The age incidence of any cancer can be explained by a one-mutation model

TL;DR

This paper introduces a one-mutation model for cancer where the mutation rate increases over time, demonstrating that the probability of developing cancer by a certain age relates directly to the integral of this mutation rate.

Contribution

It presents a novel one-mutation model with a time-dependent mutation rate, linking cancer incidence to a non-homogeneous Poisson process.

Findings

Cancer incidence can be modeled by a non-homogeneous Poisson process.

The probability of cancer up to age t is proportional to the integral of the mutation rate.

The model explains age-related cancer incidence patterns.

Abstract

We propose a one mutation model for cancer with a mutation rate that increases with time. Under rather general hypotheses the number of mutations is necessarily a (non homogeneous) Poisson process with the prescribed mutation rate. We show that the cumulative probability of cancer up to time $t$ is, up to a multiplicative constant, an antiderivative of the mutation rate.