Overview

Description

Compute confidence intervals for the population parameters estimated by Monolix.

The method used for computing the confidence intervals can be either based on the standard errors derived from an estimation of the Fisher Information Matrix (“fim”), on the profile likelihood (“proflike”) or on nonparametric bootstrap estimate (“bootstrap”). is used by default.

When method=“fim”, the FIM can be either estimated using a linearization of the model or a stochastic approximation. When method=“proflike”, the observed likelihood can be either estimated using a linearization of the model or an importance sampling Monte Carlo procedure. When method=“bootstrap”, the bootstrap estimates are obtained using the bootmlx function

Usage

r <- confintmlx(project, parameters="all", method="fim", level=0.90, 
                     linearization=TRUE, Nboot=100, settings=NULL) 

Arguments

project
a Monolix project
parameters
list of parameters for which confidence intervals are computed (default=“all”)
level
confidence level, a real number between 0 and 1 (default=0.90)
linearization
{TRUE}/FALSE whether the calculation of the standard errors or the profile likelihood is based on a linearization of the model (default=TRUE)
Nboot
number of bootstrat replicates (default=100, used when method=“bootstrap”)
settings
a list of optional settings


Example

Using the Fisher information matrix

project <- "projects/warfarinPK1.mlxtran"
r.fim <- confintmlx(project)
## [INFO] Results have been succesfully loaded
## [INFO] Results have been succesfully loaded
print(r.fim)
## $confint
##                 estimate       lower     upper
## ka_pop        0.61829333  0.41721320 0.9162861
## V_pop         7.80985201  7.42469560 8.2149884
## beta_V_lw70   0.91755189  0.67440775 1.1606960
## Cl_pop        0.12266966  0.09920912 0.1516781
## beta_Cl_sex_1 0.10332266 -0.12789084 0.3345362
## omega_ka      0.77254335  0.51873611 1.1505334
## omega_V       0.11843468  0.07763479 0.1806764
## omega_Cl      0.27435309  0.21830506 0.3447910
## a1            0.54888394  0.39479409 0.7029738
## b1            0.08235761  0.05414726 0.1105679
## 
## $level
## [1] 0.9
## 
## $method
## [1] "fim"


Using the profile likelihood

r.prl <- confintmlx(project, method="proflike", parameters = c("V_pop", "beta_V_lw70", "omega_V"))
## [INFO] Results have been succesfully loaded
## [INFO] Results have been succesfully loaded
## /**********************************************************************/ 
##  LL search on V_pop
## Upper bound search / Iteration 2 / V_pop = 9.538
## Upper bound search / Iteration 3 / V_pop = 8.369
## Upper bound search / Iteration 4 / V_pop = 8.377
## Lower bound search / Iteration 2 / V_pop = 6.394
## Lower bound search / Iteration 3 / V_pop = 7.373
## Lower bound search / Iteration 4 / V_pop = 7.399
## parameter  V_pop 
## Value  7.809 
## CI =  [7.399 , 8.377]  
## diff. =  [-0.411 , 0.567] 
## rel. diff. =  [-5.256 , 7.27] 
## /**********************************************************************/ 
##  LL search on beta_V_lw70
## Upper bound search / Iteration 2 / beta_V_lw70 = 1.117
## Upper bound search / Iteration 3 / beta_V_lw70 = 1.175
## Upper bound search / Iteration 4 / beta_V_lw70 = 1.375
## Upper bound search / Iteration 5 / beta_V_lw70 = 1.196
## Upper bound search / Iteration 6 / beta_V_lw70 = 1.207
## Upper bound search / Iteration 7 / beta_V_lw70 = 1.199
## Lower bound search / Iteration 2 / beta_V_lw70 = 0.717
## Lower bound search / Iteration 3 / beta_V_lw70 = 0.704
## Lower bound search / Iteration 4 / beta_V_lw70 = 0.504
## Lower bound search / Iteration 5 / beta_V_lw70 = 0.668
## parameter  beta_V_lw70 
## Value  0.917 
## CI =  [0.668 , 1.199]  
## diff. =  [-0.249 , 0.281] 
## rel. diff. =  [-27.13 , 30.705] 
## /**********************************************************************/ 
##  LL search on omega_V
## Upper bound search / Iteration 2 / omega_V = 0.144
## Upper bound search / Iteration 3 / omega_V = 0.172
## Lower bound search / Iteration 2 / omega_V = 0.096
## Lower bound search / Iteration 3 / omega_V = 0.022
## Lower bound search / Iteration 4 / omega_V = 0.068
## Lower bound search / Iteration 5 / omega_V = 0.064
## Lower bound search / Iteration 6 / omega_V = 0.066
## Lower bound search / Iteration 7 / omega_V = 0.067
## Lower bound search / Iteration 8 / omega_V = 0.068

## parameter  omega_V 
## Value  0.118 
## CI =  [0.068 , 0.172]  
## diff. =  [-0.051 , 0.054] 
## rel. diff. =  [-42.363 , 46.025]
## /**********************************************************************/ 
## parameter  V_pop 
## Value  7.809 
## CI =  [7.399 , 8.377]  
## diff. =  [-0.411 , 0.567] 
## rel. diff. =  [-5.256 , 7.27] 
## /**********************************************************************/ 
## parameter  beta_V_lw70 
## Value  0.917 
## CI =  [0.668 , 1.199]  
## diff. =  [-0.249 , 0.281] 
## rel. diff. =  [-27.13 , 30.705] 
## /**********************************************************************/ 
## parameter  omega_V 
## Value  0.118 
## CI =  [0.068 , 0.172]  
## diff. =  [-0.051 , 0.054] 
## rel. diff. =  [-42.363 , 46.025]
print(r.prl)
## $confint
##              estimate     lower     upper
## V_pop       7.8098520 7.3993885 8.3776492
## beta_V_lw70 0.9175519 0.6686276 1.1992865
## omega_V     0.1184347 0.0682625 0.1729449
## 
## $proflike
## $proflike[[1]]
##      param paramInit     -2LL  name   thresh tol.param tol.LL
## 1 6.394166  7.809852 885.0105 V_pop 2.705543      0.01    0.1
## 2 7.373540  7.809852 857.4106 V_pop 2.705543      0.01    0.1
## 3 7.399389  7.809852 856.6478 V_pop 2.705543      0.01    0.1
## 4 7.809852  7.809852 852.2644 V_pop 2.705543      0.01    0.1
## 5 8.369523  7.809852 854.3355 V_pop 2.705543      0.01    0.1
## 6 8.377649  7.809852 854.9957 V_pop 2.705543      0.01    0.1
## 7 9.538975  7.809852 874.8570 V_pop 2.705543      0.01    0.1
##   useLinearization
## 1             TRUE
## 2             TRUE
## 3             TRUE
## 4             TRUE
## 5             TRUE
## 6             TRUE
## 7             TRUE
## 
## $proflike[[2]]
##        param paramInit     -2LL        name   thresh tol.param tol.LL
## 1  0.5047618 0.9175519 859.6773 beta_V_lw70 2.705543      0.01    0.1
## 2  0.6686276 0.9175519 854.9032 beta_V_lw70 2.705543      0.01    0.1
## 3  0.7047618 0.9175519 853.9319 beta_V_lw70 2.705543      0.01    0.1
## 4  0.7175519 0.9175519 854.6544 beta_V_lw70 2.705543      0.01    0.1
## 5  0.9175519 0.9175519 852.2644 beta_V_lw70 2.705543      0.01    0.1
## 6  1.1175519 0.9175519 853.8870 beta_V_lw70 2.705543      0.01    0.1
## 7  1.1758086 0.9175519 854.4043 beta_V_lw70 2.705543      0.01    0.1
## 8  1.1961329 0.9175519 854.7438 beta_V_lw70 2.705543      0.01    0.1
## 9  1.1992865 0.9175519 855.1519 beta_V_lw70 2.705543      0.01    0.1
## 10 1.2075692 0.9175519 855.5637 beta_V_lw70 2.705543      0.01    0.1
## 11 1.3758086 0.9175519 859.9705 beta_V_lw70 2.705543      0.01    0.1
##    useLinearization
## 1              TRUE
## 2              TRUE
## 3              TRUE
## 4              TRUE
## 5              TRUE
## 6              TRUE
## 7              TRUE
## 8              TRUE
## 9              TRUE
## 10             TRUE
## 11             TRUE
## 
## $proflike[[3]]
##         param paramInit     -2LL    name   thresh tol.param tol.LL
## 1  0.02286273 0.1184347 860.0357 omega_V 2.705543      0.01    0.1
## 2  0.06468732 0.1184347 855.2133 omega_V 2.705543      0.01    0.1
## 3  0.06604944 0.1184347 855.6810 omega_V 2.705543      0.01    0.1
## 4  0.06771528 0.1184347 855.3994 omega_V 2.705543      0.01    0.1
## 5  0.06826250 0.1184347 855.1829 omega_V 2.705543      0.01    0.1
## 6  0.06891487 0.1184347 854.4579 omega_V 2.705543      0.01    0.1
## 7  0.09696613 0.1184347 851.8843 omega_V 2.705543      0.01    0.1
## 8  0.11843470 0.1184347 852.2644 omega_V 2.705543      0.01    0.1
## 9  0.14465647 0.1184347 853.0193 omega_V 2.705543      0.01    0.1
## 10 0.17294485 0.1184347 855.0564 omega_V 2.705543      0.01    0.1
##    useLinearization
## 1              TRUE
## 2              TRUE
## 3              TRUE
## 4              TRUE
## 5              TRUE
## 6              TRUE
## 7              TRUE
## 8              TRUE
## 9              TRUE
## 10             TRUE
## 
## 
## $level
## [1] 0.9
## 
## $method
## [1] "proflike"


Using nonparametric bootstrap

r.boot <- confintmlx(project, method="bootstrap", nboot=20)
## [INFO] Results have been succesfully loaded
## [INFO] Results have been succesfully loaded
## [INFO] Results have been succesfully loaded
## Generating data sets...
## Generating projects with bootstrap data sets...
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print(r.boot)
## $confint
##                 estimate       lower     upper
## ka_pop        0.61829333  0.41037226 1.0842762
## V_pop         7.80985201  7.46355136 8.1124139
## beta_V_lw70   0.91755189  0.72059824 1.2528169
## Cl_pop        0.12266966  0.10743047 0.1592989
## beta_Cl_sex_1 0.10332266 -0.20236383 0.2809297
## omega_ka      0.77254335  0.32595120 0.8062742
## omega_V       0.11843468  0.05597757 0.1607928
## omega_Cl      0.27435309  0.17331795 0.3148838
## a1            0.54888394  0.29615154 0.7635227
## b1            0.08235761  0.04266097 0.1235797
## 
## $level
## [1] 0.9
## 
## $method
## [1] "bootstrap"