Stratified Breast Cancer Follow-Up Using a Partially Observable MDP

Abstract

Frequency and duration of follow-up for patients with breast cancer is still under discussion. Current 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 (LRR) or second primary tumor. Aim of this study is to gain insight in how to allocate resources for optimal and personal follow-up. We formulate a discrete-time Partially Observable Markov Decision Process (POMDP) with a finite horizon in which we aim to maximize the total expected number of quality-adjusted life years (QALYs). Transition probabilities were obtained from data from the Netherlands Cancer Registry (NCR). Twice a year the decision is made whether or not a mammography will be performed. Recurrent disease can be detected by both mammography or women themselves (self-detection). The optimal policies were determined for three risk categories based on differentiation of the primary tumor. Our results suggest a slightly more intensive follow-up for patients with a high risk and poorly differentiated tumor, and a less intensive schedule for the other risk groups.

Appendix: Notation

General	This chapter	Description
S	S	State space
s	s t	State at time t
r	r t (s, a, o)	Reward at time t in state s with action a and observation o
A	A′ t	Set of actions at time t
a	a t	Action at time t
P	P t (a, o)	Transition probability at time t given action a
		and observation o
V t ∗(s)	V t ∗(π), V t ∗(b)	Optimal value function from time t onwards given
		information state π or belief state b