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(Anti)Fragility and Convex Responses in Medicine

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Unifying Themes in Complex Systems IX (ICCS 2018)

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Abstract

This paper applies risk analysis to medical problems, through the properties of nonlinear responses (convex or concave). It shows (1) necessary relations between the nonlinearity of dose-response and the statistical properties of the outcomes, particularly the effect of the variance (i.e., the expected frequency of the various results and other properties such as their average and variations); (2) The description of “antifragility” as a mathematical property for local convex response and its generalization and the designation “fragility” as its opposite, locally concave; (3) necessary relations between dosage, severity of conditions, and iatrogenics.

Iatrogenics seen as the tail risk from a given intervention can be analyzed in a probabilistic decision-theoretic way, linking probability to nonlinearity of response. There is a necessary two-way mathematical relation between nonlinear response and the tail risk of a given intervention.

In short we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based medicine and medical risk management.

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Notes

  1. 1.

    The term antifragile was coined in Taleb [7] inspired from mathematical finance and derivatives trading, by which some payoff functions respond positively to increase in volatility and other measures of variation, a term in the vernacular called “long gamma”.

  2. 2.

    Lee and Longo [9] “In the prokaryote E. coli, lack of glucose or nitrogen (comparable to protein restriction in mammals) increase resistance to high levels of \(H_2 O_2\) (15 mm) [10]”.

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Acknowledgment and Thanks

Harry Hong, Raphael Douady, Marco Manca, Matt Dubuque, Jacques Merab, Matthew DiPaola, Christian DiPaola, Yaneer Bar Yam, John Mafi, Michael Sagner, and Alfredo Morales.

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Authors and Affiliations

  1. Tandon School of Engineering, New York University, New York, NY, 11201, USA

    Nassim Nicholas Taleb

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  1. Nassim Nicholas Taleb
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Correspondence to Nassim Nicholas Taleb .

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Editors and Affiliations

  1. New England Complex Systems Institute, Cambridge, MA, USA

    Alfredo J. Morales

  2. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico, Distrito Federal, Mexico

    Carlos Gershenson

  3. New England Complex Systems Institute and University of Massachusetts, Cambridge, MA, USA

    Dan Braha

  4. Department of Electrical Engineering and Computer Science, University of Cincinnati, Cincinnati, OH, USA

    Ali A. Minai

  5. New England Complex Systems Institute, Cambridge, MA, USA

    Yaneer Bar-Yam

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Taleb, N.N. (2018). (Anti)Fragility and Convex Responses in Medicine. In: Morales, A., Gershenson, C., Braha, D., Minai, A., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems IX. ICCS 2018. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-96661-8_32

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