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diff --git a/vignettes/web_only/dimethenamid_2018.rmd b/vignettes/web_only/dimethenamid_2018.rmd new file mode 100644 index 00000000..d3541a34 --- /dev/null +++ b/vignettes/web_only/dimethenamid_2018.rmd @@ -0,0 +1,374 @@ +--- +title: Example evaluations of the dimethenamid data from 2018 +author: Johannes Ranke +date: Last change 23 June 2021, built on `r format(Sys.Date(), format = "%d %b %Y")` +output: + html_document: + toc: true + toc_float: true + code_folding: hide + fig_retina: null +bibliography: ../references.bib +vignette: > + %\VignetteEngine{knitr::rmarkdown} + %\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) + +```{r, include = FALSE} +require(knitr) +options(digits = 5) +opts_chunk$set( + comment = "", + tidy = FALSE, + cache = TRUE +) +``` + +# Introduction + +During the preparation of the journal article on nonlinear mixed-effects models in +degradation kinetics (submitted) and the analysis of the dimethenamid degradation +data analysed therein, a need for a more detailed analysis using not only nlme and saemix, +but also nlmixr for fitting the mixed-effects models was identified. + +This vignette is an attempt to satisfy this need. + +# Data + +Residue data forming the basis for the endpoints derived in the conclusion on +the peer review of the pesticide risk assessment of dimethenamid-P published by +the European Food Safety Authority (EFSA) in 2018 [@efsa_2018_dimethenamid] +were transcribed from the risk assessment report [@dimethenamid_rar_2018_b8] +which can be downloaded from the +[EFSA register of questions](https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716). + +The data are [available in the mkin +package](https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html). The +following code (hidden by default, please use the button to the right to show +it) treats the data available for the racemic mixture dimethenamid (DMTA) and +its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between +their degradation behaviour was identified in the EU risk assessment. The +observation times of each dataset are multiplied with the corresponding +normalisation factor also available in the dataset, in order to make it +possible to describe all datasets with a single set of parameters. + +Also, datasets observed in the same soil are merged, resulting in dimethenamid +(DMTA) data from six soils. + +```{r dimethenamid_data} +library(mkin) +dmta_ds <- lapply(1:8, function(i) { + ds_i <- dimethenamid_2018$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 +``` + +# Parent degradation + +We evaluate the observed degradation of the parent compound using simple +exponential decline (SFO) and biexponential decline (DFOP), using constant +variance (const) and a two-component variance (tc) as error models. + +## Separate evaluations + +As a first step, to get a visual impression of the fit of the different models, +we do separate evaluations for each soil using the mmkin function from the +mkin package: + +```{r f_parent_mkin} +f_parent_mkin_const <- mmkin(c("SFO", "DFOP"), dmta_ds, + error_model = "const", quiet = TRUE) +f_parent_mkin_tc <- mmkin(c("SFO", "DFOP"), dmta_ds, + error_model = "tc", quiet = TRUE) +``` + +The plot of the individual SFO fits shown below suggests that at least in some +datasets the degradation slows down towards later time points, and that the +scatter of the residuals error is smaller for smaller values (panel to the +right): + +```{r f_parent_mkin_sfo_const} +plot(mixed(f_parent_mkin_const["SFO", ])) +``` + +Using biexponential decline (DFOP) results in a slightly more random +scatter of the residuals: + +```{r f_parent_mkin_dfop_const} +plot(mixed(f_parent_mkin_const["DFOP", ])) +``` + +The population curve (bold line) in the above plot results from taking the mean +of the individual transformed parameters, i.e. of log k1 and log k2, as well as +of the logit of the g parameter of the DFOP model). Here, this procedure +does not result in parameters that represent the degradation well, because in some +datasets the fitted value for k2 is extremely close to zero, leading to a log +k2 value that dominates the average. This is alleviated if only rate constants +that pass the t-test for significant difference from zero (on the untransformed +scale) are considered in the averaging: + +```{r f_parent_mkin_dfop_const_test} +plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE) +``` + +While this is visually much more satisfactory, such an average procedure could +introduce a bias, as not all results from the individual fits enter the +population curve with the same weight. This is where nonlinear mixed-effects +models can help out by treating all datasets with equally by fitting a +parameter distribution model together with the degradation model and the error +model (see below). + +The remaining trend of the residuals to be higher for higher predicted residues +is reduced by using the two-component error model: + +```{r f_parent_mkin_dfop_tc_test} +plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE) +``` + +## Nonlinear mixed-effects models + +Instead of taking a model selection decision for each of the individual fits, we fit +nonlinear mixed-effects models (using different fitting algorithms as implemented in +different packages) and do model selection using all available data at the same time. +In order to make sure that these decisions are not unduly influenced by the +type of algorithm used, by implementation details or by the use of wrong control +parameters, we compare the model selection results obtained with different R +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 +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 +of 50 iterations was reached, potentially indicating overparameterisation. +However, the algorithm converges when the two-component error model is +used in combination with the DFOP model. This can be explained by the fact +that the smaller residues observed at later sampling times get more +weight when using the two-component error model which will counteract the +tendency of the algorithm to try parameter combinations unsuitable for +fitting these data. + +```{r f_parent_nlme, warning = FALSE} +f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ]) +#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ]) # error +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 and gives lots of warnings about the LME step not converging +``` + +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. + +```{r AIC_parent_nlme} +anova( + f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc +) +``` + +The selected model (DFOP with two-component error) fitted to the data assuming +no correlations between random effects is shown below. + +```{r plot_parent_nlme} +plot(f_parent_nlme_dfop_tc) +``` + +### saemix + +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. + +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. + +The convergence plot for the SFO model using constant variance is shown below. + +```{r f_parent_saemix_sfo_const, results = 'hide'} +library(saemix) +f_parent_saemix_sfo_const <- saem(f_parent_mkin_const["SFO", ], quiet = TRUE, + 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'} +f_parent_saemix_sfo_tc <- saem(f_parent_mkin_tc["SFO", ], quiet = TRUE, + transformations = "saemix") +plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence") +``` + +When fitting the DFOP model with constant variance, parameter convergence +is not as unambiguous. Therefore, the number of iterations in the first +phase of the algorithm was increased, leading to visually satisfying +convergence. + +```{r f_parent_saemix_dfop_const, results = 'hide'} +f_parent_saemix_dfop_const <- saem(f_parent_mkin_const["DFOP", ], quiet = TRUE, + control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE, + save = FALSE, save.graphs = FALSE, displayProgress = FALSE), + transformations = "saemix") +plot(f_parent_saemix_dfop_const$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 pretty stable already after 200 +iterations of the first phase. + +```{r f_parent_saemix_dfop_tc_moreiter, results = 'hide'} +f_parent_saemix_dfop_tc_moreiter <- 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$so, plot.type = "convergence") +``` + +The four combinations can be compared using the model comparison function from the +saemix package: + +```{r AIC_parent_saemix} +compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so, + f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so) +``` + +As in the case of nlme fits, the DFOP model fitted with two-component error +(number 4) gives the lowest AIC. The numeric values are reasonably close to +the ones obtained using nlme, considering that the algorithms for fitting the +model and for the likelihood calculation are quite different. + +In order to check the influence of the likelihood calculation algorithms +implemented in saemix, the likelihood from Gaussian quadrature is added +to the best fit, and the AIC values obtained from the three methods +are compared. + +```{r AIC_parent_saemix_methods} +f_parent_saemix_dfop_tc_moreiter$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") +``` + +The AIC values based on importance sampling and Gaussian quadrature are quite +similar. Using linearisation is less accurate, but still gives a similar value. + + +### nlmixr + +In the last years, a lot of effort has been put into the nlmixr package which +is designed for pharmacokinetics, where nonlinear mixed-effects models are +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. + +First, the focei algorithm is used for the four model combinations and the +goodness of fit of the results is compared. + +```{r f_parent_nlmixr_focei, results = "hide", message = FALSE, warning = FALSE} +f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei") +f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei") +f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei") +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) +``` + +The AIC values are very close to the ones obtained with nlme. + +Secondly, we use the SAEM estimation routine and check the convergence plots for +SFO with constant variance + +```{r f_parent_nlmixr_saem_sfo_const, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE)) +traceplot(f_parent_nlmixr_saem_sfo_const$nm) +``` + +for SFO with two-component error + +```{r f_parent_nlmixr_saem_sfo_tc, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE)) +nlmixr::traceplot(f_parent_nlmixr_saem_sfo_tc$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. + +```{r f_parent_nlmixr_saem_dfop_const, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15) +nlmixr::traceplot(f_parent_nlmixr_saem_dfop_const$nm) +``` + +For DFOP with two-component error, the same increase in iterations and parallel +chains was used, but using the two-component error appears to lead to a less +erratic convergence, so this may not be necessary to this degree. + + +```{r f_parent_nlmixr_saem_dfop_tc, results = "hide", warning = FALSE, message = FALSE} +f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem", + control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15)) +nlmixr::traceplot(f_parent_nlmixr_saem_dfop_tc$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. + +```{r AIC_parent_nlmixr_saem} +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) +``` + + + + +# References + +<!-- vim: set foldmethod=syntax: --> |