## Bayes Rule and Medical Tests (youtube.com)

Published:   August 7, 2021

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All medical tests do is update their probability of having disease, and not tell if we have disease or not.

There are three things

• Prevalence : How common is that disease around here? What chance of having it without tests?
• Sensitivity : If even disease is present, how good is the test at detecting it.
• Specificity : If a test is taken, there can be other issues that result. Clots in the pancreas can be because of a lot many things. How specific is test for that specific disease.

For example which he told

• Prevalence : 1%
• Sensitivity : 90%
• Specificity : 91%
1. So even if you haven’t taken test, there is 1% chance of you having that disease. So taking a test based on the test’s Sensitivity and Specificity would increase and decrease that probability.

To calculate your probability faster is to get the Bayes factor.

 ``````1 2 3 `````` ``````Bayes factor = Sensitivity / False positive Bayes factor = (Probability of having cancer after test is positive) / (Probability of not having cancer after test is positive) ``````

Bayes factor is also called likelihood ratio.

For above values :

• Probability of having cancer after test is positive : 90 in 100 (90%)
• Probability of test is false positive (100 - specificity) i.e 9
• So likelihood ratio is : 90 / 0 i.e. 10

So in the first case without test, there was 1% i.e. 1 in 100 that you’ve cancer without test. After the test, your chances just get updated. After test is positive your chances are: 1/100 * 10 ~ 1/10. So that is also not 100% sure now.

So for tests your symptoms, contacts, genetics all come up to increase the chance, but still not 100%, we need to remember. “All tests do is update the chances of having it, but not sure shot thing. Until tests are bulletproof."