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61
Maximum Likelihood Estimation of Oncogenetic Tree Models
 Biostatistics
, 2004
"... We present a new approach for modelling the dependencies between of genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, geneti ..."
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Cited by 26 (0 self)
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We present a new approach for modelling the dependencies between of genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependencies between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.
Evolution on distributive lattices
 J THEOR BIOL
, 2006
"... We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a realvalued function on that lattice. The risk of escape from intervention ..."
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Cited by 16 (9 self)
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We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a realvalued function on that lattice. The risk of escape from intervention, i.e., the probability that the population develops an escape mutant before extinction, is encoded in the risk polynomial. Tools from algebraic combinatorics are applied to compute the risk polynomial in terms of the fitness landscape. In an application to the development of drug resistance in HIV, we study the risk of viral escape from treatment with the protease inhibitors ritonavir and indinavir.
Conjunctive bayesian networks
 Bernoulli
, 2007
"... Conjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a partial order on a (finite) set of events. CBNs generalize the oncogenetic tree models of Desper et al. (1999) by allowing th ..."
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Cited by 16 (4 self)
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Conjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a partial order on a (finite) set of events. CBNs generalize the oncogenetic tree models of Desper et al. (1999) by allowing the occurrence of an event to depend on more than one predecessor event. The present paper studies the statistical and algebraic properties of CBNs. We determine the maximum likelihood parameters and present a combinatorial solution to the model selection problem. Our method performs well on two datasets where the events are HIV mutations associated with drug resistance. Concluding with a study of the algebraic properties of CBNs, we show that CBNs are toric varieties after a coordinate transformation and that their ideals possess a quadratic Gröbner basis.
S.: Markov models for accumulating mutations
 Biometrika
, 2009
"... 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 whi ..."
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Cited by 14 (5 self)
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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 poset. The model is applied to genetic data from different cancers and from drug resistant HIV samples, indicating implications for diagnosis and treatment. 1.
A MUTAGENETIC TREE HIDDEN MARKOV MODEL FOR LONGITUDINAL CLONAL HIV SEQUENCE DATA
 BIOSTATISTICS ADVANCE ACCESS PUBLISHED MARCH 28, 2006
, 2006
"... RNA viruses provide prominent examples of measurably evolving populations. In HIV infection, the development of drug resistance is of particular interest, because precise predictions of the outcome of this evolutionary process are a prerequisite for the rational design of antiretroviral treatment p ..."
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Cited by 13 (5 self)
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RNA viruses provide prominent examples of measurably evolving populations. In HIV infection, the development of drug resistance is of particular interest, because precise predictions of the outcome of this evolutionary process are a prerequisite for the rational design of antiretroviral treatment protocols. We present a mutagenetic tree hidden Markov model for the analysis of longitudinal clonal sequence data. Using HIV mutation data from clinical trials, we estimate the order and rate of occurrence of seven amino acid changes that are associated with resistance to the reverse transcriptase inhibitor efavirenz.
Moch H: Construction of evolutionary tree models for renal cell carcinoma from comparative genomic hybridization data. Cancer Res
, 2000
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Trap: A tree approach for fingerprinting subclonal tumor composition
 Nucleic Acids Research
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Estimating an oncogenetic tree when false negatives and positives are present
 Math. Biosci
"... Human solid tumors are believed to be caused by a sequence of genetic abnormalities arising in the tumor cells. The understanding of these sequences is extremely important for improving cancer treatment. Models for the occurrence of the abnormalities include linear structure and a recently proposed ..."
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Cited by 5 (0 self)
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Human solid tumors are believed to be caused by a sequence of genetic abnormalities arising in the tumor cells. The understanding of these sequences is extremely important for improving cancer treatment. Models for the occurrence of the abnormalities include linear structure and a recently proposed treebased structure. In this paper we extend the pure oncogenetic tree model by introducing false positive and false negative observations. We state conditions sufficient for the reconstruction of the generating tree. As an example we analyze a comparative genomic hybridization (CGH) dataset and show that addition of the error model significantly improves the ability of the model to describe the data. Key words: cancer genetics, carcinogenesis, error model, preferred sequence, tree 1
R: On the frequency of genome rearrangement events in cancer karyotypes
, 2007
"... Abstract. Chromosomal instability is a hallmark of cancer. The results of this instability can be observed in the karyotypes of many cancerous genomes, which often contain a variety of aberrations. In this study we introduce a new approach for analyzing rearrangement events in carcinogenesis. This a ..."
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Cited by 5 (3 self)
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Abstract. Chromosomal instability is a hallmark of cancer. The results of this instability can be observed in the karyotypes of many cancerous genomes, which often contain a variety of aberrations. In this study we introduce a new approach for analyzing rearrangement events in carcinogenesis. This approach builds on a new effective heuristic for computing a short sequence of rearrangement events that may have led to a given karyotype. We applied this heuristic on over 40,000 karyotypes reported in the scientific literature. Our analysis implies that these karyotypes have evolved predominantly via four principal event types: chromosomes gains and losses, reciprocal translocations, and terminal deletions. We used the frequencies of the reconstructed rearrangement events to measure similarity between karyotypes. Using clustering techniques, we demonstrate that in many cases, rearrangement event frequencies are a meaningful criterion for distinguishing between karyotypes of distinct tumor classes. Further investigations of this kind can provide insight on the scenarios by which particular cancer types have evolved. 1