Why clinicians are natural bayesians: Authors' replyBMJ 2005; 330 doi: https://doi.org/10.1136/bmj.330.7504.1390-d (Published 09 June 2005) Cite this as: BMJ 2005;330:1390
- Christopher J Gill, assistant professor (firstname.lastname@example.org),
- Lora Sabin, assistant professor,
- Christopher H Schmid, associate professor
- Center for International Health and Development, Department of International Health, Boston University School of Public Health, Boston, MA 02118, USA
- Biostatistics Research Center, Division of Clinical Care Research, Department of Medicine, Tufts University—New England Medical Center, Boston, MA 02111, USA
EDITOR—Hutchon is correct that Bayes's original theorem concerned probabilities rather than odds. We should have stated more clearly that expressing this is an application of Bayes's theorem expressed as odds. Odds and probabilities are interchangeable quantities [P = 1/(1 - odds); and Odds = (1 - P)/(P)]. This can be expressed more precisely by using Bayes's original equations as follows, although these are cumbersome and not as intuitively useful as the version that we presented in the paper.
Posterior odds are P(D|data)/P(not D|data) (where P = probability and D = having the disease). By Bayes's rule, the numerator is P(D)P(data|D)/P(data) …