Intended for healthcare professionals

Rapid response to:

Letters Risk illiteracy

Rather difficult calculations

BMJ 2011; 342 doi: (Published 21 April 2011) Cite this as: BMJ 2011;342:d2577

Rapid Response:

Simple arithmetic

Three points arise.

1) I tried to show that by presenting conditional probablities using
natural frequencies (ie numbers) what appears to be a confusing
calculation becomes simple. Why complicate the obvious? Bad presentation
of medical risks leads to misunderstanding and poor decision taking. [1]

2) The situation described "What would you tell a woman who tested
positive in a screening mammogram that her chances were of having breast
cancer?" should never occur. A woman must be told this before she consents
to screening. Consent is only valid if it is fully informed. [2]

Information must also include a clear explanation of the balance of
harms and benefits, including overdiagnosis and overtreatment. Techniques
to do this are well established. [3,4]

3) Demystification of diagnostic testing is not difficult. [5]

Dr John Doherty


1) Gigerenzer G, Edwards A, Simple tools for understanding risks:
from innumeracy to insight. BMJ 2003; 327 : 741 doi:

2) Baines CJ. Mammography screening: are women really giving informed
consent? J Natl Cancer Inst 2003;95:1508-1511.

3) Schwartz LM, Woloshin S, Welch HG. Risk communication in clinical
practice: putting cancer in context. J Natl Cancer Inst Monogr. 1999; 124-

4) Paling J. Strategies to help patients understand risks. BMJ 2003;

5) Perera R, Heneghan C, Making sense of diagnostic tests likelihood
ratios. Evid Based Med 2006;11:130-131 doi:10.1136/ebm.11.5.130-a

Competing interests: No competing interests

07 May 2011
John Doherty
Vienna 1040