Waiting time models of cancer progression

TL;DR

This paper develops mathematical models to understand the timing and sequence of genetic mutations in cancer progression, comparing different models including Bayesian networks and population genetics, to better predict tumor evolution.

Contribution

It introduces conjunctive Bayesian network models for mutation accumulation and derives analytical expressions for waiting times, advancing the mathematical understanding of cancer progression.

Findings

Exact waiting time formulas for linear and independent mutation orders.

Comparison of Bayesian network models with population genetics models.

Approximate analytical expression for waiting times in a mutation-selection model.

Abstract

Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is associated with the occurrence of genetic alterations and their fixation in the population. We describe the accumulation of mutations using conjunctive Bayesian networks, an exponential family of waiting time models in which the occurrence of mutations is constrained to a partial temporal order. Two opposing limit cases arise if mutations either follow a linear order or occur independently. We derive exact analytical expressions for the waiting time until a specific number of mutations have accumulated in these limit cases as well as for the general conjunctive Bayesian network. Finally, we analyze a stochastic population genetics model that explicitly accounts for mutation and selection. In this model, waves of clonal expansions sweep through the population at equidistant intervals. We present an approximate analytical expression for the waiting time in this model and compare it to the results obtained for the conjunctive Bayesian networks.