Exploring heterogeneity in tumour data using Markov chain Monte Carlo.
We describe a Bayesian approach to incorporate between-individual heterogeneity associated with parameters of complicated biological models. We emphasize the use of the Markov chain Monte Carlo (MCMC) method in this context and demonstrate the implementation and use of MCMC by analysis of simulated overdispersed Poisson counts and by analysis of an experimental data set on preneoplastic liver lesions (their number and sizes) in the presence of heterogeneity. These examples show that MCMC-based estimates, derived from the posterior distribution with uniform priors, may agree well with maximum likelihood estimates (if available). However, with heterogeneous parameters, maximum likelihood estimates can be difficult to obtain, involving many integrations. In this case, the MCMC method offers substantial computational advantages.
Department of Mathematics, Free University of Amsterdam, De Boelelaan 1081 a, 1081 HV Amsterdam, Netherlands. degunst@cs.vu.nl
Mathisca C M
MC
de Gunst
Anup
A
Dewanji
E Georg
EG
Luebeck
D000818:Animals; D001499:Bayes Theorem; D008113:Liver Neoplasms / Q000473:pathology*; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D009602:Nitrosamines; D016012:Poisson Distribution; D011230:Precancerous Conditions; D051381:Rats; D013269:Stochastic Processes
D009602:Nitrosamines; C002741:N-nitrosomorpholine