Biometrika Advance Access originally published online on June 5, 2009
Biometrika 2009 96(3):645-661; doi:10.1093/biomet/asp023
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Markov models for accumulating mutations
Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland niko.beerenwinkel{at}bsse.ethz.ch
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27607, U.S.A. smsulli2{at}ncsu.edu
Received for publication 1 January 2008. Revision received 1 November 2008.
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous-time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The partial order encodes constraints on the order in which mutations can fixate in the population, shedding light on the mutational pathways underlying the evolutionary process. We study a censored version of the model and derive equations for an EM algorithm to perform maximum likelihood estimation of the model parameters. We also show how to select the maximum likelihood partially ordered set. The model is applied to genetic data from cancer cells and from drug resistant human immunodeficiency viruses, indicating implications for diagnosis and treatment.
Key Words: Bayesian network • Cancer • Genetic progression • HIV • Partially ordered set • Poset
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