[Paper Review] A picture guide to cancer progression and monotonic accumulation models: evolutionary assumptions, plausible interpretations, and alternative uses

Ramón Díaz‐Uriarte, Johnston, Iain G.|arXiv (Cornell University)|Dec 11, 2023

Evolution and Genetic Dynamics9 citations

TL;DR

A comprehensive review of monotonic accumulation models for irreversible event accumulation (e.g., cancer mutations), detailing deterministic and stochastic approaches, their assumptions, interpretations, limitations, and potential applications beyond cancer.

ABSTRACT

Cancer progression and monotonic accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in computational oncology and virology but also in widely different problems such as malaria progression. These methods have been applied to predict future states of the system, identify routes of feature acquisition, and improve patient stratification, and they hold promise for evolutionary-based treatments. New methods continue to be developed. But these methods have shortcomings, which are yet to be systematically critiqued, regarding key evolutionary assumptions and interpretations. After an overview of the available methods, we focus on why inferences might not be about the processes we intend. Using fitness landscapes, we highlight difficulties that arise from bulk sequencing and reciprocal sign epistasis, from conflating lines of descent, path of the maximum, and mutational profiles, and from ambiguous use of the idea of exclusivity. We examine how the previous concerns change when bulk sequencing is explicitly considered, and underline opportunities for addressing dependencies due to frequency-dependent selection. This review identifies major standing issues, and should encourage the use of these methods in other areas with a better alignment between entities and model assumptions.

Motivation & Objective

• Explain the scope and purpose of monotonic accumulation models for irreversible event accumulation.
• Review deterministic and stochastic modeling approaches used to infer dependencies among events from cross-sectional data.
• Discuss common assumptions, potential violations, and the impact of sampling and bulk sequencing on inferences.
• Highlight practical uses, evaluation considerations, and opportunities for extending these methods to other domains.

Proposed method

• Survey deterministic dependency models (Oncogenetic trees, OncoBN, Conjunctive Bayesian Networks, H-ESBCN/PMCE) and stochastic dependency models (MHN, HyperTraPS, HyperHMM).
• Summarize input data requirements (binary cross-sectional matrices), output forms (rates, graphs, transition probabilities), and error modeling considerations.
• Compare interpretations of dependencies (AND/OR/XOR, mutual exclusivity) and discuss how different modeling choices affect inferences.
• Discuss software ecosystems and data handling via EvAM-Tools and related repositories.

Figure 1: Cancer progression model with linear dependencies . Left: a linear model of the dependencies in the acquisition of mutations; gaining a mutation in gene B requires having gained a mutation in A; gaining a mutation in gene C requires having gained a mutation in B and, thus, A. The only poss

Experimental results

Research questions

• RQ1 What are the evolutionary assumptions underlying monotonic accumulation models for irreversible event acquisition?
• RQ2 How do deterministic versus stochastic dependency structures differ in representation, interpretation, and inference from cross-sectional data?
• RQ3 Under what sampling and data-processing conditions do these models provide reliable inferences, and how do bulk sequencing and phylogenetic structure affect them?
• RQ4 What are the practical uses of these models beyond cancer genetics, and how can they be extended or adapted to other domains?
• RQ5 What are the main limitations and opportunities for methodological development and evaluation of monotonic accumulation models?

Key findings

• There is a rich set of models with markedly different dependency structures (deterministic vs. stochastic) that can be fitted to the same data for nuanced inference.
• Cross-sectional data are treated as replicate evolutionary experiments under shared constraints, though this assumption may be violated by heterogeneity and lineage effects.
• Bulk sequencing and frequency-dependent selection introduce interpretation challenges but can also offer opportunities to address dependencies.
• These models can be used for predicting future states, identifying different progression routes, patient stratification, and improving survival analyses.
• The review emphasizes gaps in systematic critique of evolutionary assumptions and highlights opportunities to extend methods to single-cell and phylogenetically informed data.
• Software implementations and a unified framework (EvAM-Tools) facilitate practical application and comparison across methods.

Figure 2: Cancer progression and monotonic accumulation models: main steps . (a) Features of relevance are measured on some subjects (e.g., mutations in genes or presence of malaria symptoms). (b) Data are arranged as a binary matrix of samples by features. For cancer data, each row in (b) is a muta