The MONOLIX software

This work was done to test exhaustively all the available models in the PK library of MONOLIX. In any case, this evaluation was performed in order to compare both MONOLIX and NONMEM. However, all the results were exhaustively compiled in a downloadable document. At least for NONMEM, results are given as a support and depending of the environment (PC and fortran compiler) and the degree of experience of the modeller, different results could be obtained.

The next step will be to evaluate the PD library of Monolix.

All this piece of work will be somehow published

The document containing all the results of the 150 runs can be downloaded, as well as the 84 simulated data sets, the MONOLIX files, the NONMEM V files and the NONMEM VI files. We only present here a summary of these results.

The data

The data sets used for this evaluation were simulated by Exprimo NV using TS2 version 2.1.2 (Pharsight, Mountain View , CA , USA ) installed on a Dell Dimension 9150 Workstation with Intel Pentium D CPU Processors 3.20 GHz, running under Windows XP Professional. All the random effects were simulated with a log-normal distribution. The inter-individual variability was set to 30% whatever the parameter and a residual error of 20% was used. Simulated concentrations below the value of 0.1 ng/mL were considered below the virtual limit of quantification and then not taking into account in the analyses.

For each PK model, single dose and multiple doses were simulated. The single dose was administered at time 0 and observations will be made up to 72h. Then multiple doses started at time 72h and a dose was given every day during 7 days. Trough measurements were made every day. A full profile was drawn at time 144h and after the last administration at time 216h.

The sampling scheme was:

•  Single dose: 0, 0.25h, 0.5h, 0.75h, 1h, 2h, 4h,8h,12h, 16h, 20h, 24h, 36h, 48h, 60h and 72h
•  Multiple doses:
   - Trough measurements -> 96h, 120h, 144h, 168h, 192h and 216h
   - Full profile at 144h -> 144.25h, 144.5h, 144.75h, 145h, 146h, 148h, 152h, 156h, 160h and 164h
   - Full profile at 216h -> 216.25h, 216.5h, 216.75h, 217h, 218h, 220h, 224h, 228h, 232h, 240h, 252h, 264h, 276h and 288h

Depending of the type of models 4 different doses were simulated (e.g. 1x, 3x, 6x and 12x or 1x, 2x, 4x and 8x).

Overall 120 subjects were used for each dataset with 30 subjects per group.

For each simulation, the following information was collected:

•  Subject identifier (from 1 to 120)
•  Administered dose
•  Time of dose administration
•  Observations (concentrations)
•  Duration of dose administration (or rate of administration)
•  Time of observations
•  Individual parameters
•  Individual covariate (mainly Dose)
•  NONMEM variables like EVID, RATE, …

Only one parametrization (Tlag, Tk0, ka, Cl, V1, Km,Vm, Q, V2) were used for simulating 24 data sets.
For each of the 24 simulated datasets, the parameters are estimated using several subsets of data:

• single dose data (between 0h and 72h),
• multiple dose data (between 72h and 288h),
• steady-state data (between 216h and 288h),
• full data (between 0h and 288h).

The models

There are 42 models in the PK library of MONOLIX 2.2:

bolus_1cpt_Vk; IV bolus with one compartment and parameters: V,
bolus_1cpt_VCl; IV bolus with one compartment and parameters: V, Cl
bolus_1cpt_VVmKm; IV bolus with one compartment, Michaelis Menten elimination and parameters: V, Vm, Km;

infusion_1cpt_Vk; infusion bolus with one compartment and parameters: V, k
infusion_1cpt_VCl; infusion bolus with one compartment and parameters: V, Cl
infusion_1cpt_VVmKm; infusion bolus with one compartment, Michaelis Menten elimination and parameters: V, Vm, Km

oral0_1cpt_Tk0Vk ; 0 order oral absorption with one compartment and parameters: Tk0, V, k
oral0_1cpt_Tk0VCl; 0 order oral absorption with one compartment and parameters: Tk0, V, Cl
oral0_1cpt_Tk0VVmKm; 0 order oral absorption with one compartment, Michaelis Menten elimination, and parameters: Tk0, V, Vm, Km

oral0_1cpt_TlagTk0Vk; 0 order oral absorption with one compartment, a lag time and parameters: Tlag, Tk0, V, k
oral0_1cpt_TlagTk0VCl ; 0 order oral absorption with one compartment, a lag time and parameters: Tlag, Tk0, V, Cl
oral0_1cpt_TlagTk0VVmKm; 0 order oral absorption with one compartment, Michaelis Menten elimination, a lag time and parameters: Tlag, Tk0, V, Vm, Km

oral1_1cpt_kaVk; 1st order oral absorption with one compartment and parameters: ka, V, k
oral1_1cpt_kaVCl; 1st order oral absorption with one compartment and parameters: ka, V, Cl
oral1_1cpt_kaVVmKm; 1st order oral absorption with one compartment, Michaelis Menten elimination and parameters: ka, V, Vm, Km

oral1_1cpt_TlagkaVk; 1st order oral absorption with one compartment, a lag time and parameters: Tlag, ka, V, k
oral1_1cpt_TlagkaVCl; 1st order oral absorption with one compartment, a lag time and parameters: Tlag, ka, V, Cl
oral1_1cpt_TlagkaVVmKm ; 1st order oral absorption with one compartment, Michaelis Menten elimination, a lag time and parameters: Tlag, ka, V, Vm, Km

bolus_2cpt_Vkk12k21; IV bolus with two compartments and parameters: V1, k, k12, k21
bolus_2cpt_ClV1QV2; IV bolus with two compartments and parameters: Cl, V1, Q, V2
bolus_2cpt_Vk12k21VmKm; IV bolus with two compartments, Michaelis Menten elimination and parameters: V1, k12, k21, Vm, Km
bolus_2cpt_V1QV2VmKm; IV bolus with two compartments, Michaelis Menten elimination and parameters: V1, Q, V2, Vm, Km

infusion_2cpt_Vkk12k21; infusion bolus with two compartments and parameters: V1, k, k12, k21
infusion_2cpt_ClV1QV2; infusion bolus with two compartments and parameters: Cl, V1, Q, V2
infusion_2cpt_Vk12k21VmKm; infusion bolus with two compartments, Michaelis Menten elimination and parameters: V1, k12, k21, Vm, Km
infusion_2cpt_V1QV2VmKm; infusion bolus with two compartments, Michaelis Menten elimination and parameters: V1, Q, V2, Vm, Km

oral0_2cpt_Tk0Vkk12k21; 0 order oral absorption with two compartments and parameters: Tk0, V1, k, k12, k21
oral0_2cpt_Tk0ClV1QV2; 0 order oral absorption with two compartments and parameters: Tk0, Cl, V1, Q, V2
oral0_2cpt_Tk0Vk12k21VmKm; 0 order oral absorption with two compartments, Michaelis Menten elimination and parameters: Tk0, V1, k12, k21, Vm, Km
oral0_2cpt_Tk0V1QV2VmKm; 0 order oral absorption with two compartments, Michaelis Menten elimination and parameters: Tk0, V1, Q, V2, Vm, Km

oral0_2cpt_TlagTk0Vkk12k21; 0 order oral absorption with two compartments, a lag time and parameters: Tlag, Tk0, V1, k, k12, k21
oral0_2cpt_TlagTk0ClV1QV2; 0 order oral absorption with two compartments, and a lag time and parameters: Tlag, Tk0, Cl, V1, Q, V2
oral0_2cpt_TlagTk0Vk12k21VmKm ; 0 order oral absorption with two compartments, a lag time, Michaelis Menten elimination and parameters: Tlag, Tk0, V1, k12, k21, Vm, Km
oral0_2cpt_TlagTk0V1QV2VmKm; 0 order oral absorption with two compartments, a lag time, Michaelis Menten elimination and parameters: Tlag, Tk0, V1, Q, V2, Vm, Km

oral1_2cpt_kaVkk12k21; 1st order oral absorption with two compartments and parameters: ka, V1, k, k12, k21
oral1_2cpt_kaClV1QV2; 1st order oral absorption with two compartments and parameters: ka, Cl, V1, Q, V2
oral1_2cpt_kaVk12k21VmKm; 1st order oral absorption with two compartments, Michaelis Menten elimination and parameters: ka, V1, k12, k21, Vm, Km
oral1_2cpt_kaV1QV2VmKm; 1st order oral absorption with two compartments, Michaelis Menten elimination and parameters: ka, V1, Q, V2, Vm, Km

oral1_2cpt_TlagkaVkk12k21; 1st order oral absorption with two compartments, a lag time and parameters: Tlag, ka, V1, k, k12, k21
oral1_2cpt_TlagkaClV1QV2; 1st order oral absorption with two compartments, a lag time and parameters: Tlag, ka, Cl, V1, Q, V2
oral1_2cpt_TlagkaVk12k21VmKm; 1st order oral absorption with two compartments, a lag time, Michaelis Menten elimination and parameters: Tlag, ka, V1, k12, k21, Vm, Km
oral1_2cpt_TlagkaV1QV2VmKm; 1st order oral absorption with two compartments, a lag time, Michaelis Menten elimination and parameters: Tlag, ka, V1, Q, V2, Vm, Km

The results

• For NONMEM, all analyses were performed by Exprimo NV on a Dell Precision 670 computer equipped with two 3.0 GHz Intel Xeon processors running under Windows XP. The fortran compiler used was Compaq Visual Fortran Standard Edition version 6.1. The NONMEM software version V level 1 and VI version 1 were evaluated. As first guess, the First-Order Conditional Estimate (FOCE) method with interaction was used. In case of convergence issues with the FOCE method, the First-Order (FO) method with both side log-transformed data was used. Furthermore in order to be consistent, a same model was fitted with the same method (FOCE or FO) whatever the datasets and the version of NONMEM. Finally, as a starting point, initial estimates were set approximately 20 to 50% higher than the simulated population parameters.
  
  With this approach, 57 out of 150 runs were analyzed using the FOCE method with interaction and therefore 93 with the FO method with log-transformed data. For NONMEM version V, 6 runs did not terminate successfully and it was not possible to get the variance-covariance matrix in 10 runs. While, for NONMEM version VI, all runs were successful and it was not possible to obtain the variance-covariance matrix in 25 out of 150 runs.
  
  
• For MONOLIX, all analyses were performed by Marc Lavielle on a ACER TravelMate 8100 computer equipped with one 2.26 GHz Intel M processor running under Windows XP.

True values of the parameters and initializations used with MONOLIX

% of successful runs with MONOLIX
(150 runs)

MONOLIX: Absolute relative errors of the estimated parameters
(fixed effects)

MONOLIX: Absolute relative errors of the estimated inter-patient variability
(standard-deviation of the random effects)

MONOLIX: Absolute relative errors of the estimated residual variability
(standard-deviation of the residual error)

MONOLIX: Computational time of the 150 runs

Download

Download the document with the detailed results obtained with NONMEM V, NONMEM VI and MONOLIX 2.2

Download the 84 simulated data sets

Download the MONOLIX files (a README text file and 24 folders with the data files, the projects files and all the results files)

Download the NONMEM V scripts

Download the NONMEM VI scripts