Editor—In their article on subarachnoid haemorrhage Al-Shahi et al continue the fallacy that, as 2% of subarachnoid haemorrhage is missed on computed tomography, every patient must have a lumbar puncture.1 Quoting the sensitivity of computed tomography in this way may lead the unwary into the trap of thinking that about 1 in 50 lumbar punctures will be positive after a negative computed tomography. (I would probably consent to a lumbar puncture if there was a 1 in 50 chance of finding a severe condition such as a subarachnoid haemorrhage).
However, a bayesian thinker might not be convinced so easily. The chance quoted in the article of a sudden headache being due to subarachnoid haemorrhage is 25%, which we can use as the pre-test probability before computed tomography. The quoted sensitivity of scanning is 98%, giving a likelihood ratio for a negative test of 0.02. A pre-test probability of 25% and a likelihood ratio of 0.02 give a post-test probability of 0.5%. (I don't think that I would consent to a lumbar puncture if there was only a 1 in 200 chance of finding a subarachnoid haemorrhage.)
In practice, the increasing ease of access to computed tomography means that doctors are scanning a group of patients at much lower risk than in the past. As the article emphasises, clinical diagnosis of subarachnoid haemorrhage can be very difficult, so computed tomography is often ordered. So the real life probability before computed tomography is about 10%. This gives a post-test probability of about 0.15%. (I certainly would not consent to a lumbar puncture if there was only a 1 in 650 chance of finding a subarachnoid haemorrhage.)
The dogma that every patient with “query subarachnoid haemorrhage” and a negative computed tomogram must have a lumbar puncture is wrong.2 Every such patient should have a discussion about lumbar puncture with a clinician who understands diagnostic testing, so that the clinician can, with the patient, weigh the risks and benefits, explain the uncertainty, take the patient's attitude to risk into consideration, and come to a conclusion about whether further investigation should be undertaken.
Competing interests: None declared.
References
- 1.Al-Shahi R, White PM, Davenport RJ, Lindsay KW. Subarachnoid haemorrhage. BMJ 2006;333: 235-40. (29 July.) [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Coats TJ, Loffhagen R. Diagnosis of subarachnoid haemorrhage following a negative computed tomography for acute headache: a Bayesian analysis. Eur J Emergency Med 2006;13; 80-3. [DOI] [PubMed] [Google Scholar]