Alternative statistical modeling of

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Nov 7, 2013 (3 years and 5 months ago)

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Alternative statistical modeling of
P
harmacokinetics and Pharmacodynamics


A collaboration between


Aalborg University

and

Novo Nordisk A/S

Claus Dethlefsen

Center for Cardiovascular Research

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

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 nodes


Jointly 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.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

Why Deal ?




No other software learns Bayesian networks with
mixed variables !

Hugin GUI

.net

Hugin API

Training

Data

Prior

knowledge

Parameter priors

Parameter posteriors

Network score

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
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 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



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.