Stratified breast cancer follow-up using a continuous state partially observable Markov decision process

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Abstract

Frequency and duration of follow-up for breast cancer patients is still under discussion. Currently, in the Netherlands follow-up consists of annual mammography for the first five years after treatment and does not depend on the personal risk of developing a locoregional recurrence or a second primary tumor. The aim of this study is to gain insight in how to allocate resources for optimal and personalized follow-up. We formulate a discrete-time Partially Observable Markov Decision Process (POMDP) over a finite horizon with both discrete and continuous states, in which the size of the tumor is modeled as a continuous state. Transition probabilities are obtained from data of the Netherlands Cancer Registry. We show that the optimal value function of the POMDP is piecewise linear and convex and provide an alternative representation for it. Under some reasonable conditions on the dynamics of the POMDP, the optimal value function can be obtained from the parameters of the underlying probability distributions only. Finally, we present results for a stratification of the patients based on their age to show how this model can be applied in practice.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages22
Publication statusPublished - Apr 2018

Publication series

NameTW-Memoranda
PublisherUniversity of Twente, Department of Applied Mathematics
No.2064
ISSN (Print)1874-4850

Fingerprint

Partially Observable Markov Decision Process
Breast Cancer
Optimal Value Function
Tumor
Mammography
Finite Horizon
Stratification
Transition Probability
Piecewise Linear
Recurrence
Annual
Cancer
Discrete-time
Probability Distribution
Resources
Alternatives
Model

Keywords

  • Decision processes
  • Medical decision making
  • partially observable Markov decision

Cite this

Otten, J. W. M., Timmer, J., & Witteveen, A. (2018). Stratified breast cancer follow-up using a continuous state partially observable Markov decision process. (TW-Memoranda; No. 2064). Enschede: University of Twente, Department of Applied Mathematics.
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Otten, JWM, Timmer, J & Witteveen, A 2018, Stratified breast cancer follow-up using a continuous state partially observable Markov decision process. TW-Memoranda, no. 2064, University of Twente, Department of Applied Mathematics, Enschede.

Stratified breast cancer follow-up using a continuous state partially observable Markov decision process. / Otten, Jan Willem Maarten; Timmer, Judith; Witteveen, Annemieke .

Enschede : University of Twente, Department of Applied Mathematics, 2018. 22 p. (TW-Memoranda; No. 2064).

Research output: Book/ReportReportAcademic

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AB - Frequency and duration of follow-up for breast cancer patients is still under discussion. Currently, in the Netherlands follow-up consists of annual mammography for the first five years after treatment and does not depend on the personal risk of developing a locoregional recurrence or a second primary tumor. The aim of this study is to gain insight in how to allocate resources for optimal and personalized follow-up. We formulate a discrete-time Partially Observable Markov Decision Process (POMDP) over a finite horizon with both discrete and continuous states, in which the size of the tumor is modeled as a continuous state. Transition probabilities are obtained from data of the Netherlands Cancer Registry. We show that the optimal value function of the POMDP is piecewise linear and convex and provide an alternative representation for it. Under some reasonable conditions on the dynamics of the POMDP, the optimal value function can be obtained from the parameters of the underlying probability distributions only. Finally, we present results for a stratification of the patients based on their age to show how this model can be applied in practice.

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Otten JWM, Timmer J, Witteveen A. Stratified breast cancer follow-up using a continuous state partially observable Markov decision process. Enschede: University of Twente, Department of Applied Mathematics, 2018. 22 p. (TW-Memoranda; 2064).