MONOLIX DAY

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MONOLIX DAY

• November 16th, 2009
• Maison de la Recherche, Paris

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Schedule

• 9.15 Monolix 3.1 presentation
• Monolix presentation demos, Marc Lavielle
  (INRIA)
• Monolix, an academic project, France Mentre
  (INSERM)
• The regulatory agencies promote innovation,
  Demiana Faltaos (FDA, Washington)
• 10.45 Pause
• 11.00 Monolix in the industry
• A. Vermeulen (Johnson and Johnson, Beerse)
• A. Lemenuel (Roche, Bâle)
• A. Soubret (Novartis, Bâle)
• C. Veyrat-Follet (Sanofi Aventis, Chilly-Mazarin)
• C. Laveille (Exprimo, Mechelen)
• 12.30 Buffet

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The MONOLIX software

• Free software for the analysis of nonlinear mixed
  effects models
• Result of scientific collaborations between
  academics INRIA, INSERM, Universities
  Paris-Descartes, Paris-Sud, Paris-Diderot,
• MONOLIX 2 was developed with the financial
  support of Johnson Johnson Pharmaceutical R
  D.
• Version 3.1 available at
• http//software.monolix.org

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The MONOLIX software project

• Objective develop the next versions of the
  MONOLIX software with a view to raising its level
  of functionalities and responding to major
  requirements of the bio-pharmaceutical industry.
• Actual members

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The MONOLIX Team

• Benoit CHARLES
• Kaelig CHATEL
• Morgan GUERY
• Hector MESA
• Eric BLAUDEZ (February 2010)

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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming, multiplatforms),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Residual error model
Predefined error models
Autocorrelated residual errors
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Residual error model
For example
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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Transit compartment model

not with SAEM ?
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Transit compartment model
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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Some new features in Monolix 3.1

• Technical features (multi-core architecture,
  object-oriented programming),
• Outputs (enhanced tables),
• Residual error models (autocorrelation,
  predefined error models),
• MLXTRAN for PK models (complex administrations,
  transit compartments),
• Complex data designs (IOV, Steady-State),
• Discrete data models (categorical data, count
  data and Hidden Markov models),

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Categorical data models

• Proportional odds model (K categories)
• yij 1, 2, 3, ..., K
• Modeling of probabilities
• P(yij 1) , P(yij 2), ... , P(yij K-1)
• Modeling of cumulative probabilities
• P(yij 1) , P(yij 2), ... , P(yij K-1)
• or
• P(yij 2) , P(yij 3), ... , P(yij K)

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MONOLIX IMPLEMENTATION(ordered categorical data)

• PROBLEM Ordered categorical model
• PSI th1 th2 th3 th4 th5
• REG OCC DOSE
• CATEGORICAL(0,3)
• LOGIT1(Ygt1) -th1 - th4OCC - th5DOSE
• LOGIT1(Ygt2) -th1 - th4OCC - th5DOSE - th2
• LOGIT1(Ygt3) -th1 - th4OCC - th5DOSE - th2 -
  th3
• OUTPUT
• OUTPUT1 LL1

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Results Proportional Odds Model

• Scenario B
• Baseline model
• Data with 4 categories
• Proportions of observation equal to category
  0/1/2/3 at baseline 82.5/10/5/2.5

LAPLACE in NONMEM
SAEM in MONOLIX
?2
?2
?2
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Count data models
yij - observation k - count ?i - inividual
parameter ?exp(hi)
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MONOLIX IMPLEMENTATION(count data)

• PROBLEM Basic Poisson model
• PSI lambda
• COUNT
• LL1(Yk) -lambda klog(lambda) - factln(k)
• OUTPUT
• OUTPUT1 LL1

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Results Count data model

• Models Handling overdispersion/underdispersion
• Generalized Poisson (GP)
• Negative binomial (NB)
• Zero-inflated Poisson (ZIP)

LAPLACE in NONMEM
Relative estimation error ()
SAEM in MONOLIX
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ResultsSAEM in MONOLIXRelative SEs
Categorical data
?1 ?2 ?1 ?2
?1 ?2 ?1 ?2
?1 ?2 ?1 ?2
Absolute estimation error ()
Count data
?1 ?2 ?1 ?2
?1 ?2 ?1 ?2
?1 ?2 ?1 ?2
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Run times NONMEM, SAS SAEM

• Models Handling overdispersion/underdispersion
• Generalized Poisson (GP)
• Negative binomial (NB)
• Zero-inflated Poisson (ZIP)

Run times for NONMEM and SAS kindly generated
and provided by Plan E. and Maloney A.
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Run times NONMEM, SAS SAEM

• Models Handlng overdispersion/underdispersion
• Generalized Poisson (GP)
• Negative binomial (NB)
• Zero-inflated Poisson (ZIP)

Run times for NONMEM and SAS kindly generated
and provided by Plan E. and Maloney A.
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Fitting simultaneously continuous data and
discrete data

• Warfarin PKPD
• 33 IDs, 479 obs
• PD categorized into 3 categories

Category 1 lt 34 PCA Category 2 34-50
PCA Category 3 gt 50 PCA
3
2
1
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MONOLIX IMPLEMENTATIONcontinuous and ordered
categorical data

• PROBLEM oral 1 (1 cpt with lag-time) and ordered
  categorical data
• MODEL
• COMP (Qc)
• COMP (Qe)
• PSI Tlag ka V Cl ke0 th1 th2 th3
• PK
• ALAG1Tlag
• KA1 ka
• kCl/V
• ODE
• DDT_Qc -kQc
• DDT_Qe ke0(Qc-Qe)
• CcQc/V
• CeQe/V

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Output
Estimation of the population parameters
parameter s.e. (s.a.) r.s.e.()
Tlag 0.814 0.28
34 ka 1.6 0.54
34 V 7.95 0.33
4 Cl 0.132 0.0067
5 ke0 0.0179 0.001
6 th1 15.8 1.9
12 th2 4.47
0.48 11 th3 5.36
0.75 14 omega2_Tlag 0.514
0.55 107 omega2_ka 0.962
0.69 71 omega2_V
0.0495 0.014 28 omega2_Cl
0.0796 0.021 26 omega2_ke0
0.0239 0.023 98 omega2_th1
9.65 5.5 57 omega2_th2
0 -
- omega2_th3 0 -
- a_1 0.217 0.035
16 b_1 0.065 0.0078
12 Elapsed time is 284 seconds.
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The Hidden Markov model (HMM)
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
(zi,j) is a random Markov Chain with transition
matrix
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Mixed Hidden Markov Model
- Random effects on the Poisson parameters -
Random effects on the transition matrices
(P(zjkzjm)

• Methodology
• Maximum likelihood estimation of the population
  parameters using SAEM Baum-Welch algorithm
• MAP (Maximum a Posteriori) estimation of the
  hidden states using the Viterbi algorithm

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The Hidden Markov modelSome  individual fits 
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The Hidden Markov modelSome  individual fits 
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