Skip to main content
SpringerLink
Log in

Risk and Decision Making: Modeling and Statistics in Medicine – Fundamental Aspects

  • Living reference work entry
  • First Online:
Handbook of the Mathematics of the Arts and Sciences

  • 216 Accesses

Abstract

This chapter develops fundamental aspects of risk and decision making in connection to health issues and highlights the character of statistical concepts used to describe the decision situation. The ideas and concepts are illustrated by examples from the context of medicine. Case studies that deal with the problem of risk judgment and the communication of risk related to medical contexts are the topics of a separate twin chapter on “Risk and Decision Making: Modeling and Statistics in Medicine – Case Studies.”

In the first section, a framework for decisions is developed that helps to structure the kind of decisions in health issues. Criteria for decisions and constituents of risky situations are part of the discussion. Rationality may be rationally diverging if different stakeholders meet. Decisions in medicine and health issues usually bring several stakeholders together who have different criteria for their decisions and distinct interests in the decision and its consequences. That makes it so difficult but interesting to analyze the background. The second section deals with risk management in health issues. The general difficulty to arrive at a consensus about risks is illustrated by the fact that one often is faced with hazards. This means that between the exposition to a hazardous factor and the first symptoms of a negative impact, there is a long time span that makes it difficult to recognize a causal connection between exposition and disease. This delay between hazard and disease makes it hard to provide evidence, and if evidence is available, it is least convincing for many people. The third section illustrates the constituents of diagnosing procedures, the errors, which can be made, and how variables can be used for diagnosis. Procedures that are used in medical statistics are aligned with statistical methods by an analogy between these two disciplines. Furthermore, issues are investigated about the required sample size of empirical studies so that they deliver the information, which is needed to judge the adequacy of a medical measurement.

The wider the circle of stakeholders involved in the decision, the further away in the sense of personal involvement and time, the harder it is to attain a reasonable compromise about the inherent values and to make a widely agreed decision.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Adams J, Thompson M (2002) Taking account of societal concerns about risk. Framing the problem. Health and Safety Executive, London

    Google Scholar 

  • Aktipis CA, Kurzban RO (2004) Is homo economicus extinct? Vernon Smith, Daniel Kahneman and the evolutionary perspective. In: Koppl R (ed) Evolutionary psychology and economic theory. Advances in Austrian economics, vol 7. Elsevier, Oxford, pp 135–153

    Chapter  Google Scholar 

  • ASA (2016) Statement on statistical significance and p-values. Am Stat 70(2):131–133. amstat.tandfonline.com/doi/full/10.1080/00031305.2016.1154108#.XKKMv9hS-Hs. Accessed 30 Mar 2019

    Google Scholar 

  • Baron J (2008) Thinking and deciding, 4th edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Batanero C, Borovcnik M (2016) Statistics and probability in high school. Sense Publishers, Rotterdam

    Book  Google Scholar 

  • Beck-Bornholdt H-P, Dubben H-H (2003) Der Schein der Weisen. Irrtümer und Fehlurteile im täglichen Denken 7. Aufl (The semblance of wise people. Mistakes and misjudgements in daily thinking 7 ed). Rowohlt, Reinbek

    Google Scholar 

  • Blastland M, Spiegelhalter DJ (2013) The norm chronicles. Profile Books, London

    Google Scholar 

  • Borel E (1943) Les probabilités et la vie. Presses Universitaires de France, Paris

    MATH  Google Scholar 

  • Borovcnik M (2006) Probabilistic and statistical thinking. In: Bosch M (ed) Proc fourth congress of the European Society for Research in mathematics education. European Society for Research in Mathematics Education (ERME), Barcelona, pp 484–506. ermeweb.free.fr/CERME4/. Accessed 30 Mar 2019

    Google Scholar 

  • Borovcnik M (2012) Multiple perspectives on the concept of conditional probability. Avances de Investigación en Didactica de la Matemática 2:5–27. www.aiem.es/index.php/aiem/issue/view/2. Accessed 30 Mar 2019

    Google Scholar 

  • Borovcnik M (2015) Risk and decision making: the “logic” of probability. Math Enthus 12(1–3):113–139

    Google Scholar 

  • Borovcnik M (2016a) “To screen or not to screen” … Dialoge zur medizinischen diagnose (dialogues on medical diagnosis). mathematik lehren 194:22–28

    Google Scholar 

  • Borovcnik M (2016b) Probabilistic thinking and probability literacy in the context of risk. Educação Matemática Pesquisa 18(3):1491–1516

    Google Scholar 

  • Borovcnik M (2018a) Risk and decision making – fundamental aspects. In: Lerman S (ed) Encyclopedia of mathematics education. Springer, Cham

    Google Scholar 

  • Borovcnik M (2018b) Risk and decision making – psychological and educational aspects. In: Lerman S (ed) Encyclopedia of mathematics education. Springer, Cham

    Google Scholar 

  • Borovcnik M (2019) Informal and “informal” inference. In: Contreras JM, Gea MM, López-Martín MM, Molina-Portillo E (eds) Actas del Tercer Congreso International Virtual de Educación Estadística, Granada. www.ugr.es/local/fqm126/civeest.html. Accessed 30 Mar 2019

  • Borovcnik M, Kapadia R (2011a) Risk in health: more information and more uncertainty. In: Proceedings of IASE satellite conference on “statistics education and outreach”. ISI, Voorburg, 6 pp. iase-web.org/Conference_Proceedings.php?p=Stats_Education_and_Outreach_2011. Accessed 30 Mar 2019

  • Borovcnik M, Kapadia R (2011b) Determinants of decision-making in risky situations. In: Proceedings of 58th world statistics congress. ISI, Voorburg, 6 pp. 2011.isiproceedings.org/papers/950138.pdf. Accessed 30 Mar 2019

  • Borovcnik M, Kapadia R (2018) Reasoning with risk: teaching probability and risk as twin concepts. In: Batanero C, Chernoff EJ, Engel J, Lee H, Sánchez E (eds) Research on teaching and learning probability. Springer, New York, pp 3–22

    Google Scholar 

  • Buffon GL (1777) Essai d’arithmetique morale. In: Buffon GL Histoire naturelle générale et particulière suppl. 4. Imprimérie Royale, Paris; English translation (1785), Natural history, general and particular, 2 edn. Strahan and Cadell, London

    Google Scholar 

  • CCOHS (n.d.) Hazard and risk. Canadian Centre for Occupational Health and Safety. www.ccohs.ca/oshanswers/hsprograms/hazard_risk.html. Accessed 30 Nov 2017

  • CDC (n.d.) What are the risk factors for skin cancer? Centers for Disease Control and Prevention, Washington. www.cdc.gov/cancer/skin/basic_info/risk_factors.htm. Accessed 30 Mar 2019

  • Colquhoun D (2014) An investigation of the false discovery rate and the misinterpretation of p-values. R Soc Open Sci 1:1–16. https://doi.org/10.1098/rsos.140216. Accessed 30 Mar 2019

    Article  Google Scholar 

  • Devlin K (2014) The most common misconception about probability? In: Chernoff EJ, Sriraman B (eds) Probabilistic thinking: presenting plural perspectives. Advances in mathematics education, vol 7. Springer, Berlin, pp ix–xiii

    Google Scholar 

  • Dubben H-H, Beck-Bornholdt H-P (2005) Mit an Sicherheit grenzender Wahrscheinlichkeit. Logisches Denken und Zufall (With a probability that comes close to certainty). Rowohlt, Reinbek

    Google Scholar 

  • Dubben H-H, Beck-Bornholdt H-P (2010) Mit an Sicherheit grenzender Wahrscheinlichkeit. Logisches Denken und Zufall (With a probability coming close to certainty. Logic thinking and randomness). Rowohlt, Reinbek

    Google Scholar 

  • Dürr D, Goldstein S, Tumulka R, Zanghi N (2004) Bohmian mechanics and quantum field theory. Phys Rev Lett 93(9). arxiv.org/abs/quant-ph/0303156v2. Accessed 30 Mar 2019

  • Elmore JG, Armstrong K, Lehman CD, Fletcher SW (2005) Screening for breast cancer. J Am Med Assoc 293(10):1245–1256

    Article  Google Scholar 

  • Friedman M, Savage LJ (1952) The expected-utility hypothesis and the measurability of utility. J Polit Econ 60:463–474

    Article  Google Scholar 

  • Gasche UP (2014) Das “Swiss Medical Board” stellt Früherkennungs-Programme in Frage. Promotoren reagieren mit fragwürdigen Argumenten (The “Swiss Medical Board” questions early detection programmes. Promoters react with questionable arguments). Info-Sperber, Feb. 2014. www.infosperber.ch/Artikel/Gesundheit/Screening-Brustkrebs-Fruherkennung-Swiss-Medical-Board. Accessed 30 Mar 2019

  • Gigerenzer G (2002) Calculated risks: how to know when numbers deceive you. Simon & Schuster, New York

    Google Scholar 

  • Gigerenzer G (2014) Risiko. Wie man die richtigen Entscheidungen trifft. Random House, München. Original: Risk savvy. How to make good decisions. Penguin, New York

    Google Scholar 

  • Gigerenzer G (2016) Referat von Professor Gerd Gigerenzer zu Risiko- und Gesundheitskompetenz. Helsana Versicherungen, Zürich. www.youtube.com/watch?v=imFIcRU6kZ4. Accessed 30 Mar 2019

  • Gigerenzer G, Muir Gray JA (eds) (2013) Bessere Ärzte, bessere Patienten, bessere Medizin. Medizinisch Wissenschaftliche Verlagsgesellschaft, Berlin. Original: Better doctors, better patients, better decisions: Envisioning health care 2020. MIT Press, Cambridge, MA

    Google Scholar 

  • Goldacre B (2008) Badscience. Fourth Estate, London

    Google Scholar 

  • Goodreads (n.d.) Platform for readers and book recommendations. www.goodreads.com/quotes/70299-the-art-of-medicine-consists-of-amusing-the-patient-while. Accessed 30 Mar 2019

  • Gorard S, White P (2017) Still against inferential statistics: rejoinder to Nicholson and Ridgway. Stat Educ Res J 16(1):70–75

    Google Scholar 

  • Gore SM (1995) Statistical thinking and when to stop a clinical trial. In: Phillips CI (ed) Logic in medicine. BMJ Publishing Group, London

    Google Scholar 

  • Gøtzsche PC, Nielsen M (2011) Screening for breast cancer with mammography – review. Cochrane Libr 4. https://doi.org/10.1002/14651858.CD001877.pub4. Accessed 30 Mar 2019

  • Hansson SO (2007) Risk. In: Zalta EN (ed) Stanford encyclopedia of science. Archive. plato.stanford.edu/archives/spr2014/entries/risk/. Accessed 30 Mar 2019

    Google Scholar 

  • Harding-Zentrum für Risikokompetenz (n.d.) Nutzen und Risiken der Brustkrebs-Früherkennung (Benefits and risks of early detection of breast cancer). www.harding-center.mpg.de/de/faktenboxen/krebsfrueherkennung/brustkrebs-frueherkennung. Accessed 30 Mar 2019

  • Hubbard R, Bayarri MJ (2003) Confusion over measures of evidence (p) versus errors (α) in classical statistical testing. Am Stat 57(3):171–182

    Article  MathSciNet  Google Scholar 

  • Huerta P (2009) On conditional probability problem solving research – structures and contexts. Int Electron J Math Educ 4(3):163–194

    Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):263–292

    Article  MathSciNet  Google Scholar 

  • Kahneman D, Slovic P, Tversky A (eds) (1982) Judgment under uncertainty: heuristics and biases. Cambridge University Press, Cambridge

    Google Scholar 

  • Kalager M, Zelen M, Langmark F, Adami HO (2010) Effect of screening mammography on breast-cancer mortality in Norway. N Engl J Med 363:1203–1210

    Article  Google Scholar 

  • Kapadia R (2010) Chance and necessity: the languages of probability and mathematics. In: Reading C (ed) Proceedings of the eight international conference on teaching statistics (ICOTS 8). iase-web.org/Conference_Proceedings.php?p=ICOTS_8_2010. Accessed 30 Mar 2019

    Google Scholar 

  • Khamsi R (2005) Painkiller verdict shows mistrust of Merck. Nature 436:1070. www.nature.com/nature/journal/v436/n7054/full/4361070a.html. Accessed 30 Mar 2019

    Article  Google Scholar 

  • Knight FH (1921) Risk, uncertainty, and profit. Hart, Schaffner & Marx/Houghton Mifflin Company, Boston

    Google Scholar 

  • Koubenec HJ (2000) Mammographie-Screening: Überschätzen wir den Nutzen? (Mammography screening: Do we overestimate the benefits?). Berliner Ärzte 37(8):11–16

    Google Scholar 

  • May T, Silverman RD (2005) Free-riding, fairness and the rights of minority groups in exemption from mandatory childhood vaccination. Hum Vaccin 1(1):12–15

    Article  Google Scholar 

  • Mayo Clinic (n.d.) Mammogram guidelines: What are they? www.mayoclinic.com/health/mammogram-guidelines/AN02052. Accessed 30 Mar 2019

  • Miller AB, Wall C, Baines CJ, Sun P, To T, Narod SA (2014) Twenty five year follow-up for breast cancer incidence and mortality of the Canadian National Breast Screening Study: randomised screening trial. Br Med J 348:g366. www.bmj.com/content/348/bmj.g366. Accessed 30 Mar 2019

    Article  Google Scholar 

  • Miller E (2004) The great Wikipedia authority debate. The importance of … . archive.is/nEHhz. Accessed 30 Mar 2019

  • Mongin P (1997) Expected utility theory. In: Davis J, Hands W, Maki U (eds) Handbook of economic methodology. Edward Elgar, London, pp 342–350

    Google Scholar 

  • Neyman J, Pearson E (1933) On the problem of most efficient tests of statistical hypotheses. Phil Trans R Soc A 231:289–337

    Article  Google Scholar 

  • Nicholson J, Ridgway J (2017) A response to White and Gorard: against inferential statistics: how and why current statistics teaching gets it wrong. Stat Educ Res J 16(1):62–69

    Google Scholar 

  • Pareto V (1906) Manuale di economia politica con una introduzione alla scienza sociale. Società Editoriale Libraria, Milano. English translation: Montesano A, Zanni A, Bruni L, Chipman J S, McLure M (eds) (2014) Manual of Political Economy. A critical and variorum edition. Oxford University Press, Oxford

    Google Scholar 

  • Pratt JW, Raiffa H, Schlaifer R (1996) Introduction to statistical decision theory. MIT Press, Cambridge, MA

    MATH  Google Scholar 

  • RIS (2006) Rechtsinformationssystem des Bundes. Geschäftszahl Arzthaftung im Falle der Geburt eines behinderten Kindes. 5Ob165/05h. 7.3.2006 (Law Information System of the Republic of Austria. Liability of a doctor in case of a wrongful birth). www.ris.bka.gv.at/Dokument.wxe?Abfrage=Justiz&Dokumentnummer=JJT_20060307_OGH0002_0050OB00165_05H0000_000. Accessed 30 Mar 2019

  • Sandblom G, Varenhorst E, Rosell J, Löfman O, Carlsson P (2011) Randomised prostate cancer screening trial: 20year follow-up. Br Med J Online 342. https://doi.org/10.1136/bmj.d1539. Accessed 30 Mar 2019

    Article  Google Scholar 

  • Spiegelhalter D (2012) Using speed of ageing and “microlives” to communicate the effects of lifetime habits and environment. Br Med J 345:e8223. https://doi.org/10.1136/bmj.e8223. Accessed 30 Mar 2019

    Article  Google Scholar 

  • Spiegelhalter D (2014, April) What can education learn from real-world communication of risk and uncertainty? Invited lecture at the Eight British Congress on Mathematical Education, Nottingham

    Google Scholar 

  • Spiegelhalter D, Gage J (2015) What can education learn from real-world communication of risk and uncertainty? Math Enthus 12(1–3):4–10. scholarworks.umt.edu/tme/vol12/iss1/4/. Accessed 30 Mar 2019

    Google Scholar 

  • Styer DF (2000) The strange world of quantum mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Sylvester R (1989) Phase I, II and III trials: role, description and statistical design. In: Rotmensz N (ed) Data management and clinical trials. Elsevier, Amsterdam, pp 9–35

    Google Scholar 

  • Thaler RH, Sunstein CR (2008) Nudge. Improving decisions about health, wealth, and happyness. Yale University Press, New Haven/London

    Google Scholar 

  • Todd PM, Gigerenzer G (2000) Précis of simple heuristics that make us smart. Behav Brain Sci 23:727–780

    Article  Google Scholar 

  • Tversky A, Kahneman D (1974) Judgment under uncertainty: heuristics and biases. Science 185:1124–1130

    Article  Google Scholar 

  • Wasserstein RL, Lazar NA (2016) The ASA’s statement on p-values: context, process, and purpose. Am Stat 70(2):129–131. amstat.tandfonline.com/doi/full/10.1080/00031305.2016.1154108#.XKKMv9hS-Hs. Accessed 30 Mar 2019

    Article  MathSciNet  Google Scholar 

  • White P, Gorard S (2017) Against inferential statistics: how and why current statistics teaching gets it wrong. Stat Educ Res J 16(1):51–61

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Manfred Borovcnik

Authors
  1. Manfred Borovcnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manfred Borovcnik .

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Borovcnik, M. (2019). Risk and Decision Making: Modeling and Statistics in Medicine – Fundamental Aspects. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_62-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70658-0_62-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation