Péter Bayer & Jeffrey West

Read the paperOpen-access preprint

In addition to response curvature, there is another way to think about ecological antifragility. In a paper published by Taleb in 2018, he describes antifragility in terms of threshold effects (see Figure 2) [3]. If some desired threshold is required, then only the right-tail of outcomes exceed the threshold. In fact, if the distribution variance is so low, none of the outcomes will exceed the threshold. In all cases, the mean is identical, indicating the utility of considering

This applies straightforwardly to cancer care. For example, there is a desired threshold of tumor eradication, below which we achieve cure. It may be beneficial to widen the distribution of outcomes in order to increase the number of patients who exceed this threshold effect. Of course, this may come at the risk of also maximizing likelihood of the worst-of-the-worst poor outcomes, too, so one must take care.

Back to game theory: we hypothesized that threshold effects may come into play in game theory, where a certain threshold of dosing may lead to a qualitatively change in game class. In contrast to ecological antifragility, evolutionary antifragility explicitly considers competition between heterogeneous subtypes within a tumor. This evolutionary antifragility quantifies the effect of cell-cell interactions on second-order effects of dosing.

Next, we consider the effect of treatment on the competitive dynamics between the two types. In general, games are understudied in cancer, and typically only measured quantifiably at sparse dose values. While the direct relationship between dose and game space is unknown, we made a parsimonious assumption that treatment represents a linear projection in game space (see Figure 2A, below). This assumption not without basis, as one previous study (reproduced in Figure 2B) appears to show a linear relationship between dose and game space (see Figure 7B in the Farrokhian preprint [4]) under etoposide dosing (now published in Science Advances [5]).

- Adaptive therapy trials were designed to capitalize on a cost of resistance by treating less often, in order to maintain a stable population of treatment-sensitive cells
- Evolutionary game theory is commonly used to define the nature of resistance cost and/or cell-cell interactions in cancer
- Adaptive therapy minimizes both the cumulative dose (a first-order effect) and increases the dose variance (a second-order effect)
- Therefore, it's important to study second-order effects using evolutionary game theory models

In the future, we will be taking deeper dive into "interventional antifragility" -- the idea that some adaptive treatment algorithms may be inherently more or less robust (indeed, antifragile) to perturbations in treatment regimen plans. This work will be undertaken as part of the Applied Antifragile Working Group. If you're interested in joining the working group, please contact me.

- Bayer, P., West, J. Games and the Treatment Convexity of Cancer. Dyn Games Appl (2023). https://doi.org/10.1007/s13235-023-00520-z.
- West, Jeffrey, et al. "Antifragile therapy." BioRxiv (2020): 2020-10. https://doi.org/10.1101/2020.10.08.331678.
- Taleb, Nassim Nicholas. "(anti) fragility and convex responses in medicine." Unifying Themes in Complex Systems IX: Proceedings of the Ninth International Conference on Complex Systems 9. Springer International Publishing, 2018.
- Farrokhian, N., et al. "Dose dependent evolutionary game dynamics modulate competitive release in cancer therapy." bioRxiv 2020.18.303966 (2020).
- Farrokhian, Nathan, et al. "Measuring competitive exclusion in non–small cell lung cancer." Science Advances 8.26 (2022): eabm7212.

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