Alternative statistical modeling of Pharmacokinetics and Pharmacodynamics

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Alternative statistical modeling of
Pharmacokinetics and Pharmacodynamics

• A collaboration between
• Aalborg University
• and
• Novo Nordisk A/S

Claus DethlefsenCenter for Cardiovascular
Research
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Participants

• 4 Post. Doc.s
• Kim E. Andersen
• Claus Dethlefsen
• Susanne G. Bøttcher
• Malene Højbjerre

• Steering commitee
• Novo Nordisk A/S
• Judith L. Jacobsen
• Merete Jørgensen
• Aalborg University
• Søren Lundbye-Christensen
• Susanne Christensen

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Four different backgrounds

• State Space Models
• Inverse Problems
• Bayesian Networks
• Graphical Models

PK/PD
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Learning Bayesian Networks

• Susanne Bøttcher and Claus Dethlefsen

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Bayesian Networks

• A Directed Acyclic Graph (DAG)
• To each node with parents there is attached
  a local conditional probability distribution,
• Lack of edges in corresponds to conditional
  independencies,
• Joint distribution

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Conditional Gaussian Distribution

• Observations of discrete variables multinomial
  distributed
• Continuous variables are Gaussian linear
  regressions on the continuous parents, with
  parameters depending on the configuration of the
  discrete parents. (ANCOVA)
• No continuous parents of discrete nodes
• Jointly a Conditional Gaussian (CG) distribution

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Advantages using Bayesian networks

• Qualitative representation of causal relations
• Compact description of the assumed independence
  relations among the variables
• Prior information is combined with data in the
  learning process
• Observations at all nodes are not needed for
  inference (calculation of distribution of
  unobserved given observed)

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Software

• Hugin www.hugin.comPrediction in Bayesian
  networks
• R Free software www.r-project.orgStatistical
  software
• Deal Package for R (documented) on CRANLearning
  of parameters and structure.Developed by Claus
  Dethlefsen and Susanne Bøttcher

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Why Deal ?

• No other software learns Bayesian networks with
  mixed variables !

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TrainingData
Hugin GUI
DEAL
Parameter priors
.net
Parameter posteriorsNetwork score
Priorknowledge
Hugin API
Posterior network
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Prediction of Insulin Sensitivity Index using
Bayesian Networks

• Susanne Bøttcher and Claus Dethlefsen

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Insulin Sensitivity Index

• Insulin Sensitivity Index ( ) measures the
  fractional increase in glucose clearance rate
  during an IVGTT (Intraveneous Glucose Tolerance
  Test)
• A low is associated with risk of developing
  type 2 diabetes

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Aim

• Estimate insulin sensitivity index based on
  measurements of plasma glucose and serum insulin
  levels during an OGTT (Oral Glucose Tolerance
  Test) in individuals with normal glucose tolerance

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Methods

• 187 subjects without recognised diabetes
• IVGTT determines insulin sensitivity index
• OGTT with measurements of plasma glucose and
  serum insulin levels at time points 0, 30, 60,
  105, 180, 240
• Use 140 subjects as training data and 47 subjects
  as validation data

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Previous study
Hansen et al used a multiple regression
analysis Log(S.I) BMI SEX G0 I0 G30
I30 G60 I60 G105 I105 G180 I180
G240 I240
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Prediction
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Bayesian Network
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Bayesian network
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A Bayesian Approach to the Minimal Model

• Kim E. Andersen and Malene Højbjerre

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Motivation
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Glucose Tolerance Test Protocols
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The Minimal Model of Glucose Disposal
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What can be done?
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Alternative Model Specification
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The Stochastic Minimal Model
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Results
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Comparison of MINMOD and Bayes
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References

• Andersen and Højbjerre. A Population-based
  Bayesian Approach to the Minimal Model of Glucose
  and Insulin Homeostasis, Statistics in Medicine,
  24 2381-2400, 2005.
• Andersen and Højbjerre. A Bayesian Approach to
  Bergman's Minimal Model, in C.M.Bishop B.J.Frey
  (eds), Proceedings of the Ninth International
  Workshop on Artificial Intelligence and
  Statistics, 2003.
• Bøttcher and Dethlefsen. deal A package for
  learning Bayesian networks. Journal of
  Statistical Software, 8(20)1-40, 2003.
• Bøttcher and Dethlefsen. Prediction of the
  insulin sensitivity index using Bayesian
  networks. Technical Report R-2004-14, Aalborg
  University, 2004.
• Hansen, Drivsholm, Urhammer, Palacios, Vølund,
  Borch-Johnsen and Pedersen. The BIGTT test.
  Diabetes Care, 30257-262, 2007.