1. Alternative statistical modeling of Pharmacokinetics and Pharmacodynamics A collaboration between Aalborg University and Novo Nordisk A/S Claus Dethlefsen Center for Cardiovascular Research

2. 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

3. Four different backgrounds State Space Models Inverse Problems Bayesian Networks Graphical Models PK/PD

4. Learning Bayesian Networks Susanne Bøttcher and Claus Dethlefsen

5. 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

6. 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

7. 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)

8. Software  Hugin: www.hugin.com Prediction in Bayesian networks  R: Free software www.r-project.org Statistical software  Deal: Package for R (documented) on CRAN Learning of parameters and structure. Developed by Claus Dethlefsen and Susanne Bøttcher

9. Why Deal ?  No other software learns Bayesian networks with mixed variables !

10. Hugin GUI.net Hugin API Training Data Prior knowledge Parameter priors Parameter posteriors Network score Posterior network

11. Prediction of Insulin Sensitivity Index using Bayesian Networks Susanne Bøttcher and Claus Dethlefsen

12. 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

13. 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

14. 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

15. 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

16. Prediction

17. Bayesian Network

18. Bayesian network

19. A Bayesian Approach to the Minimal Model Kim E. Andersen and Malene Højbjerre

20. Motivation

21. Glucose Tolerance Test Protocols

22. The Minimal Model of Glucose Disposal

23. What can be done?

24. Alternative Model Specification

25. The Stochastic Minimal Model

26. Results

27. Comparison of MINMOD and Bayes

28. 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, 30:257-262, 2007.