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NEW CHALLENGES
FOR MONOLIX
December 12th, 2011
I
AN OVERVIEW OF
POPIX & DDMORE
ACTIVITIES
December 12th, 2011
• 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
Popix, DDMoRe & INRIA
Popix (Inria)
Methods & Statistics
LixoftSoftware engineering,
training & support
DDMoRe – EFPIA
Applications
Proof of Concepts & Standards
4
o Common development plaforms
o Transfer
o Application expertise meets
statistical expertise
o Expression of needs
& open issues
o Standards compatibility,
interoperability
o Industrialization
5
ModellingLibrary
Shared knowledge
ModellingFramework
A modular platform for integrating and
reusing models;shortening timelines
by removing barriers
ModelDefinitionLanguage
Systeminterchangestandards
Specificdisease modelsExamples from
high priority areas
Standards for describing models, data and designs
DDMoRe – The VisionMajor deliverables
6
ModellingLibrary
Shared knowledge
Modelling Framework
A modular platform for integrating and
reusing models;shortening timelines
by removing barriers
ModelDefinitionLanguage
Systeminterchangestandards
Specificdisease modelsExamples from
high priority areas
Standards for describing models, data and designs
Work Package 6Integration of new software
(leaders: Inria & Astrazeneca)
1. Clinical Trial Simulator
2. Tools for adaptive optimal design
3. Tools for model diagnostic & model selection
4. Tools for complex models
DDMoRe – The VisionMajor deliverables
New methods for PKPD1. Flexible statistical models,
2. Bayesian estimation,
3. Errors/uncertainty in the design,
4. Hidden Markov Models,
5. Stochastic Differential Equations
Clinical Trial Simulator1. PKPD models: continuous, categorical, count, time-to-event,
2. Recruitment, drop-out, compliance models
3. Integration in a workflow,
Beyond classical PKPD1. Quantitative and Systems Pharmacology,
2. Pharmacogenetics,
3. Aggregation of predictive models
4. Partial Differential Equations models, Imaging
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
MONOLIX 4 assumptions:
Normality of the random effects
Homoscedasticity of the random effects model
Linearity of the covariate model
h is some given transformation: log, logit, probit, power, log(x – c), …
Example:
1. Flexible statistical model
70/log)log()log( WClCl pop
CClhClh pop)()(
Extension to more flexible models:
• 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
),(),()()( WgWfClhClh pop
1. Flexible statistical model
Extension to more flexible models:
• 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
),(),()()( WgWfClhClh pop
Only MCMC based algorithms allow
to handle properly such extensions
1. Flexible statistical model
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).
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)
2. Bayesian estimation
It is usely assumed that
• the design is perfectly known: doses, times of
measurement,…
• the individual covariates are perfectly known
3. Errors on the design variables
(and/or the covariates)
A more realistic model should be capable to
include errors (or uncertainty) both in the
design and in the covariates
yi,1
zi,1 zi,2 zi,3
yi,2 yi,3
zi,j-1 zi,j
yi,j-1 yi,j
zi,n
yi,n
Pi Pi Pi
(zij ) is a random Markov Chain with transition matrix Pi = (plm,i)
4. Hidden Markov Models
i) encode the model with MLXTRAN
If zij = m , then yij ~ Fm ( . ; tij , yi )
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
4. Hidden Markov Models
iii) outputs, graphics, diagnostic plots,…
« Classical » ODE based model:
k (elimination constant rate) = constant
C(t) = D x exp(- k x t)
5. Stochastic Differential Equations Models
5. Stochastic Differential Equations Models
SDE based model:
k (elimination constant rate) = diffusion process
C(t) = D x exp(- ʃk(u)du)
SDE based model:
Estimation of the population parameters: SAEM + EKF
5. Stochastic Differential Equations Models
Clinical Trial Simulator
1. PKPD models (continuous, categorical, count, time-to-event)
2. Recruitment, drop-out, compliance models
3. Integration in a workflow,
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
Example 1: continuous PKPD model
0 50 100 1500
2
4
6
8
10
12
100
0 50 100 15020
30
40
50
60
70
80
90
100
100
Concentration Effect
%% Observations modelModelFile='mlxt:pkpd';ModelPath='F:\DDMoRe\WP6\WP61\CTS\library';
ObservationName={'Concentration','PCA'};ObservationUnit={'mg/L','%'};ModelType={'continuous','continuous'};Prediction={'Cc','E'};
ResidualErrorModel{1}='combined'; residual_a{1}=0.5; residual_b{1}=0.1; ResidualErrorModel{2}='constant'; residual_a{2}=4;
LOQ{1}=0.1;
%% designArmSize={20 20 40 40};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'; ObservationTime{1}=[0.5 , 4:4:48 , 52:24:192 , 192:4:250];ObservationTime{2}=0:24:288;NumberReplicate=200;
%% Individual parameters modelListParameter={'ka', 'V', 'Cl', 'Imax', 'C50', 'Rin', 'kout'};DefaultDistribution = 'log-normal';Distribution_Imax = 'logit-normal';Covariate={'log(wt/70)','sex'};CovariateType={'continuous','categorical'};
pop_ka = 1; omega_ka = 0.6;pop_V = 8; omega_V = 0.2;pop_Cl = 0.13; omega_Cl = 0.2; pop_Imax = 0.9; omega_Imax = 2;pop_C50 = 0.4; omega_C50 = 0.4;pop_Rin = 5; omega_Rin = 0.05;pop_kout = 0.05; omega_kout = 0.05;
beta1_V = 1;beta1_Cl = 0.75;
rho_V_Cl = 0.7;
%% covariatesExtCovariatePath='F:\DDMoRe\WP6\WP61\CTS\data';ExtCovariateFile='warfarin_data.txt';ExtCovariateName={'wt','sex'};ExtCovariateType={'continuous','categorical'};ExtIdName='id';ExtWeightName='wt';
Example 1: continuous PKPD model
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
Producing graphics
- PK and PD data from a single trial
>>StatsCTS('Concentration',1)
>>StatsCTS('PCA',1)
>>StatsCTS('Cc')
>>StatsCTS('E')
Producing graphics
- Between-patient variability (exposure and effect)
>>StatsCTS('mean(Cc)','mean(Concentration)', 'CI')
Producing graphics
- Between-trial variability (concentration)
>>StatsCTS('Cc>10', 'E<20')
Producing graphics
- probability of events (toxicity and efficacy)
Producing a report
>> PublishCTS('report/Report1_CTS1.tex','display')
>>StatsCTS('Hemorrhaging',1:3)
>>StatsCTS('Hemorrhaging',1)
Example 2: PK + time-to-event
Kaplan Meier plots (hemorrhaging)
>>StatsCTS('mean(S)', 'Hemorrhaging', 'CI')
>>StatsCTS('S')
Example 2: PK + time-to-event
Probability of hemorrhaging : between-patient & between-trial variabilities
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
Matlab implementation
>>project='theophylline';
>>saem
>>simul
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
Integration of the CTS in a workflow
Example 2:
• Define a workflow
1. Estimate the population parameters2. Estimate the Fisher Information Matrix3. Estimate the log-likelihood4. Display some graphics
Matlab implementation
function workflow1(project,options)
saem
fisher
loglikelihood
graphics
Integration of the CTS in a workflow
Example 2:
• Define a workflow
1. Estimate the population parameters2. Estimate the Fisher Information Matrix3. Estimate the log-likelihood4. Display some graphics
Matlab implementation
function workflow1(project,options)
saem
fisher
loglikelihood
graphics
Integration of the CTS in a workflow
Example 2:
• Define a workflow
1. Estimate the population parameters2. Estimate the Fisher Information Matrix3. Estimate the log-likelihood4. Display some graphics
• Run this workflow
1. with the original data2. with several simulated dataset
• Compare the results
Matlab implementation
function workflow1(project,options)
saem
fisher
loglikelihood
graphics
Integration of the CTS in a workflow
>> options.numberOfReplicates=2;
>> options.graphicList={'spaghetti',’VPC'};
>> options.publish='yes';
>> replicateWF('theophylline',…
'workflow1',options)
Example 2:
• Define a workflow
1. Estimate the population parameters2. Estimate the Fisher Information Matrix3. Estimate the log-likelihood4. Display some graphics
• Run this workflow
1. with the original data2. with several simulated dataset
• Compare the results
Integration of the CTS in a workflow
Report generated automatically:
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
Beyond « classical » PKPD
1. Quantitative and Systems Pharmacology,
2. Pharmacogenetics,
3. Aggregation of predictive models
4. Partial Differential Equations models, Imaging
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.‟‟
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‟‟.
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.
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.‟‟
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
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
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,...
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
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
Aggregation of predictive models
A classical approach reduces to:
"one expert, one model, one prediction".
Challenge: integrate predictions from
• different experts
• different models
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...
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
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