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Biostatistics. 2015 Oct;16(4):713-26. doi: 10.1093/biostatistics/kxv019. Epub 2015 May 14.

Estimating the dynamics and dependencies of accumulating mutations with applications to HIV drug resistance.

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Department of Biosystems Science and Engineering, ETH Zurich, Basel 4058, Switzerland and SIB Swiss Institute of Bioinformatics, Basel 4058, Switzerland.
Division of Infectious Diseases and Hospital Epidemiology, University Hospital Zurich, University of Zurich, Zurich 8091, Switzerland Institute of Medical Virology, University of Zurich, Zurich 8057, Switzerland.
Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland and SIB Swiss Institute of Bioinformatics, Basel, Switzerland


We introduce a new model called the observed time conjunctive Bayesian network (OT-CBN) that describes the accumulation of genetic events (mutations) under partial temporal ordering constraints. Unlike other CBN models, the OT-CBN model uses sampling time points of genotypes in addition to genotypes themselves to estimate model parameters. We developed an expectation-maximization algorithm to obtain approximate maximum likelihood estimates by accounting for this additional information. In a simulation study, we show that the OT-CBN model outperforms the continuous time CBN (CT-CBN) (Beerenwinkel and Sullivant, 2009. Markov models for accumulating mutations. Biometrika 96: (3), 645-661), which does not take into account individual sampling times for parameter estimation. We also show superiority of the OT-CBN model on several datasets of HIV drug resistance mutations extracted from the Swiss HIV Cohort Study database.


Conjunctive Bayesian networks; Expectation–maximization algorithm; Genetic progression; HIV drug resistance; Maximum likelihood estimation

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