Fit several structural PK models and select the best one based on a corrected Bayesian Information Criterion for mixed effects models.
Models to compare can be defined by rate constants and/or clearances and can include or not nonlinear elimination models.
pkbuild <- function(data=NULL, project=NULL, stat=FALSE, param="clearance", new.dir=".",
MM=FALSE, linearization=T, criterion="BICc", level=NULL, settings.stat=NULL) Let us use the warfarin PK data in this example:
head(read.csv('data/warfarinPK.csv'))## id time y amount wt age sex
## 1 1 0 . 100 66.7 50 1
## 2 1 24 9.2 . 66.7 50 1
## 3 1 36 8.5 . 66.7 50 1
## 4 1 48 6.4 . 66.7 50 1
## 5 1 72 4.8 . 66.7 50 1
## 6 1 96 3.1 . 66.7 50 1warfarin is administrated orally:
library(Rsmlx)
warfarinPK <- list(
dataFile = "data/warfarinPK.csv",
headerTypes = c("id", "time", "observation", "amount", "contcov", "contcov", "catcov"),
administration = "oral")By default, PK models parameterized with clearance(s) are fitted.
warf.pk1a <- pkbuild(data=warfarinPK, new.dir="warfarinPK")##
## [1] "warfarinPK/pk_kaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 875.0286541 891.0286541 902.7545413 912.9728035 0.0467466
##
## [1] "warfarinPK/pk_Tk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 796.97249564 812.97249564 824.69838286 834.91664503 0.04163542
##
## [1] "warfarinPK/pk_TlagkaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 661.92854178 681.92854178 696.58590081 708.84781541 0.09644021
##
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 657.4535554 677.4535554 692.1109144 704.3728291 0.1275872
##
## [1] "warfarinPK/pk_TlagTk0V1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 641.5775866 669.5775866 690.0978893 706.4471087 0.2516801
##
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 640.9399316 668.9399316 689.4602342 705.8094537 0.2841378By default, comparison of these models is based on a corrected Bayesian Information Criterion (BICc) for mixed effects models:
\[{\rm BIC}_{\rm cor} = -2 LL + \log(N)\times d_N + \log(n) \times d_n\] where \(N\) is the number of individuals and \(n\) the total number of observations. Then, \(d_N\) is the number of parameters associated to the variability of the individual parameters and \(d_n\) the number of parameters associated to the variability of the observations.
According to this criterion, the best PK model for this data is oral0_1cpt_TlagTk0VCl.txt.
print(warf.pk1a)## $pop.ini
## Tlag Tk0 V Cl
## 0.9094114 2.9142311 7.9241581 0.1320154
##
## $project
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
##
## $model
## [1] "lib:oral0_1cpt_TlagTk0VCl.txt"
##
## $data
## $data$dataFile
## [1] "data/warfarinPK.csv"
##
## $data$headerTypes
## [1] "id" "time" "observation" "amount" "contcov"
## [6] "contcov" "catcov"
##
## $data$administration
## [1] "oral"
##
##
## $ofv
## [1] 657.4536
##
## $bicc
## [1] 704.3728
##
## $bic
## [1] 692.1109
##
## $aic
## [1] 677.4536
##
## $pop.est
## Tlag_pop Tk0_pop V_pop Cl_pop omega_Tlag omega_Tk0 omega_V
## 0.78774241 1.47936633 7.99749648 0.13202040 0.61408374 0.56316740 0.22380612
## omega_Cl a b
## 0.29199097 0.33300067 0.07104876
##
## $res
## model OFV AIC BIC BICc
## 1 lib:oral0_1cpt_TlagTk0VCl.txt 657.4536 677.4536 692.1109 704.3728
## 2 lib:oral1_2cpt_TlagkaClV1QV2.txt 640.9399 668.9399 689.4602 705.8095
## 3 lib:oral0_2cpt_TlagTk0ClV1QV2.txt 641.5776 669.5776 690.0979 706.4471
## 4 lib:oral1_1cpt_TlagkaVCl.txt 661.9285 681.9285 696.5859 708.8478
## 5 lib:oral0_1cpt_Tk0VCl.txt 796.9725 812.9725 824.6984 834.9166
## 6 lib:oral1_1cpt_kaVCl.txt 875.0287 891.0287 902.7545 912.9728Another critrion, such as AIC or BIC can be used instead of BICc. Computation of the likelihood can also be based on a linearization of the model (much faster than Importance Sampling):
warf.pk1b <- pkbuild(data=warfarinPK, new.dir="warfarinPK", linearization=T, criterion="AIC")##
## [1] "warfarinPK/pk_kaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 866.8906 882.8906 894.6165 904.8348
##
## [1] "warfarinPK/pk_Tk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 796.7175 812.7175 824.4434 834.6617
##
## [1] "warfarinPK/pk_TlagkaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 658.7242 678.7242 693.3816 705.6435
##
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 656.8035 676.8035 691.4609 703.7228
##
## [1] "warfarinPK/pk_TlagTk0V1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 647.8176 675.8176 696.3379 712.6871
##
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 638.7796 666.7796 687.2999 703.6491
##
## [1] "warfarinPK/pk_TlagkaV1V2V3Q2Q3Cl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 639.3326 675.3326 701.7159 722.1524print(warf.pk1b)## $pop.ini
## Tlag ka V1 V2 Q Cl
## 0.80651432 1.68633271 7.80325033 41.24319306 0.02736140 0.09860742
##
## $project
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
##
## $model
## [1] "lib:oral1_2cpt_TlagkaClV1QV2.txt"
##
## $data
## $data$dataFile
## [1] "data/warfarinPK.csv"
##
## $data$headerTypes
## [1] "id" "time" "observation" "amount" "contcov"
## [6] "contcov" "catcov"
##
## $data$administration
## [1] "oral"
##
##
## $ofv
## [1] 638.7796
##
## $bicc
## [1] 703.6491
##
## $bic
## [1] 687.2999
##
## $aic
## [1] 666.7796
##
## $pop.est
## Tlag_pop ka_pop Cl_pop V1_pop Q_pop V2_pop
## 0.86822311 1.23542836 0.06098586 7.63926798 0.07441126 69.16438571
## omega_Tlag omega_ka omega_Cl omega_V1 omega_Q omega_V2
## 0.53251214 0.64444931 0.17806529 0.22095336 0.56811834 0.85552363
## a b
## 0.30210520 0.06647686
##
## $res
## model OFV AIC BIC BICc
## 1 lib:oral1_2cpt_TlagkaClV1QV2.txt 638.7796 666.7796 687.2999 703.6491
## 2 lib:oral1_3cpt_TlagkaClV1Q2V2Q3V3.txt 639.3326 675.3326 701.7159 722.1524
## 3 lib:oral0_2cpt_TlagTk0ClV1QV2.txt 647.8176 675.8176 696.3379 712.6871
## 4 lib:oral0_1cpt_TlagTk0VCl.txt 656.8035 676.8035 691.4609 703.7228
## 5 lib:oral1_1cpt_TlagkaVCl.txt 658.7242 678.7242 693.3816 705.6435
## 6 lib:oral0_1cpt_Tk0VCl.txt 796.7175 812.7175 824.4434 834.6617
## 7 lib:oral1_1cpt_kaVCl.txt 866.8906 882.8906 894.6165 904.8348Models parameterized with rate constants can be used instead of clearances:
warf.pk2 <- pkbuild(data=warfarinPK, new.dir="warfarinPK", param="rate")##
## [1] "warfarinPK/pk_kaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 874.42902727 890.42902727 902.15491449 912.37317666 0.07974211
##
## [1] "warfarinPK/pk_Tk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 792.68073394 808.68073394 820.40662116 830.62488333 0.08323628
##
## [1] "warfarinPK/pk_TlagkaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 660.7850613 680.7850613 695.4424203 707.7043349 0.1203258
##
## [1] "warfarinPK/pk_TlagTk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 654.3904192 674.3904192 689.0477782 701.3096928 0.1886907
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 626.3613590 654.3613590 674.8816616 691.2308811 0.2238111
##
## [1] "warfarinPK/pk_TlagkaVk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 628.55224 656.55224 677.07254 693.42176 0.26789
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k13k31k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 632.3695506 668.3695506 694.7527969 715.1893212 0.5020241print(warf.pk2$res)## model OFV AIC BIC BICc
## 1 lib:oral0_2cpt_TlagTk0Vkk12k21.txt 626.3614 654.3614 674.8817 691.2309
## 2 lib:oral1_2cpt_TlagkaVkk12k21.txt 628.5522 656.5522 677.0725 693.4218
## 3 lib:oral0_1cpt_TlagTk0Vk.txt 654.3904 674.3904 689.0478 701.3097
## 4 lib:oral1_1cpt_TlagkaVk.txt 660.7851 680.7851 695.4424 707.7043
## 5 lib:oral0_3cpt_TlagTk0Vkk12k21k13k31.txt 632.3696 668.3696 694.7528 715.1893
## 6 lib:oral0_1cpt_Tk0Vk.txt 792.6807 808.6807 820.4066 830.6249
## 7 lib:oral1_1cpt_kaVk.txt 874.4290 890.4290 902.1549 912.3732print(warf.pk2$pop.est)## Tlag_pop Tk0_pop V_pop k_pop k12_pop k21_pop
## 0.787927547 1.684833934 7.412555798 0.015276566 0.007026264 0.035824779
## omega_Tlag omega_Tk0 omega_V omega_k omega_k12 omega_k21
## 0.503209926 0.519285248 0.193032922 0.083388055 0.809503136 2.526785135
## a b
## 0.283076376 0.071405473or both:
warf.pk3 <- pkbuild(data=warfarinPK, new.dir="warfarinPK", param="both")##
## [1] "warfarinPK/pk_kaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 875.0286541 891.0286541 902.7545413 912.9728035 0.0467466
##
## [1] "warfarinPK/pk_Tk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 796.97249564 812.97249564 824.69838286 834.91664503 0.04163542
##
## [1] "warfarinPK/pk_TlagkaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 661.92854178 681.92854178 696.58590081 708.84781541 0.09644021
##
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 657.4535554 677.4535554 692.1109144 704.3728291 0.1275872
##
## [1] "warfarinPK/pk_TlagTk0V1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 641.5775866 669.5775866 690.0978893 706.4471087 0.2516801
##
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 640.9399316 668.9399316 689.4602342 705.8094537 0.2841378
##
## [1] "warfarinPK/pk_kaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 874.42902727 890.42902727 902.15491449 912.37317666 0.07974211
##
## [1] "warfarinPK/pk_Tk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 792.68073394 808.68073394 820.40662116 830.62488333 0.08323628
##
## [1] "warfarinPK/pk_TlagkaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 660.7850613 680.7850613 695.4424203 707.7043349 0.1203258
##
## [1] "warfarinPK/pk_TlagTk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 654.3904192 674.3904192 689.0477782 701.3096928 0.1886907
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 626.3613590 654.3613590 674.8816616 691.2308811 0.2238111
##
## [1] "warfarinPK/pk_TlagkaVk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 628.55224 656.55224 677.07254 693.42176 0.26789
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k13k31k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 632.3695506 668.3695506 694.7527969 715.1893212 0.5020241print(warf.pk3$res)## model OFV AIC BIC BICc
## 1 lib:oral0_2cpt_TlagTk0Vkk12k21.txt 626.3614 654.3614 674.8817 691.2309
## 2 lib:oral1_2cpt_TlagkaVkk12k21.txt 628.5522 656.5522 677.0725 693.4218
## 3 lib:oral0_1cpt_TlagTk0Vk.txt 654.3904 674.3904 689.0478 701.3097
## 4 lib:oral0_1cpt_TlagTk0VCl.txt 657.4536 677.4536 692.1109 704.3728
## 5 lib:oral1_2cpt_TlagkaClV1QV2.txt 640.9399 668.9399 689.4602 705.8095
## 6 lib:oral0_2cpt_TlagTk0ClV1QV2.txt 641.5776 669.5776 690.0979 706.4471
## 7 lib:oral1_1cpt_TlagkaVk.txt 660.7851 680.7851 695.4424 707.7043
## 8 lib:oral1_1cpt_TlagkaVCl.txt 661.9285 681.9285 696.5859 708.8478
## 9 lib:oral0_3cpt_TlagTk0Vkk12k21k13k31.txt 632.3696 668.3696 694.7528 715.1893
## 10 lib:oral0_1cpt_Tk0Vk.txt 792.6807 808.6807 820.4066 830.6249
## 11 lib:oral0_1cpt_Tk0VCl.txt 796.9725 812.9725 824.6984 834.9166
## 12 lib:oral1_1cpt_kaVk.txt 874.4290 890.4290 902.1549 912.3732
## 13 lib:oral1_1cpt_kaVCl.txt 875.0287 891.0287 902.7545 912.9728If a Monolix project has been already created using the data file, it can be used for providing data information
warf.pk4 <- pkbuild(project="projects/warfarinPK.mlxtran", new.dir="warfarinPK")##
## [1] "warfarinPK/pk_kaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 850.88080099 866.88080099 878.60668821 888.82495038 0.05221115
##
## [1] "warfarinPK/pk_Tk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 772.83071891 788.83071891 800.55660613 810.77486830 0.04437503
##
## [1] "warfarinPK/pk_TlagkaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 650.9798730 670.9798730 685.6372320 697.8991466 0.1419425
##
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 648.838170 668.838170 683.495529 695.757444 0.126884
##
## [1] "warfarinPK/pk_TlagTk0V1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 630.7504153 658.7504153 679.2707179 695.6199374 0.4185244
##
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 626.3730062 654.3730062 674.8933088 691.2425283 0.3712965
##
## [1] "warfarinPK/pk_TlagkaV1V2V3Q2Q3Cl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 625.4464458 661.4464458 687.8296920 708.2662164 0.4318463Of course, the results are the same as those obtained using the data file
print(warf.pk4$res)## model OFV AIC BIC BICc
## 1 lib:oral1_2cpt_TlagkaClV1QV2.txt 626.3730 654.3730 674.8933 691.2425
## 2 lib:oral0_2cpt_TlagTk0ClV1QV2.txt 630.7504 658.7504 679.2707 695.6199
## 3 lib:oral0_1cpt_TlagTk0VCl.txt 648.8382 668.8382 683.4955 695.7574
## 4 lib:oral1_1cpt_TlagkaVCl.txt 650.9799 670.9799 685.6372 697.8991
## 5 lib:oral1_3cpt_TlagkaClV1Q2V2Q3V3.txt 625.4464 661.4464 687.8297 708.2662
## 6 lib:oral0_1cpt_Tk0VCl.txt 772.8307 788.8307 800.5566 810.7749
## 7 lib:oral1_1cpt_kaVCl.txt 850.8808 866.8808 878.6067 888.8250The “best” PK model is selected first. Then, the “best” statistical
model is built using buildAll:
warf.pk5 <- pkbuild(data=warfarinPK, stat=TRUE, new.dir="warfarinPK", param="rate")##
## [1] "warfarinPK/pk_kaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 874.42902727 890.42902727 902.15491449 912.37317666 0.07974211
##
## [1] "warfarinPK/pk_Tk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 792.68073394 808.68073394 820.40662116 830.62488333 0.08323628
##
## [1] "warfarinPK/pk_TlagkaVk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 660.7850613 680.7850613 695.4424203 707.7043349 0.1203258
##
## [1] "warfarinPK/pk_TlagTk0Vk.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 654.3904192 674.3904192 689.0477782 701.3096928 0.1886907
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 626.3613590 654.3613590 674.8816616 691.2308811 0.2238111
##
## [1] "warfarinPK/pk_TlagkaVk12k21k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 628.55224 656.55224 677.07254 693.42176 0.26789
##
## [1] "warfarinPK/pk_TlagTk0Vk12k21k13k31k.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc standardError
## 632.3695506 668.3695506 694.7527969 715.1893212 0.5020241
##
## --------------------------------------------------
##
## Building:
## - The covariate model
## - The correlation model
## - The residual error model
##
## __________________________________________________
## - - - Initialization - - -
##
## Covariate model:
## sex age wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 0
## k 0 0 0
## k12 0 0 0
## k21 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
## Sampling of the conditional distribution using the initial model ...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 654.36 674.88 691.23 0.22
## __________________________________________________
## - - - Iteration 1 - - -
##
## Covariate model:
## sex age wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 1 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 1 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Run scenario for model 1 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 634.70 659.62 675.97 0.25
## __________________________________________________
## - - - Iteration 2 - - -
##
## Covariate model:
## sex age wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 1 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Run scenario for model 2 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 637.55 661.01 677.36 0.31
## __________________________________________________
## - - - Iteration 3 - - -
##
## No difference between two successive iterations
## __________________________________________________
## - - - Further tests - - -
## _______________________
## Add parameters/covariates relationships:
## parameter covariate p.value
## 4 Tk0 sex 0.000203
## 14 k21 sex 0.021590
##
## Run scenario for model 4 ...
## Estimation of the population parameters...
## _______________________
## Remove parameters/covariates relationships:
## coefficient p.value
## 1 beta_Tk0_sex_1 0.160988
## 3 beta_V_sex_1 0.104232
## 5 beta_k21_sex_1 0.484202
## 4 beta_k21_age 0.109704
##
## Run scenario for model 5 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 633.52 655.51 671.86 0.26
## _______________________
## Add correlation:
## randomEffect.1 randomEffect.2 correlation p.value p.wald_lin p.wald_SA
## 3 eta_Tlag eta_k 0.144046 0.05364 NaN NaN
## in.model
## 3 FALSE
## [[1]]
## [1] "Tlag" "k"
##
##
## Run scenario for model 6 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 633.67 657.12 673.47 0.31
## __________________________________________________
##
## Final statistical model:
##
## Covariate model:
## age sex wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 633.52 655.51 671.86 0.26
##
## total time: 110.9s
## __________________________________________________
##
## --------------------------------------------------
##
## Building the variance model
##
## __________________________________________________
## Iteration 1
##
## removing variability...
##
## -----------------------
## Step 1
## Parameters without variability:
## Parameters with variability : Tlag Tk0 V k k12 k21
##
## Criterion (linearization): 678.2
## trying to remove omega_k : 672.8
## trying to remove omega_V : 717.6
## trying to remove omega_Tk0 : 710.9
## trying to remove omega_Tlag : 709.0
## trying to remove omega_k12 : 686.3
## trying to remove omega_k21 : 681.3
##
## Criterion: 671.9
## fitting the model with no variability on k : 665
## variability on k removed
##
## -----------------------
## Step 2
## Parameters without variability: k
## Parameters with variability : Tlag Tk0 V k12 k21
##
## Criterion (linearization): 671.2
## trying to remove omega_k12 : 722.9
## trying to remove omega_k21 : 728.4
##
## no more variability can be removed
## _______________________
##
## adding variability...
##
## -----------------------
## Step 1
## Parameters without variability: k
## Parameters with variability : Tlag Tk0 V k12 k21
##
## Criterion (linearization): 671.2
##
## no more variability can be added
##
## __________________________________________________
##
## Final variance model:
##
## Parameters without variability: k
## Parameters with variability : Tlag Tk0 V k12 k21
##
## Fitting the final model using the original settings...
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 628.00 648.52 664.87 0.18
##
## total time: 62.9s
##
##
## --------------------------------------------------
##
## Building:
## - The covariate model
## - The correlation model
## - The residual error model
##
## __________________________________________________
## - - - Initialization - - -
##
## Covariate model:
## sex age wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 628.00 648.52 664.87 0.18
## __________________________________________________
## - - - Iteration 1 - - -
##
## No difference between two successive iterations
## __________________________________________________
## - - - Further tests - - -
## __________________________________________________
##
## Final statistical model:
##
## Covariate model:
## age sex wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 628.00 648.52 664.87 0.18
##
## total time: 4.2s
## __________________________________________________
##
## --------------------------------------------------
##
## Final complete model:
##
## Variance model:
## Parameters without variability: k
## Parameters with variability : Tlag Tk0 V k12 k21
##
## Covariate model:
## age sex wt
## Tlag 0 0 0
## Tk0 0 0 0
## V 0 0 1
## k 0 0 0
## k12 0 0 0
## k21 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (importanceSampling):
## AIC BIC BICc s.e.
## 628.00 648.52 664.87 0.18
##
## total time: 179.7s
## --------------------------------------------------It is possible to define the settings used by buildAll
in a list:
warf.pk6 <- pkbuild(data=warfarinPK, stat=TRUE, new.dir="warfarinPK", linearization=T,
settings.stat =list(covToTransform = c("wt"),
criterion ="AIC",
model=c("covariate", "residualError"),
linearization=T))##
## [1] "warfarinPK/pk_kaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 866.8906 882.8906 894.6165 904.8348
##
## [1] "warfarinPK/pk_Tk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 796.7175 812.7175 824.4434 834.6617
##
## [1] "warfarinPK/pk_TlagkaVCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 658.7242 678.7242 693.3816 705.6435
##
## [1] "warfarinPK/pk_TlagTk0VCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 656.8035 676.8035 691.4609 703.7228
##
## [1] "warfarinPK/pk_TlagTk0V1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 647.8176 675.8176 696.3379 712.6871
##
## [1] "warfarinPK/pk_TlagkaV1V2QCl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 638.7796 666.7796 687.2999 703.6491
##
## [1] "warfarinPK/pk_TlagkaV1V2V3Q2Q3Cl.mlxtran"
## Estimation of the population parameters...
## Estimation of the log-likelihood...
## OFV AIC BIC BICc
## 639.3326 675.3326 701.7159 722.1524
##
## --------------------------------------------------
##
## Building:
## - The covariate model
## - The residual error model
##
## __________________________________________________
## - - - Initialization - - -
##
## Covariate model:
## sex age wt
## Tlag 0 0 0
## ka 0 0 0
## Cl 0 0 0
## V1 0 0 0
## Q 0 0 0
## V2 0 0 0
##
## Residual error model:
## y
## "combined2"
## Sampling of the conditional distribution using the initial model ...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 666.78 687.30 703.65
##
## Estimation of the population parameters using the transformed covariates ...
## Sampling of the conditional distribution using the the transformed covariates ...
## __________________________________________________
## - - - Iteration 1 - - -
##
## Covariate model:
## sex age wt logtWt
## Tlag 0 0 0 0
## ka 1 0 0 0
## Cl 0 0 0 1
## V1 1 0 0 1
## Q 0 1 0 1
## V2 0 0 0 0
##
## Residual error model:
## y
## "combined2"
##
## Run scenario for model 1 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 638.16 667.48 683.83
## __________________________________________________
## - - - Iteration 2 - - -
##
## Covariate model:
## sex age wt logtWt
## Tlag 0 0 0 0
## ka 1 0 0 0
## Cl 0 0 0 1
## V1 0 0 0 1
## Q 0 1 0 1
## V2 0 0 0 0
##
## Residual error model:
## y
## "combined2"
##
## Run scenario for model 2 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 651.06 678.91 695.26
## __________________________________________________
## - - - Iteration 3 - - -
##
## Covariate model:
## sex age wt logtWt
## Tlag 0 0 0 0
## ka 1 0 0 0
## Cl 0 0 0 1
## V1 0 0 0 1
## Q 0 1 0 0
## V2 0 0 0 0
##
## Residual error model:
## y
## "combined2"
##
## Run scenario for model 3 ...
## Estimation of the population parameters...
## Sampling from the conditional distribution...
## Estimation of the log-likelihood...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 648.16 674.54 690.89
## __________________________________________________
## - - - Iteration 4 - - -
##
## No difference between two successive iterations
## __________________________________________________
## - - - Further tests - - -
## _______________________
## Add parameters/covariates relationships:
## parameter covariate p.value
## 5 ka logtWt 2.318e-02
## 6 Cl sex 1.817e-06
##
## Run scenario for model 5 ...
## Estimation of the population parameters...
## _______________________
## Remove parameters/covariates relationships:
## coefficient p.value
## 4 beta_Cl_sex_1 0.513109
## 6 beta_V1_sex_1 0.361551
## 8 beta_Q_logtWt 0.0519279
##
## Run scenario for model 6 ...
## Estimation of the population parameters...
## Estimation of the log-likelihood...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 641.41 669.26 685.61
## _______________________
## Remove parameters/covariates relationships:
## coefficient p.value
## 1 beta_ka_sex_1 0.14197
## 4 beta_V1_sex_1 0.37607
## 6 beta_Q_logtWt 0.209595
##
## Run scenario for model 7 ...
## Estimation of the population parameters...
## Estimation of the log-likelihood...
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 635.35 660.27 676.61
## __________________________________________________
##
## Final statistical model:
##
## Covariate model:
## age logtWt sex wt
## Tlag 0 0 0 0
## ka 0 0 0 0
## Cl 0 1 0 0
## V1 0 1 0 0
## Q 1 0 0 0
## V2 0 0 0 0
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 635.35 660.27 676.61
##
## total time: 137.2s
## __________________________________________________
##
## --------------------------------------------------
##
## Final complete model:
##
## Variance model:
## Parameters without variability:
## Parameters with variability : Tlag ka Cl V1 Q V2
##
## Covariate model:
## age logtWt sex wt
## Tlag 0 0 0 0
## ka 0 0 0 0
## Cl 0 1 0 0
## V1 0 1 0 0
## Q 1 0 0 0
## V2 0 0 0 0
##
## Correlation model:
## [1] "NULL"
##
## Residual error model:
## y
## "combined2"
##
## Estimated criteria (linearization):
## AIC BIC BICc
## 635.35 660.27 676.61
##
## total time: 144.7s
## --------------------------------------------------