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08/25/2011 - V/Q scans and Bayes Theorem

posted Sep 28, 2011, 5:25 PM by Chief Resident   [ updated Sep 28, 2011, 5:28 PM by Purnema Madahar ]
In resident report, we put Bayes Theorem to work with Bob Goodman. Doing the math on a case of suspected pulmonary embolism illustrated how relative clinical certainty can be. Using a likelihood ratio of 20 for a high-probability V/Q scan, i.e. assuming that a patient with a PE is 20 times as likely to have a high-probability V/Q scan than a patient without a PE (close to the LR of 17 reported in the attached paper that nicely replicates our exercise) and a pre-test probability of 5% of having a PE in our patients, we got the following (surprising) results:

5% pre-test probability = 0.05 pre-test probability = pre-tests odds of having a PE of 0.05/(1-0.05) = 0.053

post-test odds of having a PE = pre-test odds x LR = 0.053 x 20 = 1.053 = 1.053/(1.053+1) post-test probability = 0.52 post-test probability = 52 % post-test probability (!)

This means that a 'positive' V/Q scan in a patient with a low probability of having a PE clinically only is correct half the time. Or, put differently, that we incorrectly anti-coagulate half of these patients.

Mind you, the likelihood ratio of a CT scan is similar to that of a V/Q scan, with the same implications. The attached paper repeats this exercise for d-dimer and CT scans. It then serially applies the likelihood ratios, which is only valid if the tests are truly independent of each other, which might not be true.

As a follow-up to yesterday's bit on LFTs in statin users, Alda Osinaga pointed out an important fact: since checking LFTs in patients on statins after starting or increasing the dose and q6 months thereafter is part of the FDA mandated prescribing information, you would be held liable if a patient developed liver damage and you hadn't checked LFTs. Evidence based medicine is a good exercise but should not put you at odds with federal regulations: check those LFTs until the FDA catches up!