title: Inferring tree causal models of cancer progression with probability raising.
abstract: Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel theoretical framework called CAPRESE (CAncer PRogression Extraction with Single Edges) to reconstruct such models based on the notion of probabilistic causation defined by Suppes. We consider a general reconstruction setting complicated by the presence of noise in the data due to biological variation, as well as experimental or measurement errors. To improve tolerance to noise we define and use a shrinkage-like estimator. We prove the correctness of our algorithm by showing asymptotic convergence to the correct tree under mild constraints on the level of noise. Moreover, on synthetic data, we show that our approach outperforms the state-of-the-art, that it is efficient even with a relatively small number of samples and that its performance quickly converges to its asymptote as the number of samples increases. For real cancer datasets obtained with different technologies, we highlight biologically significant differences in the progressions inferred with respect to other competing techniques and we also show how to validate conjectured biological relations with progression models.
authors.forename: Loes
authors.initials: L
authors.lastname: Olde Loohuis
authors.affiliation: Center for Neurobehavioral Genetics, University of California Los Angeles, Los Angeles, United States of America.
authors.forename: Loes Olde
authors.initials: LO
authors.lastname: Loohuis
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi, Milano-Bicocca, Milano, Italy.
authors.forename: Giulio
authors.initials: G
authors.lastname: Caravagna
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi, Milano-Bicocca, Milano, Italy.
authors.forename: Alex
authors.initials: A
authors.lastname: Graudenzi
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi, Milano-Bicocca, Milano, Italy.
authors.forename: Daniele
authors.initials: D
authors.lastname: Ramazzotti
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi, Milano-Bicocca, Milano, Italy.
authors.forename: Giancarlo
authors.initials: G
authors.lastname: Mauri
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi, Milano-Bicocca, Milano, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Antoniotti
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, United States of America.
authors.forename: Bud
authors.initials: B
authors.lastname: Mishra
mesh_terms: D000465:Algorithms; D018450:Disease Progression; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D008962:Models, Theoretical; D009369:Neoplasms / Q000473:pathology*; D009385:Neoplastic Processes; D010802:Phylogeny; D011336:Probability