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Alternative statistical modeling of
Pharmacokinetics and Pharmacodynamics
A collaboration between
Aalborg University
Novo Nordisk A/S
Claus Dethlefsen
Center for Cardiovascular Research
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
Four different backgrounds
State Space Models
Inverse Problems
Bayesian Networks
Graphical Models
Learning Bayesian Networks
Susanne Bøttcher and Claus Dethlefsen
 A Directed Acyclic Graph (DAG)
 To each node with parents
there is attached a local conditional probability
 Lack of edges in corresponds to conditional
 Joint distribution
Conditional Gaussian Distribution
Observations of discrete variables multinomial
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
Advantages using Bayesian
 Qualitative representation of causal relations
 Compact description of the assumed independence
relations among the variables
 Prior information is combined with data in the learning
 Observations at all nodes are not needed for inference
(calculation of distribution of unobserved given observed)
 Hugin:
Prediction in Bayesian networks
 R: Free software
Statistical software
 Deal: Package for R (documented) on CRAN
Learning of parameters and structure.
Developed by Claus Dethlefsen and Susanne Bøttcher
Why Deal ?
No other software learns Bayesian networks with
mixed variables !
Hugin GUI
Parameter priors
Parameter posteriors
Network score
Hugin API
Posterior network
Prediction of Insulin Sensitivity
Index using Bayesian Networks
Susanne Bøttcher and Claus Dethlefsen
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
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
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
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
Bayesian Network
Bayesian network
A Bayesian Approach to the
Minimal Model
Kim E. Andersen and Malene Højbjerre
Glucose Tolerance Test Protocols
The Minimal Model of Glucose Disposal
What can be done?
Alternative Model Specification
The Stochastic Minimal Model
Comparison of MINMOD and Bayes
 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, 30:257-262, 2007.