Alternative statistical modeling of Pharmacokinetics and Pharmacodynamics
A collaboration between
Aalborg University
and
Novo Nordisk A/S
Claus DethlefsenCenter for Cardiovascular Research
Participants
4 Post. Doc.’s Kim E. Andersen Claus Dethlefsen Susanne G. Bøttcher Malene Højbjerre
Steering commiteeNovo 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
PK/PD
Learning Bayesian Networks
Susanne Bøttcher and Claus Dethlefsen
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
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 nodesJointly a Conditional Gaussian (CG) distribution
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)
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
Why Deal ?
No other software learns Bayesian networks with mixed variables !
Hugin GUI
.net
Hugin API
TrainingData
Priorknowledge
Parameter priors
Parameter posteriorsNetwork score
Posterior network
Prediction of Insulin Sensitivity Index using
Bayesian NetworksSusanne 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 diabetes
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
Methods
187 subjects without recognised diabetesIVGTT determines insulin sensitivity indexOGTT 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 studyHansen et al used a multiple regression analysis
Log(S.I) ~ BMI + SEX + G0 + I0 + G30 + I30 + G60 + I60 + G105 + I105 + G180 + I180 + G240 + I240
Prediction
Bayesian Network
Bayesian network
A Bayesian Approach to the Minimal Model
Kim E. Andersen and Malene Højbjerre
Motivation
Glucose Tolerance Test Protocols
The Minimal Model of Glucose Disposal
What can be done?
Alternative Model Specification
The Stochastic Minimal Model
Results
Comparison of MINMOD and Bayes
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.