Modelling cancer progression using Mutual Hazard Networks

Modeling metastatic progression from cross-sectional cancer genomics data

MOTIVATION

Metastasis formation is a hallmark of cancer lethality. Yet, metastases are generally unobservable during their early stages of dissemination and spread to distant organs. Genomic datasets of matched primary tumors and metastases may offer insights into the underpinnings and the dynamics of metastasis formation.

RESULTS

We present metMHN, a cancer progression model designed to deduce the joint progression of primary tumors and metastases using cross-sectional cancer genomics data. The model elucidates the statistical dependencies among genomic events, the formation of metastasis, and the clinical emergence of both primary tumors and their metastatic counterparts. metMHN enables the chronological reconstruction of mutational sequences and facilitates estimation of the timing of metastatic seeding. In a study of nearly 5000 lung adenocarcinomas, metMHN pinpointed TP53 and EGFR as mediators of metastasis formation. Furthermore, the study revealed that post-seeding adaptation is predominantly influenced by frequent copy number alterations.

AVAILABILITY AND IMPLEMENTATION

All datasets and code are available on GitHub at https://github.com/cbg-ethz/metMHN.

A latent variable model for evaluating mutual exclusivity and co-occurrence between driver mutations in cancer

A key challenge in cancer genomics is understanding the functional relationships and dependencies between combinations of somatic mutations that drive cancer development. Such driver mutations frequently exhibit patterns of mutual exclusivity or co-occurrence across tumors, and many methods have been developed to identify such dependency patterns from bulk DNA sequencing data of a cohort of patients. However, while mutual exclusivity and co-occurrence are described as properties of driver mutations, existing methods do not explicitly disentangle functional, driver mutations from neutral, passenger mutations. In particular, nearly all existing methods evaluate mutual exclusivity or co-occurrence at the gene level, marking a gene as mutated if any mutation - driver or passenger - is present. Since some genes have a large number of passenger mutations, existing methods either restrict their analyses to a small subset of suspected driver genes - limiting their ability to identify novel dependencies - or make spurious inferences of mutual exclusivity and co-occurrence involving genes with many passenger mutations. We introduce DIALECT, an algorithm to identify dependencies between pairs of driver mutations from somatic mutation counts. We derive a latent variable mixture model for drivers and passengers that combines existing probabilistic models of passenger mutation rates with a latent variable describing the unknown status of a mutation as a driver or passenger. We use an expectation maximization (EM) algorithm to estimate the parameters of our model, including the rates of mutually exclusivity and co-occurrence between drivers. We demonstrate that DIALECT more accurately infers mutual exclusivity and co-occurrence between driver mutations compared to existing methods on both simulated mutation data and somatic mutation data from 5 cancer types in The Cancer Genome Atlas (TCGA).

Joint inference of exclusivity patterns and recurrent trajectories from tumor mutation trees

Cancer progression is an evolutionary process shaped by both deterministic and stochastic forces. Multi-region and single-cell sequencing of tumors enable high-resolution reconstruction of the mutational history of each tumor and highlight the extensive diversity across tumors and patients. Resolving the interactions among mutations and recovering recurrent evolutionary processes may offer greater opportunities for successful therapeutic strategies. To this end, we present a novel probabilistic framework, called TreeMHN, for the joint inference of exclusivity patterns and recurrent trajectories from a cohort of intra-tumor phylogenetic trees. Through simulations, we show that TreeMHN outperforms existing alternatives that can only focus on one aspect of the task. By analyzing datasets of blood, lung, and breast cancers, we find the most likely evolutionary trajectories and mutational patterns, consistent with and enriching our current understanding of tumorigenesis. Moreover, TreeMHN facilitates the prediction of tumor evolution and provides probabilistic measures on the next mutational events given a tumor tree, a prerequisite for evolution-guided treatment strategies.

Low-rank tensor methods for Markov chains with applications to tumor progression models

Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The age of a tumor at diagnosis is typically unknown. Therefore, the quantity of interest is the time-marginal distribution over all possible genotypes of tumors, defined as the transient distribution integrated over an exponentially distributed observation time. It can be obtained as the solution of a large linear system. However, the sheer size of this system renders classical solvers infeasible. We consider Markov chains whose transition rates are separable functions, allowing for an efficient low-rank tensor representation of the linear system's operator. Thus we can reduce the computational complexity from exponential to linear. We derive a convergent iterative method using low-rank formats whose result satisfies the normalization constraint of a distribution. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.

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.

HyperHMM: efficient inference of evolutionary and progressive dynamics on hypercubic transition graphs

MOTIVATION

The evolution of bacterial drug resistance and other features in biology, the progression of cancer and other diseases and a wide range of broader questions can often be viewed as the sequential stochastic acquisition of binary traits (e.g. genetic changes, symptoms or characters). Using potentially noisy or incomplete data to learn the sequences by which such traits are acquired is a problem of general interest. The problem is complicated for large numbers of traits, which may, individually or synergistically, influence the probability of further acquisitions both positively and negatively. Hypercubic inference approaches, based on hidden Markov models on a hypercubic transition network, address these complications, but previous Bayesian instances can consume substantial time for converged results, limiting their practical use.

RESULTS

Here, we introduce HyperHMM, an adapted Baum-Welch (expectation-maximization) algorithm for hypercubic inference with resampling to quantify uncertainty, and show that it allows orders-of-magnitude faster inference while making few practical sacrifices compared to previous hypercubic inference approaches. We show that HyperHMM allows any combination of traits to exert arbitrary positive or negative influence on the acquisition of other traits, relaxing a common limitation of only independent trait influences. We apply this approach to synthetic and biological datasets and discuss its more general application in learning evolutionary and progressive pathways.

AVAILABILITY AND IMPLEMENTATION

Code for inference and visualization, and data for example cases, is freely available at https://github.com/StochasticBiology/hypercube-hmm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

ToMExO: A probabilistic tree-structured model for cancer progression

Identifying the interrelations among cancer driver genes and the patterns in which the driver genes get mutated is critical for understanding cancer. In this paper, we study cross-sectional data from cohorts of tumors to identify the cancer-type (or subtype) specific process in which the cancer driver genes accumulate critical mutations. We model this mutation accumulation process using a tree, where each node includes a driver gene or a set of driver genes. A mutation in each node enables its children to have a chance of mutating. This model simultaneously explains the mutual exclusivity patterns observed in mutations in specific cancer genes (by its nodes) and the temporal order of events (by its edges). We introduce a computationally efficient dynamic programming procedure for calculating the likelihood of our noisy datasets and use it to build our Markov Chain Monte Carlo (MCMC) inference algorithm, ToMExO. Together with a set of engineered MCMC moves, our fast likelihood calculations enable us to work with datasets with hundreds of genes and thousands of tumors, which cannot be dealt with using available cancer progression analysis methods. We demonstrate our method’s performance on several synthetic datasets covering various scenarios for cancer progression dynamics. Then, a comparison against two state-of-the-art methods on a moderate-size biological dataset shows the merits of our algorithm in identifying significant and valid patterns. Finally, we present our analyses of several large biological datasets, including colorectal cancer, glioblastoma, and pancreatic cancer. In all the analyses, we validate the results using a set of method-independent metrics testing the causality and significance of the relations identified by ToMExO or competing methods.

EvAM-Tools: tools for evolutionary accumulation and cancer progression models

SUMMARY

EvAM-Tools is an R package and web application that provides a unified interface to state-of-the-art cancer progression models and, more generally, evolutionary models of event accumulation. The output includes, in addition to the fitted models, the transition (and transition rate) matrices between genotypes and the probabilities of evolutionary paths. Generation of random cancer progression models is also available. Using the GUI in the web application, users can easily construct models (modifying directed acyclic graphs of restrictions, matrices of mutual hazards or specifying genotype composition), generate data from them (with user-specified observational/genotyping error) and analyze the data.

AVAILABILITY AND IMPLEMENTATION

Implemented in R and C; open source code available under the GNU Affero General Public License v3.0 at https://github.com/rdiaz02/EvAM-Tools. Docker images freely available from https://hub.docker.com/u/rdiaz02. Web app freely accessible at https://iib.uam.es/evamtools.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Conditional prediction of consecutive tumor evolution using cancer progression models: What genotype comes next?

Accurate prediction of tumor progression is key for adaptive therapy and precision medicine. Cancer progression models (CPMs) can be used to infer dependencies in mutation accumulation from cross-sectional data and provide predictions of tumor progression paths. However, their performance when predicting complete evolutionary trajectories is limited by violations of assumptions and the size of available data sets. Instead of predicting full tumor progression paths, here we focus on short-term predictions, more relevant for diagnostic and therapeutic purposes. We examine whether five distinct CPMs can be used to answer the question "Given that a genotype with n mutations has been observed, what genotype with n + 1 mutations is next in the path of tumor progression?" or, shortly, "What genotype comes next?". Using simulated data we find that under specific combinations of genotype and fitness landscape characteristics CPMs can provide predictions of short-term evolution that closely match the true probabilities, and that some genotype characteristics can be much more relevant than global features. Application of these methods to 25 cancer data sets shows that their use is hampered by a lack of information needed to make principled decisions about method choice. Fruitful use of these methods for short-term predictions requires adapting method's use to local genotype characteristics and obtaining reliable indicators of performance; it will also be necessary to clarify the interpretation of the method's results when key assumptions do not hold.

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.