1 PFIM 3.2 User guide - R
Contents
1. time condinit lt 0 condinit lt expression c 0 source paste directory program dirsep LibraryPK r sep formED lt infusion _lcpt_VVmkm doseMM 100 Tinf 1 4 PD model using an analytical form with the library of models In this illustration th user creates a on response model using the model function implemented in the library immed lin null describing an immediate response model with a linear drug action and without baseline source paste directory program dirsep LibraryPD_PDdesign r sep formA lt immed_lin_null 1 form lt c formA 3 2 2 Example 2 Two responses defined by a PK PD model 5 PK model with a linear elimination immediate response PD model In this illustration th user creates for the PK model a one compartment model with bolus input and first order elimination for a single dose and for the PD model an immediate response model with a linear drug action and no baseline is used As shown in the example the PK model is given as an argument of the PD model Thus in the PD model the drug concentration corresponds to the expression of the PK model source paste directory program dirsep LibraryPK r sep source paste directory program dirsep LibraryPD_PKPDdesign r sep 24 formA lt bolus_lcpt_Vk 1 formB lt immedPD_lin null forma 1 form lt c formA formB 6 PK model with a linear elimination turnover response2. Logarithmic immed_log_null Alog immed_log_const Alog SO Emax immed_Emax_null Emax C50 immed_Emax_const Emax C50 SO Sigmoid Emax immed gammaEmax null Emax C50 gamma immed gammaEmax_ const Emax C50 gamma S0 Imax immed_Imax null Imax C50 immed_Imax const Imax C50 SO Sigmoid Imax immed gammaImax null Imax C50 gamma immed gammaImax const Imax C50 gamma S0 11 1 1 2 2 Pharmacodynamic models linked to pharmacokinetic model In this section we deal with a two response model with one response for the PK and the other one for the PD We thus optimise sampling times for both responses using a PK PD model Using the libraries of models we have four cases to compose the PK PD model according to the writing of each respons model ither with an analytical form AF or a differential equation system ODE Therefore there are four cases of PK PD models 1 PK model with linear elimination AF and immediate response PD model AF 2 PK model with linear elimination AF and turnover response PD model ODE 3 PK model with Mickaelis Menten elimination ODE and immediate response PD model AF 4 PK model with Mickaelis Menten elimination and turnover response PD model ODE To use PFIM for design evaluation and optimisation for a PK PD model it is necessary to have a PK response and a PD response implemented with a similar form In the first case immediate response pha
3. The PK models with a linear elimination are written using an analytical form whereas the PK models with a Mickaelis Menten are written using a differential equation system These both types of PK model are written in the file LibraryPK r available in the folder Program Thus the user has to specify the path of this file in the model file to use this library of models source paste directory program dirsep LibraryPK r sep For each type of PK models the list of models are presented in separated tables in the following sections These tables return all the information in order to use the model function chosen The model is described by a name the type of input the type of elimination the number of compartments the parameters used parameterisation the type of administration sd single dose md multiple dose ss steady state for each administration type some variables are required or not They are specified in the column named Needed variables N number of doses tau interval between two doses TInf duration of the infusion doseMM dose For models with infusion the user has to specify the duration of infusion TInf in the needed variable The rat of infusion is computed automatically in the function model by the expression dose TInf As in PFIM 3 0 for PK models with linear elimination the variable dose has to be specified in the input file For example if one
4. The tables presenting these models return all the information in order to use the model function chosen a name the parameters used parameterisation Examples of the use of the library of pharmacodynamic models are presented in section 2 2 1 1 2 1 Immediate response pharmacodynamic models alone Linear quadratic logarithmic Emax sigmoid Emax Imax sigmoid Imax models with null or constant baseline are available The list of these models is given in Table 3 These models are written with an analytical form and have to be used in the case of a model with one response PD evaluation or optimisation They are implemented in the file LibraryPD_PDdesign r Thus the user has to specify the path of this file in the model file to use this library of models source paste directory program dirsep LibraryPD_PDdesign r sep For these models the design variables are the concentrations or the doses instead of the sampling times For example if one uses a linear drug action model with a constant baseline immed lin const from the library the model uses two parameters Alin SO 10 Table 3 Immediate response pharmacodynamic models included in the PD library for PD alone and for PK PD model Baseline e a Null baseline Constant baseline PA ESAS SA Linear immed_lin null Alin immed_lin_const Alin SO Quadratic immed_quad_null Alin Aquad immed_quad_const Alin Aquad SO
5. and NOT IN THE INITIAL CONDITION OF THE MODEL IN THE INPUT FILE Consequently it is not possible to specify different doses per group for models with infusion or first order absorption input All groups of the design considered hav th sam dose Otherwise the user should use the user defined model option 13 Table 4 Immediat respons pharmacodynamic models linked to a pharmacokinetic model included in the library Drug action Baseline disease models models Linear progression Exponential increase Exponential decrease Linear immed lin lin Alins S0 immed_lin_exp Alin 50 immed_lin_dexp Alin SO kprog kprog kprog Alin i Quadratic immed_quad_lin Alin Aquad immed_quad_exp Aquad SO immed quad dexp ALA RAG SO kprog SO kprog kprog Logarithmic immed_log_lin n immed_log_exp a immed_log_dexp eo A Emax C50 Emax C50 E Emax C50 Emax immed Emax lin S0 kprog immed Emax exp S0 kprog immed Emax dexp S0 kprog Siamoid Emax C50 Emax C50 Emax C50 e immed gammaEmax lin gamma S0 immed gammaEmax exp gamma SO immed gammaEmax dexp gamma SO kprog kprog kprog Imax C50 Imax C50 E Imax C50 Imax immed_Imax_lin S0 kprog immed_Imax_exp 60 kprog immed_Imax_dexp S0 kprog cia Imax C50 Imax C50 Imax C50 immed gammaImax_ lin gamma S0 immed gammaImax exp gamma SO immed gammaImax dexp gamma S0 kprog kprog kprog In addition to those in Table 3 14 Table 5 Tu
6. corresponding to those designs residual variance error model for each model s random effect model error tolerances for the solver of differential equations system if used a summary for inter occasion variability a summary of the covariate model Ga The number of occasions Gb Each covariate not changing with occasion its their parameters associated categories with their name and their corresponding proportions of subjects Ge Each covariate changing with occasion its their parameters associated categories with their name and their corresponding proportions of subjects The list of the sequence of values of categories for each occasion and each covariate Ga If the evaluation has been performed using the full or the block diagonal expression of the Fisher information matrix population Fisher information matrix a dim dim symmetric matrix where dim is the total number of population parameters to be estimated ED The value of each population parameter with the expected standard error on each parameter and the corresponding coefficient of variation Ga The value of the variance of the random effects for inter occasion variability with the expected standard error on each parameter and the corresponding coefficient of variation 29 The value of the determinant of the Fisher information matrix and the value of the criterion determinant 1 dim where dim is the total number of population parameters
7. development of the expression of the Fisher information matrix Mp Regarding model specification the library of standard pharmacokinetic PK models has been completed with three compartment models with linear elimination and models with Mickaelis Menten elimination one two and three compartment models Furthermore a library of pharmacodynamic PD models is now available Concerning the expression of the Fisher information matrix PFIM 3 2 can handle either a block diagonal Fisher information matrix or the complete one The computation of the Fisher information matrix to perform evaluation and optimisation of individual designs i e models with no random effects can be carried out It is now also possible in PFIM 3 2 to use models including inter occasion variability IOV with replicated designs at each occasion 2 Last a new feature of PFIM 3 2 is the computation of the Fisher information matrix for models including fixed effects for the influence of discrete covariates on the parameters Specification of covariates can depend or not of the occasion The computation of the predicted power of the Wald test for comparison or equivalence test for a given distribution of a discrete covariate as well as the number of subjects needed to achieve a given power can be computed 2 3 4 The same input file named by default stdin r used in PFIM 3 0 can be used in PFIM 3 2 but the new features would then not be ac
8. ty Results from the comparison test the value and the exponential of the value of each covariate parameter with the corresponding 95 confidence interval of the parameter the predicted value of the power of the Wald test and the number of subjects needed to detect this covariate effect with the given type on rror and the given power Gp Results from the equivalence test the value and the exponential of the value of each covariate parameter with the corresponding 90 confidence interval of the parameter the power of the Wald test and the number of subjects needed to achieve the given power for this covariate effect with the given type on rror and the given interval of equivalence 30 Figure 1 Example of design evaluation output file with covariate effect and inter occasion variability stdout Bloc notes Evaluationi Mon Nov 09 12 56 17 2009 Ye Yc te Ye Ye Tc te Ye Ya Te Te te Ya Ye Fe Ve Ve c Fe Ve Ye e te Ye Ve Xe te ye INPUT SUMMARY TY Y Te de te Ye Ye Te Te Y de Fe Tc Ye Ve de Yc Ve Ve Fe Ye Ve Ve de te Ve de te ke te te a Analytical function models expression dose V ka ka C1 V Cexp C1 V t exp ka t Population design Sample times for response A Number of subjects per group ECO D L Luo 2 3 D 40 2 Number of occasions Random effect model Trand 2 COL 0 FJA2 variance error model response A Covariate model NB Covariates are additive
9. 137608e 01 37 9361098 932 mot aoo oO ooo 0 000000 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 311983e 01 304502e 02 576277e 01 603848e 03 716325e 04 639794e 01 938145e 02 0 0000000 8112567 2 607999e 03 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 694950e 01 438598e 01 655453e 02 13 608e 01 639794e 01 550467e 04 037868e 03 68337 0 0000000 00000 0 00000 0 0 799 488 37 2607 1665 593 00000 00000 00000 07325 90337 93611 99948 95731 81447 31799 1 0 0 0 0000000 0 000000 0 0 0 0 000000 0000000 0732545 32 P stdout Bloc notes COX Fichier Edition Format Affichage Te Ye Ye Ye c Yc Ye Tc Ye Fe Ve Fe e Fe Yc Fe c e Yc Ye Tc e Yc Fe Xe tc EXPECTED STANDARD ERRORS Ye Ye Ye Ye c Fe Ye Yc Ye Yc Yc Yc Yc Yc Yc Ye c Ye Yc Ye fc e Ye c A See Fixed Effects Parameters Beta StdError RSE 1 00000000 0 04931271 4 931271 V 3 50000000 0 23870821 6 820234 0000000 O OOF 7a R R A beta_V_Sex_F 0 18232156 0 09534190 52 293270 beta_Cl_Treat_B 0 09531018 0 03760359 39 453909 Variance of Inter Subject Random Effects Omega StdError RSE ka 0 09 0 02635007 29 27786 v 0 09 0 02478091 27 53434 C 0 09 0 02288005 25 42228 Variance of Inter Occasion Random Effects Gamma stdError RSE ka 0 0
10. PD model In this example the user creates a PK PD model with a one compartment bolus input for the PK and a turnover response model with an inhibition on the input for the PD using the function create_formED The dose is specified in a part of the R script file stdin r source paste directory program dirsep CreateModel PKPDdesign r sep create formED bolus_lcpt_Vk turn_input_Imax 7 PK model with a Mickaelis Menten elimination immediate response PD model In this example the user creates a PK PD model with a one compartment infusion input with Mickaelis Menten elimination for the PK and an immediate response model with a linear drug action and no baseline for the PD using the function create_formED In this case the user needs to specify the dose her qual to 100 and the duration of infusion here equal to 1 hour as arguments not in the initial condition described in a part of the R script file stdin r source paste directory program dirsep CreateModel PKPDdesign r sep create formED infusion lcpt_VVmkm immedPD_lin_ null doseMM 100 TInf 1 3 3 General objects required for Evaluation and Optimisation According to the new features in PFIM 3 2 only some objects have been added or modified in the input file named by default stdin r 3 3 1 Full or block diagonal fisher information matrix The following object has been added option integer indicating exp
11. design using an analytical form to describe the model o PfimOPT3 20p2 r To compute the full Fisher Information matrix option 2 to optimise a population design using an analytical form to describe the model o EQPfim3 20p2 r To compute the full Fisher Information matrix option 2 to evaluate a population design using a differential equation system to describe the model o EQPfimOPT3 20p2 r To compute the full Fisher Information matrix option 2 to optimise a population design using a differential equation system to describe the model o Algosimplex3 2 r To use the Simplex algorithm o initfedoR c and classfed h To compile the dll o libFED dll The dynamic library of the Federov Wynn algorithm o algofedorov3 2 r To use the dynamic library libFED dll 22 o librayPK r To use the library of pharmacokinetic models o librayPD PDdesign r To use the library of immediate response pharmacodynamic models alone o librayPD PKPDdesign r To use the library of pharmacodynamic models linked to pharmacokinetic models both written using analytical form o CreateModel PKPDdesign r To use the libraries of pharmacokinetic and pharmacodynamic models when they ar writing either with different forms or both with differential equation systems Y The files in the folder Program should not be changed The folder called Examples contains th xample files The documentation whi
12. input and Mickaelis Menten elimination only single dose models are implemented For infusion and first order absorption input single dose and multiple dose are implemented There is no steady stae conditions for PK models with Mickaelis Menten elimination The list of these PK models is given in Table 2 Pro models with a bolus input the dose has to be specified in the input file stdin r by default as the initial condition of the differential equation system For models with infusion or first order absorption input dose has to be specified as an argument and NOT IN THE INITIAL CONDITION OF THE MODEL IN THE INPUT FILE Q As the dose is an argument it is not possible to specify different doses per group for models with infusion or first order absorption input All groups of the design considered have the same dose Otherwise the user should use the user defined model option Table 2 Pharmacokinetic models with Mickaelis Menten elimination included in the library of models Name Input Cpt Elimination Parameterisation Administration Needed Variable s bolus_lcpt_VVmkm IV bolus 1 Mickaelis Mente V Vm km sd sd doseMM TInf infusion lcpt_VVmkm IV infusion 1 Mickaelis Mente V Vm km i md doseMM TInf tau sd doseMM orall_lcpt_kaVVmkm lst order 1 Mickaelis Mente ka V Vm km md doseMM tau bol
13. m and l 1 p IM y 4 ok BEN VO TV with m and 1 dim A cena ya with 1 1 dim 4 and m l p dA 94 In the previous versions of PFIM the dependence of V in u was neglected so that FILA Then the population Fisher information matrix is approximated u a block diagonal matrix that is to say the block C of the matrix was supposed to be 0 see details in 1 Also the block A is simplified and expressed as OE JE ACE VO at 2 V with m and l 1 p du m du 1 In the present version the user can now choose if a full or block diagonal information matrix is needed Muonever this implementation is not developed yet for models with covariates and or inter occasion variability 13 Models with no random effects PFIM 3 2 can also address the problem of evaluation and optimisation of individual designs by assuming no random effect in the model This is done by specifying inter subject variability equal to 0 The user specifies an individual design i e only one individual subject with a number of sampling times and their allocation in time However it is also possible to specify a design composed of several groups with different sampling times involving different numbers of subjects In that case as there is no random effect model design evaluation and optimisation with PFIM 3 2 is performed as a na ve pooled data approach Indeed the model is fitted to the pooled data from all individuals as
14. modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version The document PFIM3 2_Examples pdf with fully described examples is also available You should have received a copy of the GNU General Public License along with this program If not see lt http www gnu org licenses gt THIS SOFTWARE IS PROVIDED AS IS AND ANY EXPRESSED OR IMPLIED WARRANTIES INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE UNIVERSITE PARIS DIDEROT OR INSERM OR ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT INDIRECT INCIDENTAL SPECIAL EXEMPLARY OR CONSEQUENTIAL DAMAGES INCLUDING BUT NOT LIMITED TO PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES LOSS OF USE DATA OR PROFITS OR BUSINESS INTERRUPTION HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY WHETHER IN CONTRACT STRICT LIABILITY OR TORT INCLUDING NEGLIGENCE OR OTHERWISE ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE Redistribution and use in source and binary forms with or without modification are permitted under the terms of the GNU General Public Licence and provided that the following conditions are met 1 Redistributions of source code must retain the above copyright notice this list of conditions and the fo
15. on log parameters Covariates not changing with occasion EBD Covariate 1 Sex CV Categories References Proportions M 0 5 F 0 5 Covariates changing with occasion Covariate 1 Treat C Categories References A 2 B Sequences Proportions A BA 0 5 P stdout Bloc notes Fichier Edition Format Affichage Fe Ye c Ye Ye Ye Tc Ye W Ye i POPULATION FISHER INFORMATION MATRIX Ye Ye e Ye He Ye I s2 416 506227 13 4811500 2 9544192 20 133552 0 0000000 0 0000000 0 000000e 00 13 481150 35 9417231 0 7377353 63 862547 0 9205728 0 0000000 0 0000000 0 000000e 00 2 954419 0 7377353 118 8958000 1 219084 97 7874996 0 0000000 0 0000000 0 000000e 00 s2 20 133552 63 8625471 1 2190840 223 518915 1 5772928 0 0000000 0 0000000 0 000000e 00 3 338525 0 9205728 97 7874996 2577293 6304989 0 0000000 0 0000000 0 000000e 00 0 000000 0 0000000 0 0000000 000000 0000000 19 4161602 0 2982775 7 435142e 02 0 000000 0 0000000 0 0000000 0000000 1655 4320267 0 2283933 1 193624e 01 0000000 0000000 0000000 0000000 3 3385249 0000000 0000000 0000000 0000000 0000000 4533533 4161602 2982775 9141701 9362439 1694860 000000 0 000000 0 0000000 0 2283933 1931 0450129 1 694860e 01 0 000000 0 0000000 0 0000000 13 1198267 0 1694950 1 698208e 04 0 000000 0 0000000 0 0000000 0 1438598 4 603848e 03 0 0000000 000000 000000 0 0000000 000000 0 1576277 965 5452976 6
16. pu ka ge if B 0 A 5 romo vb ela where is the cumulative distribution function of the standard normal distribution and Z is such that Q z 1 0 Pin equivalence test is usually chosen to be zero Using the covariate effect P fixed by the user the corresponding standard error SE B is predicted by PFIM 3 2 for a given design and the values of population parameters Computation of the number of subjects needed The number of subjects needed to achieve a power P to show equivalence between two covariate effects using the Wald test is also computed First from equations 4 and 5 we compute the SE needed on fB to obtain a power of P Called NSE P using the following relation B A NSE P e 1 P if B e A 0 6 _ P A i MERE ep if B lt 0 A 7 20 where is the cumulative distribution function of the standard normal distribution and Z is such that 6 z l a Last we compute the number of subjects needed to be included to obtained a power of P called NNI P using the equation 3 like for comparison test 1 7 References 1 Bazzoli C Retout S Mentr F Fisher information matrix for nonlinear mixed effects multipl respons models evaluation of the first order linearization using a pharmacokinetic pharmacodynamics model Statistics in Medicine 2009 28 14 1940 56 2 Retout S Mentr F Further developments of the Fisher information matrix in no
17. 225 0 007966128 35 40501 V 0 0225 0 006265291 27 84574 C 0 0225 0 004714039 20 95128 Standard deviation of residual error SIG StdError RSE sig interA 0 1 0 003847404 3 847404 We ve Ye Ye Te Ye e He Te Te Ye Ye Te de Ye Yc fe de ve te de dee eee te teo DETERMINANT Yk ve ve de de ve de de ve de He de de He Ye de de de de de de ete de kkk 8 332381e 38 Ye Ye Ye Ye He T Ye He Ye Te Ye He He He He He He He fe Ye He He te He He keke He He HHH CRITERION to e de de He Fe ve se e de de He Fe He He He Fe He He Je Fe He Fe He He He He He Xe 1751 449 Ye Ye He Ye Ye Ye Ye Ye Ye He He Ye Ye He fe de de tek ee keke ke eke keke COMPARISON TEST Ye de Ye Yc Ye e Ye Ye Tc e Yc Ye Ye Fe Yc Y Ye e Yc Ve Fe Y Ye e Fe Fe Ye e Ye He e a Beta 95 CI exp Beta 95 CI beta_V_Sex_F 0 18232156 0 0 37 1 2 E E R 451 beta_Cl_Treat_B 0 09531018 0 02 0 17 1 1 1 02 1 18 Type I error 0 05 Expected_power Number_subjects_needed given power 0 9 beta_V_Sex_F 0 6056216 93 67431 beta_C _Treat_B 0 8132144 5332231 Ye Yc Ye Ye fe Y Ya Ye Te A e Y OOOO iio EQUIVALENCE TEST Beta 90 CI exp Beta 90 CI beta_V_Sex_F 0 18232156 0 03 0 34 1 2 1 03 1 4 beta_Cl_Treat_B 0 09531018 0 03 0 16 1 4 11 031 127 Type I error 0 05 Equivalence interval log 0 8 log 1 25 Expected_power Number_subjects_needed I given power 0 9 beta_V_Sex_F 0 1118612 1868 56459 beta_Cl_Treat_B 0 9603400 29 64143 33 Moreover the P
18. FIM function returns the following R objects Dose prot design evaluated for each respons subjects number of subjects for each group mfisher the population Fisher information matrix determinant the determinant of the population Fisher information matrix crit the value of the criterion p the vector of the fixed effect parameters se the vector of the expected standard errors for each parameter cv the corresponding coefficients of variation expressed in percent summary exp power a matrix with each row corresponding to each covariate the name of the covariates the associated effect parameter the 95 confidence interval and the predicted power as columns summary nni a matrix with each row corresponding to each covariate the name of the covariates the associated effect parameter the 95 confidence interval and the number of subjects needed as column 34
19. WISSU il DIDEROT PARIS k K KKK k k k k K k k k k k k K k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k PFIM 3 2 Caroline Bazzoli Thu Thuy Nguyen Anne Dubois Sylvie Retout Emanuelle Comets France Mentr INSERM UMR738 Paris France Universit Paris 7 Paris France Janvier 2010 www pfim biostat fr User guide Q This document is an adds on to PFIM 3 0 documentation Thus it only outlines the new features implemented in PFIM 3 2 and explains how to carry out to use them This documentation version does not detail the features that were previously released in version 3 0 of PFIM KKAKXAAKKKAKKAKKKAKAKAKAKAAAKAKAAAKAKAKAAAKAKAAKAAKAAKAAAAKAAKAAAAKAKAAKAAAAKAKAAAKAAKAKAAAKAAAAAAKAA PFIM 3 2 is free library of functions The Universit Paris Diderot and INSERM are the co owners of this library of functions Disclaimer We inform users that the PFIM 3 2 is a tool developed by the Laboratory Models and methods of the therapeutic evaluation of the chronic diseases UMR S 738 under R and GCC PFIM 3 2 is a library of functions The functions are published after a scientific validation However it may be that only extracts are published By using this library of functions the user accepts all the conditions of use set forth hereinafter Licence This program is free software you can redistribute it and or
20. ated to each covariate as well as the number of categories for each covariate are not limited But in this version of PFIM the distribution of the covariates are supposed independent 18 1 6 Computation of power and number of subjects needed to treat 1l 6 1 Comparison test Computation of th xpected power The Wald test can be used to asses the difference of a covariate effect In PFIM the Wald test is performed on the of each category for each covariate a global Wald test on the vector 6 all effect coefficients is not implemented For one covariate and an effect of one category 6 K 2 the null hypothesis is Ho B 0 while the alternative hypothesis is H 0 The B A statistic of the Wald test is defined as Sy with B the covariate SE B effect estimates and SE B its associated standard error Under Hi when B fB we then compute the power of the Wald test defined as B B where is the cumulative distribution function of the standard normal distribution and Zy is such that 6 Zj2 1 a 2 Using the covariate effect P fixed by the user the corresponding standard error SE B is predicted by PFIM 3 2 for a given design and the values of population parameters Computation of the number of subjects needed The number of subjects needed to achieve a power P to detect a covariate effect using the Wald test is also computed First from the equation 1 we compute the SE need
21. ategory for which beta 0 Example beta covariate lt list Gender list c 0 5 0 6 345 25 Covariates changing with occasion If the user wants to deal with covariates which change with occasion he has to specify the following object covariate_occ model If the user has filled in following objects covariate_occ name covariate_occ category covariate_occ sequence logical value if T covariates changing with occasion are added to the model by T the previous object he has to specify the list of character indicating the name of the covariate s Example covariate _occ name lt list c Treat list of vectors of categories Each vector is associated to one covariate and defines its corresponding categories They can be written as character or integer Example covariate_occ category lt list Treat c A B list of vectors of sequences Each vector is associated to one sequence of values of covariates at each occasion Th size of each sequence has to be equal to the number of occasions n_occ for each covariate Example covariate_occ sequence lt list Treat list c A B c B A covariate_occ proportions list of vectors of proportions Each vector is parameter_occ associated associated to one covariate and defines the proportions of elementary designs corresponding to each sequence of covariate values The size of each
22. ch gives their description is included in the package PFIM3 2 with this documentation To install PFIM 3 2 create a directory for example directory U My Documents PFIM 3 2 and download the package PFIM 3 2 3 Use 3 1 Working directory Create a working directory for example U My Documents PFIM 3 2 examplesXlExamplel Copy the files PFIM3 2 r Stdin r and model r in this directory In the file PFIM3 2 r specify your working directory directory lt U My Documents PFIM 3 2 _ examples Examplel Then specify your program directory i e where is the folder called Program directory program lt U My Documents PFIM 3 2 Program Save the file PFIM3 2 r 3 2 Model writting Compared to PFIM 3 0 there is no change in the way to write a model using an analytical form or a differential equation system for single or multiple response models using the user defined option The main change is to write a PK PD model using the libraries of models Thus several xamples ar presented below with the different ways of writing models 3 2 1 Example 1 Single response with a PK or a PD model 23 1 PK model using an analytical form with the library of models In this illustration th user creates a on response model using the model function implemented in the pharmacokinetic library Orall_ lcpt_kaVCl describing a one compartment oral absorption after a multiple d
23. dose conditions by default NA TInf time of infusion to specify only for PK model with infusion input by default NA Using this function a new file named model created r is created in the directory currently used This new file contains the complete writing of the differential equation system describing the corresponding PK PD model 12 created by the function Create formED This file can be deleted after running PFIM It will be erased at each new use of the function Create formeD For these cases the user has thus to fill in the sdtin r using differential eguation options The list of the immediate response PD models is thus given in Table 3 plus those of Table 4 The list of the turnover response PD models is given in Table 5 For the second case where a PK model with linear elimination is associated to a turnover PD response model the PK model is written with a differential equations system Consequently only some PK models from the Table 1 are implemented for bolus input only single dose models for infusion input single dose and multiple dose for first order absorption input single dose and multiple dose Pro models with a bolus input the dose has to be specified in the input file stdin r by default as the initial condition of the differential equation system For models with infusion or first order absorption input dose has to be specified as an argument of the function Create formED
24. ed on 6 to obtain a power of P called NSE P using the following relation Bi NSE P i 2 Zo 2 0 Last we compute the number of subjects needed to be included to obtained a power of P called NNI P using NNI P Nx SE Bi 3 NSE P where N is the initial number of subjects in the given design and SE B the corresponding predicted SE of 6 for the given design 19 1 6 2 Equivalence test Computation of th xpected power The Wald test can be used to asses the equivalence of a covariate effect In PFIM the Wald test is performed on the 6 of each category for each covariate a global Wald test on the vector 6 all effect coefficients is not implemented For one covariate and an effect of one category 6 K 2 the null hypothesis is Ho BS A or B2 A while the alternative hypothesis is Hi A SBS A Ho is composed of two unilateral hypothesis Hy fPS A and Hosa B2 A Equivalence between two covariate effects can be concluded if and only if the two hypotheses Hy and H are rejected The two statistics of the unilateral Wald test under the null hypothesis A A A are defined as S and Sy P with B the covariate effect SE B SE B estimates and its associated standard error Under Hi when f with fi A Ai we then compute the power of the equivalence Wald test defined as B A A Pei 1 0 ione if B e A 0 4 wines BR spe B A Pe
25. ion Library of pharmacodynamic models 1 Immediate response pharmacodynamic models alone 2 Pharmacodynamic models linked to pharmacokinetic model L 1 2 2 Full expression of the Fisher information matrix Models with no random effects Inter occasion variability IOV specification Discrete covariate specification Computation of power and number of subjects needed to treat 1 Comparison test sibs Equivalence test References INSTALLATION Pre requirement Components USE Working directory Model writting Example 1 Single response with a PK or a PD model s2 Example 2 Two responses defined by a PK PD model General objects required for Evaluation and Optimisation Full or block diagonal fisher information matrix Graph option Objects required only for IOV option Objects required only for covariate option Covariates not changing with occasion Covariates changing with occasion Objects required only for computation of power and number of subjects needed for comparison test or equivalence test 4 RESULTS A Uds a 10 12 16 16 17 17 19 19 20 21 22 22 22 23 23 23 23 24 25 25 25 26 26 26 27 28 29 1 Description of the new features in PFIM 3 2 PFIM 3 2 is a new release of the R script function PFIM 3 0 1 dedicated to design evaluation and optimisation for multiple response models This version incorporates new features in terms of model specification and
26. llowing disclaimer 2 Redistributions in binary form must reproduce the above copyright notice this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution 3 The end user documentation included with the redistribution if any must include the following acknowledgment This product includes software developed by Universit Paris Diderot and INSERM http www biostat fr Alternately this acknowledgment may appear in the software itself if and wherever such third party acknowledgments normally appear 4 The names PFIM must not be used to endorse or promote products derived from this software without prior written permission For written permission please contact france mentre inserm fr 5 Products derived from this software may not be called PFIM nor may PFIM appear in their name without prior written permission of the Universit Paris Diderot and INSERM Copyright PFIM 3 2 Caroline Bazzoli Thu Thuy Nguyen Anne Dubois Sylvie Retout Emmanuelle Comets France Mentr Universit Paris Diderot INSERM www pfim biostat fr 3 6 w w w w 5 3 3 ou NF PHEHFHNH RADAR o P NF CONTENT DESCRIPTION OF THE NEW FEATURES IN PFIM 3 2 Model specification Library of pharmacokinetic models 1 Pharmacokinetic models with a linear elimination 2 Pharmacokinetic models with a Mickaelis Menten eliminat
27. ni logical value if T the number of subjects needed for a given power for comparison test is computed for each covariate Example compute nni lt T interval_eq vector of equivalence interval Example interval_eq lt c log 0 8 log 1 25 compute power_eq logical value if T the expected power for equivalence test is computed for each covariate Example compute power_eq lt T compute nni_eq logical value if T the number of subjects needed for a given power for equivalence test is computed for each covariate Example compute nni_eq lt T given power the value of the given power for comparison and or equivalence test Example given power lt 0 9 28 4 Results The results are written in the output file called by default stdout r This file is different when only evaluation or optimisation is performed Compared to the one computed in PFIM 3 0 the file is only modified when inter occasion variability and or covariate options are added It is only detailed below for evaluation but it is similar for optimisation Figure 1 represents the output file from the design evaluation of a model with covariates effect and inter occasion variability The user can read on the Figure 1 Grp The name of the function used PFIM 3 2 ED The name of the project and the date ED summary of the input model s sampling times in the elementary designs for each model s doses or initial conditions and subjects
28. nlinear mixed effects models with evaluation in population pharmacokinetics Journal of Biopharmaceutical Statistics 2003 13 2 209 27 3 Retout S Comets E Samson A Mentr F Design in nonlinear mixed effects models Optimization using the Federov Wynn algorithm and power of the Wald test for binary covariates Statistics in Medicine 2007 26 28 5162 79 4 Nguyen TT Bazzoli C Mentr F Design evaluation and optimization in crossover pharmacokinetic studies analysed by nonlinear mixed effect models Application to bioequivalence or interaction trials American Conference on Pharmacometrics 2009 Mystic United States 5 Bertrand J Mentr F Mathematical Expressions of the Pharmacokinetic and Pharmacodynamic Models implemented in the MONOLIX software http www monolix org 2008 21 2 Installation 2 1 Pre requirement Like for PFIM 3 0 the software R is required For an optimal use of PFIM 3 2 several packages might be needed in the R library directory for differential equation system to describe the model odesolve and nlme packages for the Federov Wynn algorithm combinat package F compared to PFIM 3 0 an additional package numDeriv is needed for the computation of the full Fisher information matrix The easiest way to install packages is directly from the web To install the packages odesolve nlme combinat and numDeriv start R and choose the Packages item from the men
29. occasion 3 5 1 Covariates not changing with occasion If the user wants to deal with covariates which do not change with occasion he has to specify the following object Covariate model logical value if T covariates are added to the model If the user has filled in by T the previous object he has to specify the following objects covariate list of character indicating the name of the covariate s Example covariate name lt list c Gender Covariate category list of vectors of categories Each vector is associated to one covariate and defines its corresponding categories They can be written as character or integer Example covariate category lt list Gender c F M covariate proportions list of vectors of proportions Each vector is associated to one covariate and defines the corresponding proportions of subjects involved in each corresponding categories Example covariate proportions lt list Gender c 0 5 0 5 parameter associated list of vectors of parameter s associated with each covariate Each vector is associated to one covariate and is defined by the corresponding parameters on which is added the covariate Example parameter associated lt list Gender c Cl V Q Name of the parameter s has to be identical to those entered in the object parameters 26 beta covariate list of the values of parameters for all other categories than th referenc c
30. ose administration md N and tau are the needed variables and thus they have to be specified by the user in the function model Here w havi five oral administration doses with an interval between two doses equal to twelve hours source paste directory program dirsep LibraryPK r sep formA lt Orall_lcpt_kaVCl_md N 5 tau 12 1 form lt c formA 2 PK model using a differential equation form with the library of models In this illustration th user creates a on respons model using the model function implemented in the pharmacokinetic library bolus_lcpt_VVmkm describing a one compartment bolus input with Mickaelis Menten elimination after a single dose administration sd The dose is specified in a part of the R script file stdin r time condinit lt 0 condinit lt expression c 100 dose 100 source paste directory program dirsep LibraryPK r sep formED lt bolus_lcpt_VVmkm 3 PK model using a differential equation form with the library of models In this illustration th user creates a on respons model using the model function implemented in the pharmacokinetic library infusion_lcpt_VVmkm describing a one compartment infusion input with Mickaelis Menten elimination after a single dose administration sd The dose is specified as an argument of the PK function in the file model r not in the initial condition described in a part of the R script file stdin r
31. ression of the information matrix 1 for block diagonal 2 for full 3 342 Graph option This list of objects has been modified in the version PFIM 3 2 It allows to draw a graph with the evaluated design evaluation step or the optimised design optimisation step Compared to the version 3 0 of PFIM the object names data has to be replaced by the two followings objects names datax character vector for the names of X axis for each graph that corresponds to each type of measurement the length of this vector must be equal to the number of responses names datay character vector for the names of Y axis for each graph that corresponds to each type of measurement the length of this vector must be equal to the number of responses 25 3 4 Objects required only for IOV option The following list of objects is associated to the specification of the inter occasion variability in the model n_occ integer indicating the number of occasions Example n_occ 2 gamma vector of the p variances of the random effects for inter occasion variability 3 5 Objects required only for covariate option This list of objects allows to specify the inclusion of covariate effects on some parameters of the model In the stdin r it appears just before the object required for the optimisation The user can now include in the model covariates that do not change with occasion and or covariates that change with
32. rmacodynamic models are written with an analytical form in the file LibraryPD_PKPDdesign r and thus they can be associated to pharmacokinetic models with first order linear elimination Table 1 implemented in the file libraryPK r which are also written with analytical forms In these PD functions the expression of the PK model is given as an argument In this case the user has to fill in the stdin r using analytical form options and to specify the paths of the library files in model r source paste directory program dirsep LibraryPK r sep source paste directory program dirsep LibraryPD_PKPDdesign r sep However for the three other cases the PK response and the PD response are written either with different forms or both with a differential equation system Case 4 That is why the user has to call a specific function in order to create a system of differential equations describing the corresponding PK PD model This function named Create formED is implemented in the file CreateModel PKPDdesign r and has to be used in the model file as follows source paste directory program dirsep CreateModel PKPDdesign r sep create _formED fun_pk fun _ pd dose NA tau NA TInf NA where fun pk and fun pd the names of the PK and PD models respectively dose value of the dose only for a PK model with infusion or oral input by default NA tau dosing interval to specify only for multiple
33. rnover response pharmacodynamic models linked to a pharmacokinetic model included in the library Types Models with impact on the of response Input Output Emax turn_input_Emax Rin kout Emax C50 turn_output_Emax Rin kout Emax C50 Sigmoid Emax turn_input_gammaEmax Rin kout Emax C50 gamma turn_output_gammaEmax Rin kout Emax C50 gamma Imax turn_input_Imax Rin kout Imax C50 turn_output_Imax Rin kout Imax C50 Sigmoid Imax turn_input_gammalmax Rin kout Imax C50 gamma turn_output_gammalmax Rin kout Imax C50 gamma Full Imax turn_input_Imaxfull Rin kout C50 turn_output_Imaxfull Rin kout C50 a ala Turr turn_input_gammaImaxfull Rin kout C50 gamma turn_output_gammaImaxfull Rin kout C50 gamma 2 Full Imax means Imax is fixed equal to 1 15 1 2 Full expression of the Fisher information matrix The population Fisher information matrix M amp for multiple response models for an individual with an elementary design E for the vector of population parameters W is given as M gal A E V C E V MS O CT E V B E V with E and V the approximated marginal expectation and the variance of the observations of the individual The vector of population parameter Y is defined by V u with u the p vector of the fixed effects and the vector of the variance terms Mp is given as a block matrix more details are given in 1 with E ACE V mi 2 v mo v ay V with
34. st order lst order ka V k md N tau ss tau sd orall_lcpt_kaVCl lst order lst order ka V Cl md N tau ss tau sd bolus_2cpt_Vkk12k21 IV bolus lst order V k k12 k21 md N tau ss tau sd bolus_2cpt_C1V10V2 IV bolus lst order Cl Vi O V2 md N tau ss tau sd TInf infusion_2cpt_Vkk12k21 IV infusion lst order Veky 125 K21 md TInf N tau SS TInf tau sd TInf infusion _2cpt_Cl1V10V2 IV infusion 2 lst order Cl Vl O V2 md TInf N tau SS TInf tau sd oral1l_2cpt_kaVkk12k21 lst order 2 lst order ka V k k12 k21 md N tau ss tau sd orall_2cpt_kaClv1ov2 lst order 2 lst order ka Cl Vl O V2 md N tau ss tau sd bolus_3cpt_Vkk12k21k13k31 IV bolus 3 lst order V k k12 k21 k13 k31 md N tau ss tau sd bolus_3cpt_C1V101V202V3 IV bolus 3 lst order Cl Vi Oly V2 02 V3 md N tau ss tau sd Tine infusion_3cpt_Vkk12k21k13k31 IV infusion 3 lst order V k k12 k21 k13 k31 md TInf N tau ss TInf tau sd TINE infusion _3cpt_C1V101V202V3 IV infusion 3 lst order C1 V1 Q1 V2 02 V3 md TInf N tau ss TInf tau sd orall_3cpt_kaVkk12k21k13k31 lst order 3 lst order ka V k k12 k21 k13 k31 md N tau ss tau sd orall_3cpt_kaC1V101V202V3 lst order 3 lst order ka Cl V1 Ol V2 02 V3 md N tau ss tau 1 1 1 2 wPharmacokinetic models with a Mickaelis Menten elimination One two and three compartment models are implemented for the thr types of input For bolus
35. the case where the same elementary designs are used at each occasion The user can include inter occasion variability in the model as well as covariates 1 5 Discrete covariate specification The present expression of the Fisher information matrix accommodates models with parameters quantifying the influence of discrete covariates Two or more categories can be included In PFIM 3 2 it can be assumed either that covariates are additive on parameter if the random effect model is additive or that covariates are additive on log parameters if the random effect model is exponential For instance the individual parameter 0 is described as the function of a discrete covariate Ci which takes K values defining K categories with additive effect model 0 h gt Pilo b k 2 where here k 1 is defined as the reference group and B 0 17 For each covariate the user has to specify B the vector of covariate ffect coefficients and the proportions of subjects associated to the K categories However it can be specified if covariates change or not through the different occasions In the latter case additional objects are needed the vector of sequences of values of each covariate at each occasion and the vector of proportions of the elementary designs corresponding to each sequence of covariate values The expected Fisher information matrix is computed for each covariate The number of covariates the number of parameters associ
36. thought it comes from one giant subject 16 Voesign optimisation for models with no random effect can be executed only with the Simplex algorithm and no optimisation of the number of subjects is possible 1 4 Inter occasion variability IOV specification The expression of the population Fisher information matrix has been extended for model including additional random effects for inter occasion variability or within subject variability The individual parameters of an individual i at occasion h are thus expressed by the following relation which can be additive as 0 4 b K or exponential as 9 exp 0 K where u is the p vector of fixed effects b the vector of random effects associated to the individual i and K the vector of random effects associated to the individual i for occasion h h 1 H with H the number of occasions b and K are independent It is assumed thatb N 0 Q and k N 0 T with Q and T defined as diagonal matrices of size p x p Each element O of Q and Y of I represent the inter individual variability of the J component of b and the inter occasion variability of the qe component of K respectively The size of the block C and the block B of the expression of the Fisher information matrix are thus modified to incorporate the elements of rF his new development was performed for any number of occasions H It is implemented in PFIM 3 2 for
37. tive PFIM 3 2 is also developed for R 2 4 1 and higher versions 1 1 Model specification Models can be specified either with their analytical form or with systems of differential equations using the libraries of models or the user defined model option In the later case users can define their own model analytically or use a system of differential equations This option has not been modified in PFIM 3 2 only the libraries of models have been completed Compared to PFIM 3 0 three compartment models with linear elimination and models with Mickaelis Menten limination one two and three compartment models have been added to the library of PK models Moreover a library of PD models is now available supporting immediate response models alone or linked to a pharmacokinetic model and the turnover response models linked to pharmacokinetic model These libraries have been derived from the PKPD library developed by Bertrand and Mentr 5 for the MONOLIX software and all analytical expressions are in that document Presently there is no model with lag time in both libraries As in PFIM 3 0 to use the library of models the user has to specify the path of the file in the modelfile named by default model r 1 1 1 Library of pharmacokinetic models Two types of PK models can now be used in PFIM 3 2 PK models with a first order linear elimination or PK models with a Mickaelis Menten elimination
38. u Choose Install package s from CRAN to install from the web you will see a list of all available packages pop up choose odesolve nlme combinat and numDeriv To install PFIM 3 2 the user has to download the package named PFIM 3 2 available on the webpage www pfim biostat fr 2 2 Components The PFIM 3 2 package includes two main folders called PPIM 3 2 Examples The folder PFIM 3 2 is composed of 3 principal files and one folder The 3 principal files are o The main function program file PFIM3 2 r o The input file Stdin r o The model file model r The folder is called Program and contains 10 files of functions o Pfim3 2op1 r To compute the block diagonal Fisher Information matrix option 1 to evaluate a population design using an analytical form to describe the model o PfimOPT3 2op1 r To compute the block diagonal Fisher Information matrix option 1 to optimise a population design using an analytical form to describe the model o EQPfim3 2opl r To compute the block diagonal Fisher Information matrix option 1 to evaluate a population design using a differential equation system to describe the model o EQPfimOPT3 20pl r To compute the block diagonal Fisher Information matrix option 1 to optimise a population design using a differential equation system to describe the model o Pfim3 20p2 r To compute the full Fisher Information matrix option 2 to evaluate a population
39. us_2cpt_Vk12k21Vmkm IV bolus 2 Mickaelis Mente My a viy sd bolus_2cpt_V10V2Vmkm IV bolus 2 Mickaelis Mente Via a vie sd _ d a MM TIn f infusion_2cpt_Vk12k21Vmkm IV infusion 2 Mickaelis Mente Ve boe Rel Vm ce Km md doseMM TInf tau a a MM TInf infusion_2cpt_ V10V2Vmkm IV infusion 2 Mickaelis Mente viy K Fip 2 ai Km md doseMM TInf tau da d MM oral1_2cpt_kaVk12k21Vmkm lst order 2 Mickaelis Mente K r Vi deroga i BaD Vm km md doseMM tau a d MM orall_2cpt_kaV10V2Vmkm lst order 2 Mickaelis Mente kar Mir Or Via p i Vm km md doseMM tau V k12 k21 1 Vk12k21k31k13Vmkm Mi is Ment i bolus_3cpt_ 3 3 IV bolus 3 ickaelis Mente k13 k31 Vm km sd bolus_3cpt_ V101V202V3Vmkm IV bolus 3 Mickaelis Mente Vl Q1 V2 02 sd V3 Vm km da a MM TIn f infusion_3cpt_Vk12k21k13k31Vmkm IV infusion 3 Mickaelis Mente Me klar Beaty e Sa k13 k31 Vm km md doseMM TInf tau a d MM TInf infusion_3cpt_V1Q1V2Q2V3Vmkm IV infusion 3 Mickaelis Mente Vl Ql V2 02 SA V3 Vm km md doseMM TInf tau d d MM orall_3cpt_kak12k21k13k31Vmkm lst order 3 Mickaelis Mente ka Kk12 Kk21 ra k13 k31 Vm km md doseMM tau d d MM orall_3cpt_kaV101V202V3Vmkm lst order 3 Mickaelis Mente Ka Vl Qh V2 i pS Q2 V3 Vm km md doseMM tau 1 1 2 Library of pharmacodynamic models The library of PD models supports immediat respons models alone or linked to a pharmacokinetic model and turnover response models linked to pharmacokinetic models
40. uses after a multiple dose administration the first order oral absorption with one compartment model orall_lcpt_kaVCl with option md from the library the function of th model uses three parameters ka Cl and V and two needed variables N tau the number of doses N and the interval between two doses tau Examples of the use of the library of pharmacokinetic models are presented in section 2 2 of the present document as in section 2 1 of the PFIM 3 0 documentation 1 1 1 1 Pharmacokinetic models with a linear elimination Compared to PFIM 3 0 the library of PK models with linear elimination has been completed by the three compartment models for the three types of input bolus infusion and first order oral absorption and the thr types of administration single dose multiple dose steady state The list of these PK models is given in Table 1 It is an update of the Table 1 presented in the documentation of PFIM 3 0 Table 1 Pharmacokinetic models with first order linear elimination included in the library of models Name Input Cpt Elimination Parameterisation Administration Rai sd bolus_lcpt_Vk IV bolus lst order V k md N tau ss tau sd bolus_lcpt_VCl IV bolus lst order V Cl md N tau ss tau sd TInf infusion_lcpt_Vk IV infusion lst order V k md TInf N tau ss TInf tau sd TInf infusion _lcpt_VCl IV infusion lst order Y Gi md TInf N tau SS TInf tau sd orall_lcpt_kaVk l
41. vector has to be equal to the number of sequences Example covariate occ proportions lt list Treat list 0 5 0 5 list of vectors of parameter s associated with each covariate Each vector is associated to one covariate and is defined by the corresponding parameters on which is added the covariate Example parameter_occ associated lt list Treat c Cl Name of the parameter s has to be identical to those entered in the object parameters 27 beta covariate_occ list of the values of parameters for all other categories than the reference category for which beta 0 Example beta covariate_occ lt list Treat list c log 1 1 3 6 Objects required only for computation of power and number of subjects needed for comparison test or equivalence test To comput th xpected power to detect covariate effects as to compute the number of subjects needed to achieve a given power the previous object covariate model has to be filling in by T Additional R objects are required to be created The following object is needed for both options alpha the value of the type one error for the Wald test Example alpha lt 0 05 It is possible to comput ither th xpected power only or the number of subjects needed for a given power or both of them together compute power logical value if T the expected power for comparison test is computed for each covariate Example compute power lt T compute n
Download Pdf Manuals
Related Search