Errors in Applying Bayes’ Rule to Medical Diagnoses
Bayes’ rule is a theorem that relates the probability of a conditional event to the probability of the independent events occurring. It has many medical applications, including medical diagnosis. Clinicians can develop an initial probability that any patient has a disorder and can use that to come up with a good estimate of probability that a specific patient has a disorder based on the patient’s medical history, physical examinations, and diagnostic testing. Lots of research have been done looking into how clinicians employ the Bayesian Method to do this and the following error patterns have been observed. Most clinicians overestimate how common rare disorders are and use an initial probability estimate that is too large. They also do not revise the initial estimate to the same degree as Bayes’ method advises. Additionally, clinicians assign more weight to information they learn about the patient later on and they overestimate the importance of diagnostic testing.
In a web-based survey run by University of Pittsburgh’s Department of Medicine, students from three different medicals were given information about a series of examination scenarios and pre-examination probabilities. They had to come up with their diagnosis for the patient as well as estimate post examination probabilities. The results of the survey showed that the mean post examination probabilities the participants estimated were significantly lower that the estimates predicted by the literature. This observation leads to the conclusion that students tend to underestimate the impact of examination findings. Another trend detected by the survey is that students also tended to order more tests that the probabilities suggest are necessary.
Source:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427763/