New challenges monolixday2011

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

http://www.ddmore.eu/

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


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


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 )


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


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


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


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


Example 1:

1. Select a MONOLIX project

2. estimate the population parameters

3. Simulate a new dataset with the estimated parameters


Example 2:

• Define a workflow

1. Estimate the population parameters2. Estimate the Fisher Information Matrix3. Estimate the log-likelihood4. Display some graphics


function workflow1(project,options)

saem

fisher

loglikelihood

graphics


Example 2:





saem

fisher

loglikelihood

graphics


Example 2:



• Run this workflow

1. with the original data2. with several simulated dataset

• Compare the results



saem

fisher

loglikelihood

graphics


>> options.numberOfReplicates=2;

>> options.graphicList={'spaghetti',’VPC'};

>> options.publish='yes';

>> replicateWF('theophylline',…

'workflow1',options)

Example 2:



• Run this workflow

1. with the original data2. with several simulated dataset

• Compare the results


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.‟‟


“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‟‟.


“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.


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






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






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

Technology

New challenges monolixday2011