The Annals of Applied Probability

Dynamics of cancer recurrence

Jasmine Foo and Kevin Leder

Full-text: Open access

Abstract

Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as initial tumor size, mutation rates and growth kinetics of drug-sensitive and resistance cells. To study this phenomenon we characterize the dynamics of escape from extinction of a subcritical branching process, where the establishment of a clone of escape mutants can lead to total population growth after the initial decline. We derive uniform in-time approximations for the paths of the escape process and its components, in the limit as the initial population size tends to infinity and the mutation rate tends to zero. In addition, two stochastic times important in cancer recurrence will be characterized: (i) the time at which the total population size first begins to rebound (i.e., become supercritical) during treatment, and (ii) the first time at which the resistant cell population begins to dominate the tumor.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 4 (2013), 1437-1468.

Dates
First available in Project Euclid: 21 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1371834034

Digital Object Identifier
doi:10.1214/12-AAP876

Mathematical Reviews number (MathSciNet)
MR3098438

Zentralblatt MATH identifier
1272.92023

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching processes population genetics cancer

Citation

Foo, Jasmine; Leder, Kevin. Dynamics of cancer recurrence. Ann. Appl. Probab. 23 (2013), no. 4, 1437--1468. doi:10.1214/12-AAP876. https://projecteuclid.org/euclid.aoap/1371834034


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