Editor—Gill et al say that the pretest odds multiplied by the likelihood ratio of a test provides the post test odds.1 However, Bayes's work referred to probability rather than odds.
Figure 1.
Every part of clinical history and examination can be seen as a diagnostic test
Credit: ROYAL ASIATIC SOCIETY/BAL
Bayes developed his famous theorem about conditional probability. He showed that the probability of some event A occurring given that event B has occurred is equal to the probability of event B occurring given that event A has occurred, multiplied by the probability of event A occurring and divided by the probability of event B occurring. Bayes theorem states: P(A|B) = P(A)× P(B|A) divided by P(B).
The fact that Bayes refers to probability and articles such as those by Gill et al refer to odds has led to confusion, with some people thinking that it does not make any difference whether odds or probability are used or even that it is “debatable” which is used in correct bayesian calculations.2,3
As the authors say, the pretest odds should be multiplied by the likelihood ratio to reach the post-test odds. The likelihood ratio is a simple calculation from the sensitivity and specificity of a test, but the likelihood ratio as such is never used in Bayes's work. As we have shown, however, it is a simple calculation to show that multiplying the pretest odds by the likelihood ratio and deriving the post test odds is equivalent to the proposal of Bayes.4
Competing interests: None declared.
References
- 1.Gill CJ, Sabin I, Schmid CH. Why clinicians are natural bayesians. BMJ 2005;330: 1080-3. (7 May.) [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Hutchon DJR. Absence of nasal bone and detection of trisomy 21. Lancet 2002;359: 1343. [DOI] [PubMed] [Google Scholar]
- 3.Hutchon DJR. Trisomy 21:91% detection rate using second-trimester ultrasound markers. Ultrasound Obstet Gynecol 2001;18: 83. [DOI] [PubMed] [Google Scholar]
- 4.Hutchon DJR, Khattab A. How to use Bayes theorem to estimate sequential conditional risks. Odds ratio or risk: that is the question! www.obgyn.net/us/us.asp?page=/us/news_articles/hutchon_bayes (accessed 24 May 2005).