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.