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- 1. NEW CHALLENGES FOR MONOLIX December 12th, 2011
- 2. I AN OVERVIEW OFPOPIX & DDMORE ACTIVITIES December 12th, 2011
- 3. • The main objective of POPIX is to develop new methods for population modelling in different fields (pharmacology, toxicity, biology, agronomy,…)• Our key application is population PK/PD (pharmacokinetics/pharmacodynamics) modelling• We are partner of the DDMoRe (Drug and Disease Model Resources) project, supported by the Innovative Medicines Initiative (IMI)• Several of the methods we have developed are implemented in the MONOLIX software• LIXOFT and Inria have a research partnership which guarantees close collaboration and rapid technology transfer
- 4. Popix, DDMoRe & INRIA Popix (Inria) Methods & Statisticso Application expertise meets o Common development plaforms statistical expertise o Transfero Expression of needs & open issues o Standards compatibility, DDMoRe – EFPIA interoperability Lixoft Applications Software engineering,Proof of Concepts & Standards training & support o Industrialization 4
- 5. DDMoRe – The Vision Major deliverables5 Standards for describing models, data and designs Modelling Modelling Library Framework Model Shared knowledge System A modular platformDefinition for integrating and interchangeLanguage reusing models; standards Specific shortening timelines by removing disease barriers models Examples from high priority areas
- 6. DDMoRe – The Vision Major deliverables6 Standards for describing models, data and designs Work Package 6 Integration of new software ModellingInria & Astrazeneca) (leaders: Modelling Library Framework Model 1. Shared knowledge Clinical Trial Simulator System A modular platformDefinition for integrating and interchangeLanguage 2. Tools for adaptive optimal design reusing models; standards Specific shortening timelines by removing 3. disease Tools for model diagnostic & barriers selection model models 4. Tools for complex models Examples from high priority areas
- 7. POPIX & DDMoRe activities New methods for PKPD 1. Flexible statistical models, 2. Bayesian estimation, 3. Errors/uncertainty in the design, 4. Hidden Markov Models, 5. Stochastic Differential Equations Clinical Trial Simulator 1. PKPD models: continuous, categorical, count, time-to-event, 2. Recruitment, drop-out, compliance models 3. Integration in a workflow, Beyond classical PKPD 1. Quantitative and Systems Pharmacology, 2. Pharmacogenetics, 3. Aggregation of predictive models 4. Partial Differential Equations models, Imaging
- 8. New methods for PKPD 1. Flexible statistical models, 2. Bayesian estimation, 3. Errors/uncertainty in the design, 4. Hidden Markov Models, 5. Stochastic Differential Equations
- 9. 1. Flexible statistical modelMONOLIX 4 assumptions: Normality of the random effects Homoscedasticity of the random effects model Linearity of the covariate model h(Cl) h(Cl pop) C h is some given transformation: log, logit, probit, power, log(x – c), …Example: log(Cl) log(Cl pop) logW / 70
- 10. 1. Flexible statistical model Extension to more flexible models: h(Cl ) h(Cl pop) f (W , ) g (W , )• Covariate model on the inter-individual variability,• Random effects not necessarily normally distributed (« outliers » better described with a t-distribution),• Covariate model not necessarily linear
- 11. 1. Flexible statistical model Extension to more flexible models: h(Cl ) h(Cl pop) f (W , ) g (W , )• Covariate model on the inter-individual variability,• Random effects not necessarily normally distributed (« outliers » better described with a t-distribution),• Covariate model not necessarily linear Only MCMC based algorithms allow to handle properly such extensions
- 12. 2. Bayesian estimationCurrently available softwares for NLME propose - a full Bayesian approach (a prior is required for all the parameters of the model)or - a full (penalized) Maximum Likelihood approach (no prior can be used for any parameter).
- 13. 2. Bayesian estimationCurrently available softwares for NLME propose - a full Bayesian approach (a prior is required for all the parameters of the model)or - a full (penalized) Maximum Likelihood approach (no prior can be used for any parameter).We propose to combine these two approaches:If some prior information is available for a subset qB of the parametersto estimate but not for a subset qA , then estimate qA by maximizing the likelihood p(y ; qA) estimate the posterior distribution p(qB | y ; qA)
- 14. 3. Errors on the design variables (and/or the covariates)It is usely assumed that • the design is perfectly known: doses, times of measurement,… • the individual covariates are perfectly known A more realistic model should be capable to include errors (or uncertainty) both in the design and in the covariates
- 15. 4. Hidden Markov Models i) encode the model with MLXTRANyi,1 yi,2 yi,3 yi,j-1 yi,j yi,nzi,1 zi,2 zi,3 zi,j-1 zi,j zi,n Pi Pi Pi(zij ) is a random Markov Chain with transition matrix Pi = (plm,i) If zij = m , then yij ~ Fm ( . ; tij , yi )
- 16. 4. Hidden Markov Models ii) implement the methodsIn the context of mixed effects models: - estimate the population parameters using SAEM + Baum Welch - estimate the unknown states using Viterbi
- 17. 4. Hidden Markov Models iii) outputs, graphics, diagnostic plots,…
- 18. 5. Stochastic Differential Equations Models« Classical » ODE based model: k (elimination constant rate) = constant C(t) = D x exp(- k x t)
- 19. 5. Stochastic Differential Equations ModelsSDE based model: k (elimination constant rate) = diffusion process C(t) = D x exp(- ʃk(u)du)
- 20. 5. Stochastic Differential Equations ModelsSDE based model: Estimation of the population parameters: SAEM + EKF
- 21. Clinical Trial Simulator1. PKPD models (continuous, categorical, count, time-to-event)2. Recruitment, drop-out, compliance models3. Integration in a workflow,
- 22. Capabilities of the first prototype of the CTS• First prototype based on MONOLIX and MLXTRAN• Parallel group study design used in Phase 2,• Simulations of Patients sampled from known distributions or populations Covariates sampled using an external datafile Exposure to the investigational drug Several types of drug effects related to drug exposure: Continuous, Time-to-event, Categorical, Count• Evaluations of the different sources of variability within patient variability between patient variability between group variability between trial variability• Automatic reporting
- 23. Example 1: continuous PKPD model 100 100 1001210 Concentration 90 Effect 80 8 70 60 6 50 4 40 2 30 0 20 0 50 100 150 0 50 100 150
- 24. Example 1: continuous PKPD model%% Observations model %% Individual parameters modelModelFile=mlxt:pkpd; ListParameter={ka, V, Cl, Imax, C50, Rin, kout};ModelPath=F:DDMoReWP6WP61CTSlibrary; DefaultDistribution = log-normal; Distribution_Imax = logit-normal;ObservationName={Concentration,PCA}; Covariate={log(wt/70),sex};ObservationUnit={mg/L,%}; CovariateType={continuous,categorical};ModelType={continuous,continuous};Prediction={Cc,E}; pop_ka = 1; omega_ka = 0.6; pop_V = 8; omega_V = 0.2;ResidualErrorModel{1}=combined; residual_a{1}=0.5; pop_Cl = 0.13; omega_Cl = 0.2;residual_b{1}=0.1; pop_Imax = 0.9; omega_Imax = 2;ResidualErrorModel{2}=constant; residual_a{2}=4; pop_C50 = 0.4; omega_C50 = 0.4; pop_Rin = 5; omega_Rin = 0.05;LOQ{1}=0.1; pop_kout = 0.05; omega_kout = 0.05;%% design beta1_V = 1;ArmSize={20 20 40 40}; beta1_Cl = 0.75;DoseTime={0:24:192 0:48:192 0:24:192 0:48:192} ; TimeUnit=h;DoseSize={0.25 0.5 0.5 1}; DosePerKg=yes; DoseUnit=mg/kg; rho_V_Cl = 0.7;ObservationTime{1}=[0.5 , 4:4:48 , 52:24:192 , 192:4:250];ObservationTime{2}=0:24:288; %% covariatesNumberReplicate=200; ExtCovariatePath=F:DDMoReWP6WP61CTSdata; ExtCovariateFile=warfarin_data.txt; ExtCovariateName={wt,sex}; ExtCovariateType={continuous,categorical}; ExtIdName=id; ExtWeightName=wt;
- 25. Saving the simulated data in a file >>WriteCTS(simdata.txt,1) ID TIME AMT Y YTYPE CENS wt sex 1 0 19.22 . . . 76.9 1 1 0 . 89.2 2 0 76.9 1 1 0.5 . 0.911 1 0 76.9 1 1 4 . 3.18 1 0 76.9 1 1 8 . 2.41 1 0 76.9 1 1 12 . 2.52 1 0 76.9 1 1 16 . 2.73 1 0 76.9 1 1 20 . 0.1 1 1 76.9 1 1 24 19.22 . . . 76.9 1 1 24 . 1.51 1 0 76.9 1 1 24 . 47.9 2 0 76.9 1 >>WriteCTS(simdata.txt,1:5) REP ID TIME AMT Y YTYPE CENS wt sex 1 1 0 21.86 . . . 67.6 0 1 1 0 . 98.9 2 0 67.6 0 1 1 0.5 . 0.239 1 0 67.6 0 1 1 4 . 1.16 1 0 67.6 0
- 26. Producing graphics - PK and PD data from a single trial>>StatsCTS(Concentration,1)>>StatsCTS(PCA,1)
- 27. Producing graphics - Between-patient variability (exposure and effect)>>StatsCTS(Cc)>>StatsCTS(E)
- 28. Producing graphics - Between-trial variability (concentration)>>StatsCTS(mean(Cc),mean(Concentration), CI)
- 29. Producing graphics - probability of events (toxicity and efficacy) >>StatsCTS(Cc>10, E<20)
- 30. Producing a report >> PublishCTS(report/Report1_CTS1.tex,display)
- 31. Example 2: PK + time-to-eventKaplan Meier plots (hemorrhaging) >>StatsCTS(Hemorrhaging,1) >>StatsCTS(Hemorrhaging,1:3)
- 32. Example 2: PK + time-to-eventProbability of hemorrhaging : between-patient & between-trial variabilities >>StatsCTS(S) >>StatsCTS(mean(S), Hemorrhaging, CI)
- 33. Integration of the CTS in a workflowExample 1: 1. Select a MONOLIX project 2. estimate the population parameters 3. Simulate a new dataset with the estimated parameters
- 34. Integration of the CTS in a workflowExample 1: Matlab implementation 1. Select a MONOLIX project >>project=theophylline; 2. estimate the population parameters >>saem 3. Simulate a new dataset with the >>simul estimated parameters
- 35. Integration of the CTS in a workflowExample 2:• Define a workflow 1. Estimate the population parameters 2. Estimate the Fisher Information Matrix 3. Estimate the log-likelihood 4. Display some graphics
- 36. Integration of the CTS in a workflowExample 2: Matlab implementation• Define a workflow function workflow1(project,options) 1. Estimate the population parameters saem 2. Estimate the Fisher Information Matrix fisher 3. Estimate the log-likelihood loglikelihood 4. Display some graphics graphics
- 37. Integration of the CTS in a workflowExample 2: Matlab implementation• Define a workflow function workflow1(project,options) 1. Estimate the population parameters saem 2. Estimate the Fisher Information Matrix fisher 3. Estimate the log-likelihood loglikelihood 4. Display some graphics graphics• Run this workflow 1. with the original data 2. with several simulated dataset• Compare the results
- 38. Integration of the CTS in a workflowExample 2: Matlab implementation• Define a workflow function workflow1(project,options) 1. Estimate the population parameters saem 2. Estimate the Fisher Information Matrix fisher 3. Estimate the log-likelihood loglikelihood 4. Display some graphics graphics• Run this workflow >> options.numberOfReplicates=2; 1. with the original data >> options.graphicList={spaghetti,’VPC}; 2. with several simulated dataset >> options.publish=yes; >> replicateWF(theophylline,…• Compare the results workflow1,options)
- 39. Integration of the CTS in a workflowReport generated automatically:
- 40. CTS – Future Developments Inclusion of repeated time-to-event outcomes in order to simulate safety Complex models including combination treatments Multiple output types Additional levels of variability Sampling virtual patients from existing data bases Inclusion of disease progression models Fully comprehensive trial simulations Recruitment model Compliance model Dropout model Simulation of trial duration and cost Trials of adaptive design Simulation of probability of success
- 41. Beyond « classical » PKPD1. Quantitative and Systems Pharmacology,2. Pharmacogenetics,3. Aggregation of predictive models4. Partial Differential Equations models, Imaging
- 42. Quantitative and Systems Pharmacology“QSP is defined as an approach to translational medicine that combinescomputational and experimental methods to elucidate, validate andapply new pharmacological concepts to the development and use of smallmolecule and biologic drugs.”„„The goal of QSP is to understand, in a precise, predictive manner, howdrugs modulate cellular networks in space and time and how they impacthuman pathophysiology.‟‟
- 43. Quantitative and Systems Pharmacology“The distinguishing feature of QSP is its interdisciplinaryapproach to an inherently multi-scale problem. QSP will createunderstanding of disease mechanisms and therapeutic effects that spanbiochemistry and structural studies, cell and animal-based experimentsand clinical studies in human patients. Mathematical modeling andsophisticated computation will be critical in spanning multiplespatial and temporal scales. Models must be grounded in thoroughand careful experimentation performed at many biological scales‟‟.
- 44. Quantitative and Systems Pharmacology“The distinguishing feature of QSP is its interdisciplinaryapproach to an inherently multi-scale problem. QSP will createunderstanding of disease mechanisms and therapeutic effects that spanbiochemistry and structural studies, cell and animal-based experimentsand clinical studies in human patients. Mathematical modeling andsophisticated computation will be critical in spanning multiplespatial and temporal scales. Models must be grounded in thoroughand careful experimentation performed at many biological scales‟‟. Developping new predictive models, based on novel, multi-dimensional and high resolution data will require new statistical methods and new computational tools.
- 45. Quantitative and Systems Pharmacology p19: Patient-specific variation in drug responses and resistance mechanisms “One way in which systems pharmacology will differ from traditional pharmacology is that it will address variability in drug responses between tissues and cells in a single patient as well as between patients.‟‟
- 46. Quantitative and Systems Pharmacology p19: Patient-specific variation in drug responses and resistance mechanisms “One way in which systems pharmacology will differ from traditional pharmacology is that it will address variability in drug responses between tissues and cells in a single patient as well as between patients.‟‟ • POWER studies conducted by TIBOTEC • Viral load data from 578 HIV infected patients
- 47. Quantitative and Systems Pharmacology p19: Patient-specific variation in drug responses and resistance mechanisms “One way in which systems pharmacology will differ from traditional pharmacology is that it will address variability in drug responses between tissues and cells in a single patient as well as between patients.‟‟We have developed and implemented in MONOLIXmixture of models for describing different viral loadprofiles of HIV infected patients under treatment: • responders • no responders • rebounders
- 48. Quantitative and Systems Pharmacology p19: Patient-specific variation in drug responses and resistance mechanisms “One way in which systems pharmacology will differ from traditional pharmacology is that it will address variability in drug responses between tissues and cells in a single patient as well as between patients.‟‟We have developed and implemented in MONOLIXmixture of models for describing different viral loadprofiles of HIV infected patients under treatment: • responders • no responders • rebounders Between-subject model mixtures (BSMM) assume that there exist subpopulations of patients. Within-subject model mixtures (WSMM) assume that there exist subpopulations of cells, of virus,...
- 49. Population PKPD & Pharmacogenetics Pharmacogenetics is the study of genetic variation that gives rise to differing response to drugs Challenge: determine which genetic covariates (among hundreds…) are associated to some PKPD parameters
- 50. Population PKPD & Pharmacogenetics Pharmacogenetics is the study of genetic variation that gives rise to differing response to drugs Challenge: determine which genetic covariates (among hundreds…) are associated to some PKPD parameters variable selection problem in a population context combine shrinkage and selection methods for linear regression, and methods for Non Linear Mixed Effects Models. (see Bertrand et al., PAGE 2011) combine the LARS procedure for the LASSO approach with SAEM for maximum likelihood estimation and variable selection
- 51. Aggregation of predictive models A classical approach reduces to: "one expert, one model, one prediction". Challenge: integrate predictions from • different experts • different models
- 52. Aggregation of predictive models A classical approach reduces to: "one expert, one model, one prediction". Challenge: integrate predictions from • different experts • different models New statistical learning approaches: bagging, boosting, random forests...
- 53. Partial Differential Equations models Nonlinear partial differential equations (PDEs) are widely used for various image processing applications Challenge: use PDEs based models in a population context
- 54. Partial Differential Equations models Nonlinear partial differential equations (PDEs) are widely used for various image processing applications Challenge: use PDEs based models in a population context Extend the methods developed for ODEs based mixed effects models to PDEs based mixed effects models Integrate numerical solvers for PDEs in the methods used for Non Linear Mixed Effects Models

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