Bayesian Networks used in PK/PD modelling
Susanne Bøttcher and Claus Dethlefsen
Aalborg University, DenmarkA Bayesian network is a graphical model that encodes the joint probability distribution of stochastic variables, which in our case may be continuous and/or discrete. By specifying the dependency structure through a Directed Acyclic Graph (DAG), the joint probablility distribution factorizes according to this DAG. Here we restrict us to Conditional Gaussian (CG) networks. This is to ensure availability of exact local computation methods. The class of models comprise linear models with a complex dependency structure, for example time series models.
A method for estimating the parameters and learning the dependence structure of networks with mixed variables is presented in Bøttcher (2001). If used on networks with only discrete or continuous variables, it coincides with the methods developed in Heckerman et al. (1995) and Geiger and Heckerman (1994).
We are developing a package, written in R, which provides methods for analysing datasets using Bayesian networks, see Bøttcher and Dethlefsen (2002). In particular the package includes procedures for defining priors, estimating parameters, calculating network score, performing heuristics search as well as simulating datasets with a given dependency structure.
We illustrate the methodology by examples from PK/PD studies of drugs for use in the treatment of Type II diabetes.
Bøttcher (2001), Learning Bayesian Networks with Mixed Variables, Proceedings of the Eighth International Workshop in Artificial Intelligence and Statistics 2001.
Bøttcher and Dethlefsen (2002), A package for Learning Bayesian Networks, ongoing work.
Geiger and Heckerman (1994), Learning Gaussian Networks, Technical Report MSR-TR-94-10, Microsoft Research.
Heckerman, Geiger and Chickering (1995), Learning Bayesian networks: The combination of knowledge and statistical data, Machine Learning.