# Cancer recurrence times from a branching process model

## TL;DR

This paper models cancer metastasis formation using a branching process, showing that early surgical resection is crucial to prevent recurrence and that delays significantly increase recurrence risk.

## Contribution

It introduces a simple, parameterized model of metastasis formation that links primary tumor size, metastasis initiation, and recurrence timing across multiple cancer types.

## Key findings

- Early resections can prevent recurrence in some cases.
- Small delays in surgery increase recurrence probability.
- Model predictions align with clinical literature data.

## Abstract

As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where metastatic lesions are initiated at a rate which depends on the size of the primary tumor. The evolution of each metastasis is described as an independent branching process. We assume that the primary tumor is resected at a given size and study the earliest time at which any metastasis reaches a minimal detectable size. The parameters of our model are estimated independently for breast, colorectal, headneck, lung and prostate cancers. We use these estimates to compare predictions from our model with values reported in clinical literature. For some cancer types, we find a remarkably wide range of resection sizes such that metastases are very likely to be present, but none of them are detectable. Our model predicts that only very early resections can prevent recurrence, and that small delays in the time of surgery can significantly increase the recurrence probability.