Intended for healthcare professionals

Letters Risk illiteracy

Rather difficult calculations

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

Mental arithmetic

Maybe it's not so difficult to work out.

A prevalence of 1% means that one women in a hundred has the disease.

If a hundred women are screened the one true case will test positive
and be picked up (90% of the time anyway: that's what sensitivity meaans).

The 99 women who don't have the disease have a 9% chance of testing
positive (that's what false positive means).

So that's ten positive results (1+9) but only one of them is true.

The difficulty doctors have in understanding conditional probability
has been exacerbated by the lack of clarity and obfuscation of the
infomation leaflets produced by advocates of screening [1,2,3]


[1] Susan Mayor. NHS breast screening leaflet glosses over harms, say
critics. BMJ 2010;341:c7267

[2] Baum M, McCartney M, Thornton H. et al. Breast cancer screening
peril. Negative consequences of the breast screening programme . The Times
19th February 2009.

[3] "Who evaluates public health programmes? A review of the NHS
Breast Screening Programme" KJ Jorgensen, PC Gotzsche J R Soc Med 2010:
103: 14-20.

Competing interests: No competing interests

01 May 2011
John Doherty
Vienna 1040