A Partially Observable Markov Decision Process for Breast Cancer Screening

University essay from Linköpings universitet/Statistik och maskininlärning

Abstract: In the US, breast cancer is one of the most common forms of cancer and the most lethal. There are many decisions that must be made by the doctor and/or the patient when dealing with a potential breast cancer. Many of these decisions are made under uncertainty, whether it is the uncertainty related to the progression of the patient's health, or that related to the accuracy of the doctor's tests. Each possible action under consideration can have positive effects, such as a surgery successfully removing a tumour, and negative effects: a post-surgery infection for example. The human mind simply cannot take into account all the variables involved and possible outcomes when making these decisions. In this report, a detailed Partially Observable Markov Decision Process (POMDP) for breast cancer screening decisions is presented. It includes 151 states, covering 144 different cancer states, and 2 competing screening methods. The necessary parameters were first set up using relevant medical literature and a patient history simulator. Then the POMDP was solved optimally for an infinite horizon, using the Perseus algorithm. The resulting policy provided several recommendations for breast cancer screening. The results indicated that clinical breast examinations are important for screening younger women. Regarding the decision to operate on a woman with breast cancer, the policy showed that invasive cancers with either a tumour size above 1.5 cm or which are in metastasis, should be surgically removed as soon as possible. However, the policy also recommended that patients who are certain to be healthy should have a breast biopsy. The cause of this error was explored further and the conclusion was reached that a finite horizon may be more appropriate for this application.

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