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Markov models for accumulating mutations

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  • N. Beerenwinkel
  • S. Sullivant

Abstract

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. Copyright 2009, Oxford University Press.

Suggested Citation

  • N. Beerenwinkel & S. Sullivant, 2009. "Markov models for accumulating mutations," Biometrika, Biometrika Trust, vol. 96(3), pages 645-661.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:645-661
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    File URL: http://hdl.handle.net/10.1093/biomet/asp023
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    Cited by:

    1. Xiang Ge Luo & Jack Kuipers & Niko Beerenwinkel, 2023. "Joint inference of exclusivity patterns and recurrent trajectories from tumor mutation trees," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    2. Beerenwinkel Niko & Knupfer Patrick & Tresch Achim, 2011. "Learning Monotonic Genotype-Phenotype Maps," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, January.
    3. Sahand Khakabimamaghani & Dujian Ding & Oliver Snow & Martin Ester, 2019. "Uncovering the subtype-specific temporal order of cancer pathway dysregulation," PLOS Computational Biology, Public Library of Science, vol. 15(11), pages 1-19, November.
    4. Moritz Gerstung & Niko Beerenwinkel, 2010. "Waiting Time Models of Cancer Progression," Mathematical Population Studies, Taylor & Francis Journals, vol. 17(3), pages 115-135.

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