(Anti)Fragility and Convex Responses in Medicine

  • Nassim Nicholas TalebEmail author
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


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.


Evidence based medicine Risk management Nonlinear responses 


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.


  1. 1.
    Brewster, J.F., Graham, M.R., Mutch, W.A.C.: Convexity, Jensen’s inequality and benefits of noisy mechanical ventilation. J. R. Soc. Interface 2(4), 393–396 (2005)CrossRefGoogle Scholar
  2. 2.
    Graham, M.R., Haberman, C.J., Brewster, J.F., Girling, L.G., McManus, B.M., Mutch, W.A.C.: Mathematical modelling to centre low tidal volumes following acute lung injury: a study with biologically variable ventilation. Respir. Res. 6(1), 64 (2005)CrossRefGoogle Scholar
  3. 3.
    Funk, D.J., Graham, M.R., Girling, L.G., Thliveris, J.A., McManus, B.M., Walker, E.K., Rector, E.S., Hillier, C., Scott, J.E., Mutch, W.A.C.: A comparison of biologically variable ventilation to recruitment manoeuvres in a porcine model of acute lung injury. Respir. Res. 5(1), 22 (2004)CrossRefGoogle Scholar
  4. 4.
    Arold, S.P., Suki, B., Alencar, A.M., Lutchen, K.R., Ingenito, E.P.: Variable ventilation induces endogenous surfactant release in normal guinea pigs. Am. J. Physiol. Lung Cell. Mol. Physiol. 285(2), L370–L375 (2003)CrossRefGoogle Scholar
  5. 5.
    Amato, M.B.P., Barbas, C.S.V., Medeiros, D.M., Magaldi, R.B., Schettino, G.P., Lorenzi-Filho, G., Kairalla, R.A., Deheinzelin, D., Munoz, C., Oliveira, R., et al.: Effect of a protective-ventilation strategy on mortality in the acute respiratory distress syndrome. N. Engl. J. Med. 338(6), 347–354 (1998)CrossRefGoogle Scholar
  6. 6.
    Jensen, J.L.W.V.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math. 30(1), 175–193 (1906)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Taleb N.N.: Antifragile: Things That Gain from Disorder. Random House and Penguin (2012)Google Scholar
  8. 8.
    Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2(4), 303–314 (1989)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lee, C., Longo, V.: Fasting vs dietary restriction in cellular protection and cancer treatment: from model organisms to patients. Oncogene 30(30), 3305–3316 (2011)CrossRefGoogle Scholar
  10. 10.
    Jenkins, D., Schultz, J., Matin, A.: Starvation-induced cross protection against heat or H2O2 challenge in Escherichia coli. J. Bacteriol. 170(9), 3910–3914 (1988)CrossRefGoogle Scholar
  11. 11.
    Kaiser, J.: Sipping from a poisoned chalice. Science 302(5644), 376 (2003)CrossRefGoogle Scholar
  12. 12.
    Rattan, S.I.: Hormesis in aging. Ageing Res. Rev. 7(1), 63–78 (2008)CrossRefGoogle Scholar
  13. 13.
    Calabrese, E.J., Baldwin, L.A.: Defining hormesis. Hum. Exp. Toxicol. 21(2), 91–97 (2002)CrossRefGoogle Scholar
  14. 14.
    Calabrese, E.J., Baldwin, L.A.: Hormesis: the dose-response revolution. Ann. Rev. Pharmacol. Toxicol. 43(1), 175–197 (2003)CrossRefGoogle Scholar
  15. 15.
    Calabrese, E.J., Baldwin, L.A.: The hormetic dose-response model is more common than the threshold model in toxicology. Toxicol. Sci. 71(2), 246–250 (2003)CrossRefGoogle Scholar
  16. 16.
    Arumugam, T.V., Gleichmann, M., Tang, S.-C., Mattson, M.P.: Hormesis/preconditioning mechanisms, the nervous system and aging. Ageing Res. Rev. 5(2), 165–178 (2006)CrossRefGoogle Scholar
  17. 17.
    Martin, B., Mattson, M.P., Maudsley, S.: Caloric restriction and intermittent fasting: two potential diets for successful brain aging. Ageing Res. Rev. 5(3), 332–353 (2006)CrossRefGoogle Scholar
  18. 18.
    Longo, V.D., Mattson, M.P.: Fasting: molecular mechanisms and clinical applications. Cell Metab. 19(2), 181–192 (2014)CrossRefGoogle Scholar
  19. 19.
    Longo, V.D., Fontana, L.: Calorie restriction and cancer prevention: metabolic and molecular mechanisms. Trends Pharmacol. Sci. 31(2), 89–98 (2010)CrossRefGoogle Scholar
  20. 20.
    Safdie, F.M., Dorff, T., Quinn, D., Fontana, L., Wei, M., Lee, C., Cohen, P., Longo, V.D.: Fasting and cancer treatment in humans: a case series report. Aging (Albany NY) 1(12), 988–1007 (2009)CrossRefGoogle Scholar
  21. 21.
    Raffaghello, L., Safdie, F., Bianchi, G., Dorff, T., Fontana, L., Longo, V.D.: Fasting and differential chemotherapy protection in patients. Cell Cycle 9(22), 4474–4476 (2010)CrossRefGoogle Scholar
  22. 22.
    Lee, C., Raffaghello, L., Brandhorst, S., Safdie, F.M., Bianchi, G., Martin-Montalvo, A., Pistoia, V., Wei, M., Hwang, S., Merlino, A., et al.: Fasting cycles retard growth of tumors and sensitize a range of cancer cell types to chemotherapy. Sci. Transl. Med. 4(124), 124ra27 (2012)CrossRefGoogle Scholar
  23. 23.
    Fontana, L., Kennedy, B.K., Longo, V.D., Seals, D., Melov, S.: Medical research: treat ageing. Nature 511(7510), 405–407 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    Anson, R.M., Guo, Z., de Cabo, R., Iyun, T., Rios, M., Hagepanos, A., Ingram, D.K., Lane, M.A., Mattson, M.P.: Intermittent fasting dissociates beneficial effects of dietary restriction on glucose metabolism and neuronal resistance to injury from calorie intake. Proc. Natl. Acad. Sci. 100(10), 6216–6220 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    Halagappa, V.K.M., Guo, Z., Pearson, M., Matsuoka, Y., Cutler, R.G., LaFerla, F.M., Mattson, M.P.: Intermittent fasting and caloric restriction ameliorate age-related behavioral deficits in the triple-transgenic mouse model of alzheimer’s disease. Neurobiol. Dis. 26(1), 212–220 (2007)CrossRefGoogle Scholar
  26. 26.
    Stranahan, A.M., Mattson, M.P.: Recruiting adaptive cellular stress responses for successful brain ageing. Nat. Rev. Neurosci. 13(3), 209–216 (2012)CrossRefGoogle Scholar
  27. 27.
    Fabrizio, P., Pozza, F., Pletcher, S.D., Gendron, C.M., Longo, V.D.: Regulation of longevity and stress resistance by Sch9 in yeast. Science 292(5515), 288–290 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    Longo, V.D., Kennedy, B.K.: Sirtuins in aging and age-related disease. Cell 126(2), 257–268 (2006)CrossRefGoogle Scholar
  29. 29.
    Michán, S., Li, Y., Chou, M.M.-H., Parrella, E., Ge, H., Long, J.M., Allard, J.S., Lewis, K., Miller, M., Xu, W., et al.: SIRT1 is essential for normal cognitive function and synaptic plasticity. J. Neurosci. 30(29), 9695–9707 (2010)CrossRefGoogle Scholar
  30. 30.
    Taylor, R.: Pathogenesis of type 2 diabetes: tracing the reverse route from cure to cause. Diabetologia 51(10), 1781–1789 (2008)CrossRefGoogle Scholar
  31. 31.
    Lim, E.L., Hollingsworth, K., Aribisala, B.S., Chen, M., Mathers, J., Taylor, R.: Reversal of type 2 diabetes: normalisation of beta cell function in association with decreased pancreas and liver triacylglycerol. Diabetologia 54(10), 2506–2514 (2011)CrossRefGoogle Scholar
  32. 32.
    Boucher, A., Lu, D., Burgess, S.C., Telemaque-Potts, S., Jensen, M.V., Mulder, H., Wang, M.-Y., Unger, R.H., Sherry, A.D., Newgard, C.B.: Biochemical mechanism of lipid-induced impairment of glucose-stimulated insulin secretion and reversal with a malate analogue. J. Biol. Chem. 279(26), 27263–27271 (2004)CrossRefGoogle Scholar
  33. 33.
    Wilson, E.A., Hadden, D., Merrett, J., Montgomery, D., Weaver, J.: Dietary management of maturity-onset diabetes. Br. Med. J. 280(6228), 1367–1369 (1980)CrossRefGoogle Scholar
  34. 34.
    Couzin, J.: Deaths in diabetes trial challenge a long-held theory. Science 319(5865), 884–885 (2008)CrossRefGoogle Scholar
  35. 35.
    Skyler, J.S., Bergenstal, R., Bonow, R.O., Buse, J., Deedwania, P., Gale, E.A., Howard, B.V., Kirkman, M.S., Kosiborod, M., Reaven, P., et al.: Intensive glycemic control and the prevention of cardiovascular events: implications of the accord, advance, and va diabetes trials: a position statement of the American diabetes association and a scientific statement of the American college of cardiology foundation and the American heart association. J. Am. Coll. Cardiol. 53(3), 298–304 (2009)CrossRefGoogle Scholar
  36. 36.
    Westman, E.C., Vernon, M.C.: Has carbohydrate-restriction been forgotten as a treatment for diabetes mellitus? A perspective on the accord study design. Nutr. Metab. 5(1), 1 (2008)CrossRefGoogle Scholar
  37. 37.
    Pories, W.J., Swanson, M.S., MacDonald, K.G., Long, S.B., Morris, P.G., Brown, B.M., Barakat, H.A., et al.: Who would have thought it? An operation proves to be the most effective therapy for adult-onset diabetes mellitus. Ann. Surg. 222(3), 339 (1995)CrossRefGoogle Scholar
  38. 38.
    Guidone, C., Manco, M., Valera-Mora, E., Iaconelli, A., Gniuli, D., Mari, A., Nanni, G., Castagneto, M., Calvani, M., Mingrone, G.: Mechanisms of recovery from type 2 diabetes after malabsorptive bariatric surgery. Diabetes 55(7), 2025–2031 (2006)CrossRefGoogle Scholar
  39. 39.
    Rubino, F., Forgione, A., Cummings, D.E., Vix, M., Gnuli, D., Mingrone, G., Castagneto, M., Marescaux, J.: The mechanism of diabetes control after gastrointestinal bypass surgery reveals a role of the proximal small intestine in the pathophysiology of type 2 diabetes. Ann. Surg. 244(5), 741–749 (2006)CrossRefGoogle Scholar
  40. 40.
    Trabelsi, K., Stannard, S.R., Maughan, R.J., Jamoussi, K., Zeghal, K.M., Hakim, A.: Effect of resistance training during ramadan on body composition, and markers of renal function, metabolism, inflammation and immunity in tunisian recreational bodybuilders. Int. J. Sport Nutr. Exer. Metab. 22(6), 267–275 (2012)CrossRefGoogle Scholar
  41. 41.
    Kondo, Y., Kanzawa, T., Sawaya, R., Kondo, S.: The role of autophagy in cancer development and response to therapy. Nat. Rev. Cancer 5(9), 726–734 (2005)CrossRefGoogle Scholar
  42. 42.
    Danchin, A., Binder, P.M., Noria, S.: Antifragility and tinkering in biology (and in business) flexibility provides an efficient epigenetic way to manage risk. Genes 2(4), 998–1016 (2011)CrossRefGoogle Scholar
  43. 43.
    He, C., Bassik, M.C., Moresi, V., Sun, K., Wei, Y., Zou, Z., An, Z., Loh, J., Fisher, J., Sun, Q., et al.: Exercise-induced bcl2-regulated autophagy is required for muscle glucose homeostasis. Nature 481(7382), 511–515 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Wu, J.T., Peak, C.M., Leung, G.M., Lipsitch, M.: Fractional dosing of yellow fever vaccine to extend supply: a modeling study. bioRxiv, p. 053421 (2016)Google Scholar
  45. 45.
    Schnohr, P., Marott, J.L., Jensen, J.S., Jensen, G.B.: Intensity versus duration of cycling, impact on all-cause and coronary heart disease mortality: the Copenhagen city heart study. Eur. J. Cardiovasc. Prev. Rehabil. 19, 73–80 (2011). Scholar
  46. 46.
    Yaffe, K., Blackwell, T., Kanaya, A., Davidowitz, N., Barrett-Connor, E., Krueger, K.: Diabetes, impaired fasting glucose, and development of cognitive impairment in older women. Neurology 63(4), 658–663 (2004)CrossRefGoogle Scholar
  47. 47.
    Razay, G., Wilcock, G.K.: Hyperinsulinaemia and alzheimer’s disease. Age Ageing 23(5), 396–399 (1994)CrossRefGoogle Scholar
  48. 48.
    Luchsinger, J.A., Tang, M.-X., Shea, S., Mayeux, R.: Caloric intake and the risk of alzheimer disease. Arch. Neurol. 59(8), 1258–1263 (2002)CrossRefGoogle Scholar
  49. 49.
    Luchsinger, J.A., Tang, M.-X., Shea, S., Mayeux, R.: Hyperinsulinemia and risk of alzheimer disease. Neurology 63(7), 1187–1192 (2004)CrossRefGoogle Scholar
  50. 50.
    Janson, J., Laedtke, T., Parisi, J.E., O’Brien, P., Petersen, R.C., Butler, P.C.: Increased risk of type 2 diabetes in alzheimer disease. Diabetes 53(2), 474–481 (2004)CrossRefGoogle Scholar
  51. 51.
    Dhabhar, F.S.: A hassle a day may keep the pathogens away: the fight-or-flight stress response and the augmentation of immune function. Integr. Comp. Biol. 49(3), 215–236 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    Dhabhar, F.S., Saul, A.N., Daugherty, C., Holmes, T.H., Bouley, D.M., Oberyszyn, T.M.: Short-term stress enhances cellular immunity and increases early resistance to squamous cell carcinoma. Brain Behav. Immun. 24(1), 127–137 (2010)CrossRefGoogle Scholar
  53. 53.
    Dhabhar, F.S., Saul, A.N., Holmes, T.H., Daugherty, C., Neri, E., Tillie, J.M., Kusewitt, D., Oberyszyn, T.M.: High-anxious individuals show increased chronic stress burden, decreased protective immunity, and increased cancer progression in a mouse model of squamous cell carcinoma. PLoS ONE 7(4), e33069 (2012)ADSCrossRefGoogle Scholar
  54. 54.
    Aschbacher, K., O’Donovan, A., Wolkowitz, O.M., Dhabhar, F.S., Su, Y., Epel, E.: Good stress, bad stress and oxidative stress: insights from anticipatory cortisol reactivity. Psychoneuroendocrinology 38(9), 1698–1708 (2013)CrossRefGoogle Scholar
  55. 55.
    Rook, G.A.: Hygiene and other early childhood influences on the subsequent function of the immune system. Dig. Dis. 29(2), 144–153 (2011)CrossRefGoogle Scholar
  56. 56.
    Rook, G.A.: Hygiene hypothesis and autoimmune diseases. Clin. Rev. Allergy Immunol. 42(1), 5–15 (2012)CrossRefGoogle Scholar
  57. 57.
    Mégraud, F., Lamouliatte, H.: Helicobacter pylori and duodenal ulcer. Dig. Dis. Sci. 37(5), 769–772 (1992)CrossRefGoogle Scholar
  58. 58.
    Taleb, N.N., Douady, R.: Mathematical definition, mapping, and detection of (anti)fragility. Quant. Financ. 13, 1677–1689 (2013)MathSciNetCrossRefGoogle Scholar
  59. 59.
    Neumaier, T., Swenson, J., Pham, C., Polyzos, A., Lo, A.T., Yang, P., Dyball, J., Asaithamby, A., Chen, D.J., Bissell, M.J., et al.: Evidence for formation of dna repair centers and dose-response nonlinearity in human cells. Proc. Natl. Acad. Sci. 109(2), 443–448 (2012)ADSCrossRefGoogle Scholar
  60. 60.
    Tubiana, M., Aurengo, A., Averbeck, D., Masse, R.: Recent reports on the effect of low doses of ionizing radiation and its dose-effect relationship. Radiat. Environ. Biophys. 44(4), 245–251 (2006)CrossRefGoogle Scholar
  61. 61.
    Bharadwaj, A., Stafford III, K.C.: Hormones and endocrine-disrupting chemicals: low-dose effects and nonmonotonic dose responses. J. Med. Entomol. 47(5), 862–867 (2010)CrossRefGoogle Scholar
  62. 62.
    Kalager, M., Adami, H.-O., Bretthauer, M., Tamimi, R.M.: Overdiagnosis of invasive breast cancer due to mammography screening: results from the Norwegian screening program. Ann. Intern. Med. 156(7), 491–499 (2012)CrossRefGoogle Scholar
  63. 63.
    Morrell, S., Barratt, A., Irwig, L., Howard, K., Biesheuvel, C., Armstrong, B.: Estimates of overdiagnosis of invasive breast cancer associated with screening mammography. Cancer Causes Control 21(2), 275–282 (2010)CrossRefGoogle Scholar
  64. 64.
    Pearce, K.A., Furberg, C.D., Psaty, B.M., Kirk, J.: Cost-minimization and the number needed to treat in uncomplicated hypertension. Am. J. Hypertens. 11(5), 618–629 (1998)CrossRefGoogle Scholar
  65. 65.
    Makridakis, S., DiNicolantonio, J.J.: Hypertension: empirical evidence and implications in 2014. Open Heart 1(1), e000048 (2014)CrossRefGoogle Scholar
  66. 66.
    Rosansky, S.: Is hypertension overtreatment a silent epidemic? Arch. Intern. Med. 172(22), 1769–1770 (2012)CrossRefGoogle Scholar
  67. 67.
    Abramson, J., Wright, J.: Are lipid-lowering guidelines evidence-based? Lancet 369(9557), 168–169 (2007)CrossRefGoogle Scholar
  68. 68.
    Speed, W., Total, L.S.T., Care, E.B.: Statins and musculoskeletal pain (2012)Google Scholar
  69. 69.
    Hilton-Jones, D.: I-7. statins and muscle disease. Acta Myol. 28(1), 37 (2009)Google Scholar
  70. 70.
    Hu, M., Cheung, B.M., Tomlinson, B.: Safety of statins: an update. Ther. Adv. Drug Saf. 3, 133–144 (2012). Scholar
  71. 71.
    Roberts, B.H.: The Truth About Statins: Risks and Alternatives to Cholesterol-Lowering Drugs. Simon and Schuster, New York (2012)Google Scholar
  72. 72.
    Fernandez, G., Spatz, E.S., Jablecki, C., Phillips, P.S.: Statin myopathy: a common dilemma not reflected in clinical trials. Clevel. Clin. J. Med. 78(6), 393–403 (2011)CrossRefGoogle Scholar
  73. 73.
    Blaha, M.J., Nasir, K., Blumenthal, R.S.: Statin therapy for healthy men identified as “increased risk”. JAMA 307(14), 1489–1490 (2012)CrossRefGoogle Scholar
  74. 74.
    Redberg, R.F., Katz, M.H.: Healthy men should not take statins. JAMA 307(14), 1491–1492 (2012)CrossRefGoogle Scholar
  75. 75.
    Hamazaki, T., Okuyama, H., Tanaka, A., Kagawa, Y., Ogushi, Y., Hama, R.: Rethinking cholesterol issues. J. Lipid Nutr. 21(1), 67–75 (2012). Scholar
  76. 76.
    File Jr., T.M.: Another perspective: reducing the overtreatment of pneumonia. Clevel. Clin. J. Med. 80(10), 619–620 (2013)CrossRefGoogle Scholar
  77. 77.
    Hadler, N.M.: Stabbed in the Back: Confronting Back Pain in an Overtreated Society. University of North Carolina Press, Chapel Hill (2009)Google Scholar
  78. 78.
    Cook, R.J., Sackett, D.L.: The number needed to treat: a clinically useful measure of treatment effect. BMJ Br. Med. J. 310(6977), 452 (1995)CrossRefGoogle Scholar
  79. 79.
    Kannel, W.B.: Risk stratification in hypertension: new insights from the framingham study. Am. J. Hypertens. 13(S1), 3S–10S (2000)CrossRefGoogle Scholar
  80. 80.
    Cunningham, S.A., Mitchell, K., Narayan, K.V., Yusuf, S.: Doctors’ strikes and mortality: a review. Soc. Sci. Med. 67(11), 1784–1788 (2008)CrossRefGoogle Scholar
  81. 81.
    Siegel-Itzkovich, J.: Doctors’ strike in Israel may be good for health. BMJ 320(7249), 1561–1561 (2000)CrossRefGoogle Scholar
  82. 82.
    Gruber, J., Kleiner, S.A.: Do strikes kill? Evidence from New York state. National Bureau of Economic Research, Technical report (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Tandon School of EngineeringNew York UniversityNew YorkUSA

Personalised recommendations