Quantifying cancer progression with conjunctive Bayesian networks

Motivation: Cancer is an evolutionary process characterized by accumulating mutations. However, the precise timing and the order of genetic alterations that drive tumor progression remain enigmatic. Results: We present a specific probabilistic graphical model for the accumulation of mutations and their interdependencies. The Bayesian network models cancer progression by an explicit unobservable accumulation process in time that is separated from the observable but error-prone detection of mutations. Model parameters are estimated by an Expectation-Maximization algorithm and the underlying interaction graph is obtained by a simulated annealing procedure. Applying this method to cytogenetic data for different cancer types, we find multiple complex oncogenetic pathways deviating substantially from simplified models, such as linear pathways or trees. We further demonstrate how the inferred progression dynamics can be used to improve genetics-based survival predictions which could support diagnostics and prognosis. Availability: The software package ct-cbn is available under a GPL license on the web site cbg.ethz.ch/software/ct-cbn Contact: [email protected]

Quantifying cancer progression with conjunctive Bayesian networks

Motivation: Cancer is an evolutionary process characterized by accumulating mutations. However, the precise timing and the order of genetic alterations that drive tumor progression remain enigmatic

Modeling cumulative biological phenomena with Suppes-Bayes Causal Networks

Several diseases related to cell proliferation are characterized by the accumulation of somatic DNA changes, with respect to wildtype conditions. Cancer and HIV are two common examples of such diseases, where the mutational load in the cancerous/viral population increases over time. In these cases, selective pressures are often observed along with competition, cooperation and parasitism among distinct cellular clones. Recently, we presented a mathematical framework to model these phenomena, based on a combination of Bayesian inference and Suppes' theory of probabilistic causation, depicted in graphical structures dubbed Suppes-Bayes Causal Networks (SBCNs). SBCNs are generative probabilistic graphical models that recapitulate the potential ordering of accumulation of such DNA changes during the progression of the disease. Such models can be inferred from data by exploiting likelihood-based model-selection strategies with regularization. In this paper we discuss the theoretical foundations of our approach and we investigate in depth the influence on the model-selection task of: (i) the poset based on Suppes' theory and (ii) different regularization strategies. Furthermore, we provide an example of application of our framework to HIV genetic data highlighting the valuable insights provided by the inferred

Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena

Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is further complicated by many theoretical issues, such as the I-equivalence among different structures. In this work, we focus on a specific subclass of BNs, named Suppes-Bayes Causal Networks (SBCNs), which include specific structural constraints based on Suppes' probabilistic causation to efficiently model cumulative phenomena. Here we compare the performance, via extensive simulations, of various state-of-the-art search strategies, such as local search techniques and Genetic Algorithms, as well as of distinct regularization methods. The assessment is performed on a large number of simulated datasets from topologies with distinct levels of complexity, various sample size and different rates of errors in the data. Among the main results, we show that the introduction of Suppes' constraints dramatically improve the inference accuracy, by reducing the solution space and providing a temporal ordering on the variables. We also report on trade-offs among different search techniques that can be efficiently employed in distinct experimental settings. This manuscript is an extended version of the paper "Structural Learning of Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018 International Conference on Computational Science

Efficient sampling for Bayesian inference of conjunctive Bayesian networks

Motivation: Cancer development is driven by the accumulation of advantageous mutations and subsequent clonal expansion of cells harbouring these mutations, but the order in which mutations occur remains poorly understood. Advances in genome sequencing and the soon-arriving flood of cancer genome data produced by large cancer sequencing consortia hold the promise to elucidate cancer progression. However, new computational methods are needed to analyse these large datasets. Results: We present a Bayesian inference scheme for Conjunctive Bayesian Networks, a probabilistic graphical model in which mutations accumulate according to partial order constraints and cancer genotypes are observed subject to measurement noise. We develop an efficient MCMC sampling scheme specifically designed to overcome local optima induced by dependency structures. We demonstrate the performance advantage of our sampler over traditional approaches on simulated data and show the advantages of adopting a Bayesian perspective when reanalyzing cancer datasets and comparing our results to previous maximum-likelihood-based approaches. Availability: An R package including the sampler and examples is available at http://www.cbg.ethz.ch/software/bayes-cbn. Contacts: [email protected]

Computational Cancer Biology: An Evolutionary Perspective

ISSN:1553-734XISSN:1553-735

The Temporal Order of Genetic and Pathway Alterations in Tumorigenesis

Cancer evolves through the accumulation of mutations, but the order in which mutations occur is poorly understood. Inference of a temporal ordering on the level of genes is challenging because clinically and histologically identical tumors often have few mutated genes in common. This heterogeneity may at least in part be due to mutations in different genes having similar phenotypic effects by acting in the same functional pathway. We estimate the constraints on the order in which alterations accumulate during cancer progression from cross-sectional mutation data using a probabilistic graphical model termed Hidden Conjunctive Bayesian Network (H-CBN). The possible orders are analyzed on the level of genes and, after mapping genes to functional pathways, also on the pathway level. We find stronger evidence for pathway order constraints than for gene order constraints, indicating that temporal ordering results from selective pressure acting at the pathway level. The accumulation of changes in core pathways differs among cancer types, yet a common feature is that progression appears to begin with mutations in genes that regulate apoptosis pathways and to conclude with mutations in genes involved in invasion pathways. H-CBN models provide a quantitative and intuitive model of tumorigenesis showing that the genetic events can be linked to the phenotypic progression on the level of pathways