Learning oncogenetic networks by reducing to mixed integer linear programming

Timed hazard networks: Incorporating temporal difference for oncogenetic analysis

Oncogenetic graphical models are crucial for understanding cancer progression by analyzing the accumulation of genetic events. These models are used to identify statistical dependencies and temporal order of genetic events, which helps design targeted therapies. However, existing algorithms do not account for temporal differences between samples in oncogenetic analysis. This paper introduces Timed Hazard Networks (TimedHN), a new statistical model that uses temporal differences to improve accuracy and reliability. TimedHN models the accumulation process as a continuous-time Markov chain and includes an efficient gradient computation algorithm for optimization. Our simulation experiments demonstrate that TimedHN outperforms current state-of-the-art graph reconstruction methods. We also compare TimedHN with existing methods on a luminal breast cancer dataset, highlighting its potential utility. The Matlab implementation and data are available at https://github.com/puar-playground/TimedHN.

An Analysis of Transcriptomic Burden Identifies Biological Progression Roadmaps for Hematological Malignancies and Solid Tumors

Biological paths of tumor progression are difficult to predict without time-series data. Using median shift and abacus transformation in the analysis of RNA sequencing data sets, natural patient stratifications were found based on their transcriptomic burden (TcB). Using gene-behavior analysis, TcB groups were evaluated further to discover biological courses of tumor progression. We found that solid tumors and hematological malignancies (n = 4179) share conserved biological patterns, and biological network complexity decreases at increasing TcB levels. An analysis of gene expression datasets including pediatric leukemia patients revealed TcB patterns with biological directionality and survival implications. A prospective interventional study with PI3K targeted therapy in canine lymphomas proved that directional biological responses are dynamic. To conclude, TcB-enriched biological mechanisms detected the existence of biological trajectories within tumors. Using this prognostic informative novel informatics method, which can be applied to tumor transcriptomes and progressive diseases inspires the design of progression-specific therapeutic approaches.

Inferring tumor progression in large datasets

Identification of mutations of the genes that give cancer a selective advantage is an important step towards research and clinical objectives. As such, there has been a growing interest in developing methods for identification of driver genes and their temporal order within a single patient (intra-tumor) as well as across a cohort of patients (inter-tumor). In this paper, we develop a probabilistic model for tumor progression, in which the driver genes are clustered into several ordered driver pathways. We develop an efficient inference algorithm that exhibits favorable scalability to the number of genes and samples compared to a previously introduced ILP-based method. Adopting a probabilistic approach also allows principled approaches to model selection and uncertainty quantification. Using a large set of experiments on synthetic datasets, we demonstrate our superior performance compared to the ILP-based method. We also analyze two biological datasets of colorectal and glioblastoma cancers. We emphasize that while the ILP-based method puts many seemingly passenger genes in the driver pathways, our algorithm keeps focused on truly driver genes and outputs more accurate models for cancer progression.

Cancer is a disease caused by the accumulation of somatic mutations in the genome. This process is mainly driven by mutations in certain genes that give the harboring cells some selective advantage. The rather few driver genes are usually masked amongst an abundance of so-called passenger mutations. Identification of the driver genes and the temporal order in which the mutations occur is of great importance towards research and clinical objectives. In this paper, we introduce a probabilistic model for cancer progression and devise an efficient inference algorithm to train the model. We show that our method scales favorably to large datasets and provides superior performance compared to an ILP-based counterpart on a wide set of synthetic data simulations. Our Bayesian approach also allows for systematic model selection and confidence quantification procedures in contrast to the previous non-probabilistic progression models. We also study two large datasets on colorectal and glioblastoma cancers and validate our inferred model in comparison to the ILP-based method.

Modelling cancer progression using Mutual Hazard Networks

MOTIVATION

Cancer progresses by accumulating genomic events, such as mutations and copy number alterations, whose chronological order is key to understanding the disease but difficult to observe. Instead, cancer progression models use co-occurrence patterns in cross-sectional data to infer epistatic interactions between events and thereby uncover their most likely order of occurrence. State-of-the-art progression models, however, are limited by mathematical tractability and only allow events to interact in directed acyclic graphs, to promote but not inhibit subsequent events, or to be mutually exclusive in distinct groups that cannot overlap.

RESULTS

Here we propose Mutual Hazard Networks (MHN), a new Machine Learning algorithm to infer cyclic progression models from cross-sectional data. MHN model events by their spontaneous rate of fixation and by multiplicative effects they exert on the rates of successive events. MHN compared favourably to acyclic models in cross-validated model fit on four datasets tested. In application to the glioblastoma dataset from The Cancer Genome Atlas, MHN proposed a novel interaction in line with consecutive biopsies: IDH1 mutations are early events that promote subsequent fixation of TP53 mutations.

AVAILABILITY AND IMPLEMENTATION

Implementation and data are available at https://github.com/RudiSchill/MHN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A probabilistic method for leveraging functional annotations to enhance estimation of the temporal order of pathway mutations during carcinogenesis

BACKGROUND

Cancer arises through accumulation of somatically acquired genetic mutations. An important question is to delineate the temporal order of somatic mutations during carcinogenesis, which contributes to better understanding of cancer biology and facilitates identification of new therapeutic targets. Although a number of statistical and computational methods have been proposed to estimate the temporal order of mutations, they do not account for the differences in the functional impacts of mutations and thus are likely to be obscured by the presence of passenger mutations that do not contribute to cancer progression. In addition, many methods infer the order of mutations at the gene level, which have limited power due to the low mutation rate in most genes.

RESULTS

In this paper, we develop a Probabilistic Approach for estimating the Temporal Order of Pathway mutations by leveraging functional Annotations of mutations (PATOPA). PATOPA infers the order of mutations at the pathway level, wherein it uses a probabilistic method to characterize the likelihood of mutational events from different pathways occurring in a certain order. The functional impact of each mutation is incorporated to weigh more on a mutation that is more integral to tumor development. A maximum likelihood method is used to estimate parameters and infer the probability of one pathway being mutated prior to another. Simulation studies and analysis of whole exome sequencing data from The Cancer Genome Atlas (TCGA) demonstrate that PATOPA is able to accurately estimate the temporal order of pathway mutations and provides new biological insights on carcinogenesis of colorectal and lung cancers.

CONCLUSIONS

PATOPA provides a useful tool to estimate temporal order of mutations at the pathway level while leveraging functional annotations of mutations.

Uncovering the subtype-specific temporal order of cancer pathway dysregulation

Cancer is driven by genetic mutations that dysregulate pathways important for proper cell function. Therefore, discovering these cancer pathways and their dysregulation order is key to understanding and treating cancer. However, the heterogeneity of mutations between different individuals makes this challenging and requires that cancer progression is studied in a subtype-specific way. To address this challenge, we provide a mathematical model, called Subtype-specific Pathway Linear Progression Model (SPM), that simultaneously captures cancer subtypes and pathways and order of dysregulation of the pathways within each subtype. Experiments with synthetic data indicate the robustness of SPM to problem specifics including noise compared to an existing method. Moreover, experimental results on glioblastoma multiforme and colorectal adenocarcinoma show the consistency of SPM's results with the existing knowledge and its superiority to an existing method in certain cases. The implementation of our method is available at https://github.com/Dalton386/SPM.

Every which way? On predicting tumor evolution using cancer progression models

Successful prediction of the likely paths of tumor progression is valuable for diagnostic, prognostic, and treatment purposes. Cancer progression models (CPMs) use cross-sectional samples to identify restrictions in the order of accumulation of driver mutations and thus CPMs encode the paths of tumor progression. Here we analyze the performance of four CPMs to examine whether they can be used to predict the true distribution of paths of tumor progression and to estimate evolutionary unpredictability. Employing simulations we show that if fitness landscapes are single peaked (have a single fitness maximum) there is good agreement between true and predicted distributions of paths of tumor progression when sample sizes are large, but performance is poor with the currently common much smaller sample sizes. Under multi-peaked fitness landscapes (i.e., those with multiple fitness maxima), performance is poor and improves only slightly with sample size. In all cases, detection regime (when tumors are sampled) is a key determinant of performance. Estimates of evolutionary unpredictability from the best performing CPM, among the four examined, tend to overestimate the true unpredictability and the bias is affected by detection regime; CPMs could be useful for estimating upper bounds to the true evolutionary unpredictability. Analysis of twenty-two cancer data sets shows low evolutionary unpredictability for several of the data sets. But most of the predictions of paths of tumor progression are very unreliable, and unreliability increases with the number of features analyzed. Our results indicate that CPMs could be valuable tools for predicting cancer progression but that, currently, obtaining useful predictions of paths of tumor progression from CPMs is dubious, and emphasize the need for methodological work that can account for the probably multi-peaked fitness landscapes in cancer.

Mutational interactions define novel cancer subgroups

Large-scale genomic data highlight the complexity and diversity of the molecular changes that drive cancer progression. Statistical analysis of cancer data from different tissues can guide drug repositioning as well as the design of targeted treatments. Here, we develop an improved Bayesian network model for tumour mutational profiles and apply it to 8198 patient samples across 22 cancer types from TCGA. For each cancer type, we identify the interactions between mutated genes, capturing signatures beyond mere mutational frequencies. When comparing mutation networks, we find genes which interact both within and across cancer types. To detach cancer classification from the tissue type we perform de novo clustering of the pancancer mutational profiles based on the Bayesian network models. We find 22 novel clusters which significantly improve survival prediction beyond clinical information. The models highlight key gene interactions for each cluster potentially allowing genomic stratification for clinical trials and identifying drug targets.

Tumour heterogeneity hinders translation of large-scale genomic data into the clinic. Here the authors develop a method for the stratification of cancer patients based on the molecular gene status, including genetic interactions, rather than clinico-histological data, and apply it to TCGA data for over 8000 cases across 22 cancer types.

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 wild-type conditions. Cancer and HIV are 2 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, co-operation, 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). The 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 article, we discuss the theoretical foundations of our approach and we investigate in depth the influence on the model selection task of (1) the poset based on Suppes’ theory and (2) 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 SBCN

Variable selection for disease progression models: methods for oncogenetic trees and application to cancer and HIV

Background

Disease progression models are important for understanding the critical steps during the development of diseases. The models are imbedded in a statistical framework to deal with random variations due to biology and the sampling process when observing only a finite population. Conditional probabilities are used to describe dependencies between events that characterise the critical steps in the disease process.

Many different model classes have been proposed in the literature, from simple path models to complex Bayesian networks. A popular and easy to understand but yet flexible model class are oncogenetic trees. These have been applied to describe the accumulation of genetic aberrations in cancer and HIV data. However, the number of potentially relevant aberrations is often by far larger than the maximal number of events that can be used for reliably estimating the progression models. Still, there are only a few approaches to variable selection, which have not yet been investigated in detail.

Results

We fill this gap and propose specifically for oncogenetic trees ten variable selection methods, some of these being completely new. We compare them in an extensive simulation study and on real data from cancer and HIV. It turns out that the preselection of events by clique identification algorithms performs best. Here, events are selected if they belong to the largest or the maximum weight subgraph in which all pairs of vertices are connected.

Conclusions

The variable selection method of identifying cliques finds both the important frequent events and those related to disease pathways.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1762-1) contains supplementary material, which is available to authorized users.

The evolution of tumour phylogenetics: principles and practice

Rapid advances in high-throughput sequencing and a growing realization of the importance of evolutionary theory to cancer genomics have led to a proliferation of phylogenetic studies of tumour progression. These studies have yielded not only new insights but also a plethora of experimental approaches, sometimes reaching conflicting or poorly supported conclusions. Here, we consider this body of work in light of the key computational principles underpinning phylogenetic inference, with the goal of providing practical guidance on the design and analysis of scientifically rigorous tumour phylogeny studies. We survey the range of methods and tools available to the researcher, their key applications, and the various unsolved problems, closing with a perspective on the prospects and broader implications of this field.

Classifying the Progression of Ductal Carcinoma from Single-Cell Sampled Data via Integer Linear Programming: A Case Study

Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints.

FISHtrees 3.0: Tumor Phylogenetics Using a Ploidy Probe

Advances in fluorescence in situ hybridization (FISH) make it feasible to detect multiple copy-number changes in hundreds of cells of solid tumors. Studies using FISH, sequencing, and other technologies have revealed substantial intra-tumor heterogeneity. The evolution of subclones in tumors may be modeled by phylogenies. Tumors often harbor aneuploid or polyploid cell populations. Using a FISH probe to estimate changes in ploidy can guide the creation of trees that model changes in ploidy and individual gene copy-number variations. We present FISHtrees 3.0, which implements a ploidy-based tree building method based on mixed integer linear programming (MILP). The ploidy-based modeling in FISHtrees includes a new formulation of the problem of merging trees for changes of a single gene into trees modeling changes in multiple genes and the ploidy. When multiple samples are collected from each patient, varying over time or tumor regions, it is useful to evaluate similarities in tumor progression among the samples. Therefore, we further implemented in FISHtrees 3.0 a new method to build consensus graphs for multiple samples. We validate FISHtrees 3.0 on a simulated data and on FISH data from paired cases of cervical primary and metastatic tumors and on paired breast ductal carcinoma in situ (DCIS) and invasive ductal carcinoma (IDC). Tests on simulated data show improved accuracy of the ploidy-based approach relative to prior ploidyless methods. Tests on real data further demonstrate novel insights these methods offer into tumor progression processes. Trees for DCIS samples are significantly less complex than trees for paired IDC samples. Consensus graphs show substantial divergence among most paired samples from both sets. Low consensus between DCIS and IDC trees may help explain the difficulty in finding biomarkers that predict which DCIS cases are at most risk to progress to IDC. The FISHtrees software is available at ftp://ftp.ncbi.nih.gov/pub/FISHtrees.

Simultaneous inference of cancer pathways and tumor progression from cross-sectional mutation data

Recent cancer sequencing studies provide a wealth of somatic mutation data from a large number of patients. One of the most intriguing and challenging questions arising from this data is to determine whether the temporal order of somatic mutations in a cancer follows any common progression. Since we usually obtain only one sample from a patient, such inferences are commonly made from cross-sectional data from different patients. This analysis is complicated by the extensive variation in the somatic mutations across different patients, variation that is reduced by examining combinations of mutations in various pathways. Thus far, methods to reconstruct tumor progression at the pathway level have restricted attention to known, a priori defined pathways. In this work we show how to simultaneously infer pathways and the temporal order of their mutations from cross-sectional data, leveraging on the exclusivity property of driver mutations within a pathway. We define the pathway linear progression model, and derive a combinatorial formulation for the problem of finding the optimal model from mutation data. We show that with enough samples the optimal solution to this problem uniquely identifies the correct model with high probability even when errors are present in the mutation data. We then formulate the problem as an integer linear program (ILP), which allows the analysis of datasets from recent studies with large numbers of samples. We use our algorithm to analyze somatic mutation data from three cancer studies, including two studies from The Cancer Genome Atlas (TCGA) on large number of samples on colorectal cancer and glioblastoma. The models reconstructed with our method capture most of the current knowledge of the progression of somatic mutations in these cancer types, while also providing new insights on the tumor progression at the pathway level.

Identifying restrictions in the order of accumulation of mutations during tumor progression: effects of passengers, evolutionary models, and sampling

BACKGROUND

Cancer progression is caused by the sequential accumulation of mutations, but not all orders of accumulation are equally likely. When the fixation of some mutations depends on the presence of previous ones, identifying restrictions in the order of accumulation of mutations can lead to the discovery of therapeutic targets and diagnostic markers. The purpose of this study is to conduct a comprehensive comparison of the performance of all available methods to identify these restrictions from cross-sectional data. I used simulated data sets (where the true restrictions are known) but, in contrast to previous work, I embedded restrictions within evolutionary models of tumor progression that included passengers (mutations not responsible for the development of cancer, known to be very common). This allowed me to assess, for the first time, the effects of having to filter out passengers, of sampling schemes (when, how, and how many samples), and of deviations from order restrictions.

RESULTS

Poor choices of method, filtering, and sampling lead to large errors in all performance measures. Having to filter passengers lead to decreased performance, especially because true restrictions were missed. Overall, the best method for identifying order restrictions were Oncogenetic Trees, a fast and easy to use method that, although unable to recover dependencies of mutations on more than one mutation, showed good performance in most scenarios, superior to Conjunctive Bayesian Networks and Progression Networks. Single cell sampling provided no advantage, but sampling in the final stages of the disease vs. sampling at different stages had severe effects. Evolutionary model and deviations from order restrictions had major, and sometimes counterintuitive, interactions with other factors that affected performance.

CONCLUSIONS

This paper provides practical recommendations for using these methods with experimental data. It also identifies key areas of future methodological work and, in particular, it shows that it is both possible and necessary to embed assumptions about order restrictions and the nature of driver status within evolutionary models of cancer progression to evaluate the performance of inferential approaches.

Cancer evolution: mathematical models and computational inference

Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.

Algorithms to model single gene, single chromosome, and whole genome copy number changes jointly in tumor phylogenetics

We present methods to construct phylogenetic models of tumor progression at the cellular level that include copy number changes at the scale of single genes, entire chromosomes, and the whole genome. The methods are designed for data collected by fluorescence in situ hybridization (FISH), an experimental technique especially well suited to characterizing intratumor heterogeneity using counts of probes to genetic regions frequently gained or lost in tumor development. Here, we develop new provably optimal methods for computing an edit distance between the copy number states of two cells given evolution by copy number changes of single probes, all probes on a chromosome, or all probes in the genome. We then apply this theory to develop a practical heuristic algorithm, implemented in publicly available software, for inferring tumor phylogenies on data from potentially hundreds of single cells by this evolutionary model. We demonstrate and validate the methods on simulated data and published FISH data from cervical cancers and breast cancers. Our computational experiments show that the new model and algorithm lead to more parsimonious trees than prior methods for single-tumor phylogenetics and to improved performance on various classification tasks, such as distinguishing primary tumors from metastases obtained from the same patient population.

Cancer is an evolutionary system whose growth and development is attributed to aberrations in well-known genes and to cancer-type specific genomic imbalances. Here, we present methods for reconstructing the evolution of individual tumors based on cell-to-cell variations between copy numbers of targeted regions of the genome. The methods are designed to work with fluorescence in situ hybridization (FISH), a technique that allows one to profile copy number changes in potentially thousands of single cells per study. Our work advances the prior art by developing theory and practical algorithms for building evolutionary trees of single tumors that can model gain or loss of genetic regions at the scale of single genes, whole chromosomes, or the entire genome, all common events in tumor evolution. We apply these methods on simulated and real tumor data to demonstrate substantial improvements in tree-building accuracy and in our ability to accurately classify tumors from their inferred evolutionary models. The newly developed algorithms have been released through our publicly available software, FISHtrees.