the convergence plots show considerable instability
-of the fit, which can be alleviated by increasing the number of iterations and
-the number of parallel chains for the first phase of algorithm.
+For DFOP with constant variance, the convergence plots show considerable
+instability of the fit, which indicates overparameterisation which was already
+observed earlier for this model combination.
 
-```{r f_parent_nlmixr_saem_dfop_const, results = "hide", warning = FALSE, message = FALSE}
+```{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",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15)
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 ```
 
-For DFOP with two-component error, the same increase in iterations and parallel
-chains was used, but using the two-component error appears to lead to a less
-erratic convergence, so this may not be necessary to this degree.
-
+For DFOP with two-component error, a less erratic convergence is seen.
 
-```{r f_parent_nlmixr_saem_dfop_tc, results = "hide", warning = FALSE, message = FALSE}
+```{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",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
 ```
 
 The AIC values are internally calculated using Gaussian quadrature. For an
-unknown reason, the AIC value obtained for the DFOP fit using the two-component
-error model is given as Infinity.
+unknown reason, the AIC value obtained for the DFOP fit using constant error
+is given as Infinity.
 
-```{r AIC_parent_nlmixr_saem}
+```{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)
 ```
 
 The following table gives the AIC values obtained with the three packages.
 
-```{r AIC_all}
+```{r AIC_all, cache = FALSE}
 AIC_all <- data.frame(
+  check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
   "Error model" = c("const", "tc", "const", "tc"),
   nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
   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),
   saemix = sapply(list(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
-    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so), AIC),
+    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc$so), AIC),
   nlmixr_saem = sapply(list(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), AIC)
 )
-- 
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