Misleading models in mathematical oncology

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I have an awkward relationship with mathematical oncology, mostly because oncology has an awkward relationship with math. Although I was vaguely familiar that evolutionary game theory (EGT) could be used in cancer research, mostly through Axelrod et al. (2006), I never planned to work on cancer. I wasn’t eager to enter the field because I couldn’t see how heuristic models could be of use in medicine; I thought only insilications could be useful, but EGT was not at a level of sophistication where it could build predictive models. I worried that selling non-predictive models as advice for treatment would only cause harm. However, the internet being the place it is, I ended up running into David Basanta — one of the major advocates of EGT in oncology — and Jacob Scott on twitter. After looking through some of the literature, I realized that most of experimental cancer research was more piecemeal than I expected and theory was based mostly on ad-hoc mental models. This convinced me that there is room for clear mathematical (and maybe computational) reasoning to help formalize and explore these mental models. Now we have a paper applying the Ohtsuki-Nowak transform to studying edge effects in the go-grow game prepped (Kaznatcheev, Scott, & Basanta, 2013), and David and I have a project on chronic myeloid leukemia in the works. The first is a heuristic model building on top of previously developed tools (from my experience, it is rather uncommon to build directly on others’ work in evolutionary game theory and mathematical oncology) and the other an abductive model using a combination of analytic and machine learning techniques to produce a predictive tool useful in the clinic.
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