Bayes’ Theorem for Medical Tests
In this article, the author introduces how Bayes’s theorem is applied to medical tests. Bayes’ theory is one of the most applied formulae in science. It describes the likelihood of an event, based on prior knowledge of conditions that might be related to the event. Around 1740 Bayes performed a thought experiment: he imagined putting his back against a square table and launching a ball onto the table without knowing where it would land.
To evaluate the performance of diagnostic tests, we need to use a confusion matrix. This is a simple 2-by-2 table grid in which are counted the prediction of the test vs the true reality of the patient. If a patient is predicted Positive and has truly been affected by the disease it would be referred to as a True Positive. On opposite to that, there is the True Negative, the patient is healthy and predicted so.
A logical error is often referred to, although improperly, as a Medical Paradox. Let’s assume we have a medical test, that has been advertised as having an accuracy of 99%, for a disease that affects 0.1% of the population. And if performed on 100,000 people, this test has the following results:.
Using the confusion matrix, we can construct another matrix that can help us with our problem. We want to understand what is the probability to result positive for the test P(+) and, being affected by the disease P(D|+? Given the accuracy of the test of 99%, we might think that there is 99% that test is accurate. But the Bayesian Theorem tells us something else.
We can adjust our beliefs in light of new tests, which is one of the best things about the Bayesian test. By using the Bayes theorem, one can determine the likelihood of a hypothesis based on its prior probability, the likelihood of different types of data being observed given the hypothesis, and the actual observed data.Besides medical tests, Bayes’ theorem can also be applied to many other different areas in areas like sciences and maths to prove the hypothesis.
Source: https://towardsdatascience.com/bayes-theorem-for-medical-test-f1fb12b579c6