Medical Diagnosis

Probability · Axiom Academy

Understanding test accuracy and why rare disease screening is tricky You take a medical test for a rare disease that affects only 0.1% of the population (1 in 1,000 people). The test comes back positive . Sensitivity: 99% - If you have the disease, the test will be positive 99% of the time Specificity: 95% - If you don't have the disease, the test will be negative 95% of the time You test positive on a 99% accurate test. What's the probability you actually have the disease? Most people guess the probability is around 99% because the test is "99% accurate." But the actual answer is only about 2% ! This seems impossible at first. How can a 99% accurate test be so wrong? The key is understanding base rates - how common the disease is in the first place. Breaking Down the Test Results Now let's apply the test's accuracy rates to both groups: Among the 100 people with the disease: Among the 99,900 people without the disease: Notice something important: Even though the false positive rate is only 5%, when you apply it to 99,900 healthy people, you get 4,995 false alarms ! Now we can calculate the probability you actually have the disease given a positive test: Total people who test positive: Only about 2% chance you actually have the disease! This is Bayes' Theorem in action: the posterior probability depends not just on test accuracy, but also on the prior probability (base rate) of the disease.

This is the written version of the interactive lesson above. See the full Probability course.