2. I
AN OVERVIEW OF
POPIX & 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 & Statistics
o Application expertise meets o Common development plaforms
statistical expertise o Transfer
o 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 deliverables
5
Standards for describing models, data and designs
Modelling Modelling
Library Framework
Model Shared knowledge System
A modular platform
Definition for integrating and interchange
Language reusing models; standards
Specific shortening timelines
by removing
disease barriers
models
Examples from
high priority areas
6. DDMoRe – The Vision
Major deliverables
6
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 platform
Definition for integrating and interchange
Language 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 model
MONOLIX 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 estimation
Currently 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 estimation
Currently 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 parameters
to 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 MLXTRAN
yi,1 yi,2 yi,3 yi,j-1 yi,j yi,n
zi,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 methods
In the context of mixed effects models:
- estimate the population parameters using SAEM + Baum Welch
- estimate the unknown states using Viterbi
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
32. Example 2: PK + time-to-event
Probability of hemorrhaging : between-patient & between-trial variabilities
>>StatsCTS('S')
>>StatsCTS('mean(S)', 'Hemorrhaging', 'CI')
33. Integration of the CTS in a workflow
Example 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 workflow
Example 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 workflow
Example 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 workflow
Example 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 workflow
Example 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 workflow
Example 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)
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 » PKPD
1. Quantitative and Systems Pharmacology,
2. Pharmacogenetics,
3. Aggregation of predictive models
4. Partial Differential Equations models, Imaging
42. Quantitative and Systems Pharmacology
“QSP is defined as an approach to translational medicine that combines
computational and experimental methods to elucidate, validate and
apply new pharmacological concepts to the development and use of small
molecule and biologic drugs.”
„„The goal of QSP is to understand, in a precise, predictive manner, how
drugs modulate cellular networks in space and time and how they impact
human pathophysiology.‟‟
43. Quantitative and Systems Pharmacology
“The distinguishing feature of QSP is its interdisciplinary
approach to an inherently multi-scale problem. QSP will create
understanding of disease mechanisms and therapeutic effects that span
biochemistry and structural studies, cell and animal-based experiments
and clinical studies in human patients. Mathematical modeling and
sophisticated computation will be critical in spanning multiple
spatial and temporal scales. Models must be grounded in thorough
and careful experimentation performed at many biological scales‟‟.
44. Quantitative and Systems Pharmacology
“The distinguishing feature of QSP is its interdisciplinary
approach to an inherently multi-scale problem. QSP will create
understanding of disease mechanisms and therapeutic effects that span
biochemistry and structural studies, cell and animal-based experiments
and clinical studies in human patients. Mathematical modeling and
sophisticated computation will be critical in spanning multiple
spatial and temporal scales. Models must be grounded in thorough
and 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 MONOLIX
mixture of models for describing different viral load
profiles 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 MONOLIX
mixture of models for describing different viral load
profiles 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
