Markov models for accumulating mutations

TL;DR

This paper presents a continuous-time Markov model for the sequential accumulation of genetic mutations, providing a framework to understand mutational pathways and estimate model parameters from genetic data.

Contribution

It introduces a novel waiting time model based on conjunctive Bayesian networks with partial orders, and develops an EM algorithm for parameter estimation and model selection.

Findings

Applied to cancer and HIV data, revealing mutational pathways.

Demonstrated the model's utility in diagnosis and treatment implications.

Provided equations for maximum likelihood estimation.

Abstract

We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The partial order encodes constraints on the order in which mutations can fixate in the population, shedding light on the mutational pathways underlying the evolutionary process. We study a censored version of the model and derive equations for an EM algorithm to perform maximum likelihood estimation of the model parameters. We also show how to select the maximum likelihood poset. The model is applied to genetic data from different cancers and from drug resistant HIV samples, indicating implications for diagnosis and treatment.