Disease Testing Analysis

Discrete Math · Axiom Academy

REAL WORLD Disease Testing Analysis Discover why even highly accurate medical tests can produce surprising numbers of false positives when testing for rare diseases. Imagine a medical test that is 99% accurate. Sounds reliable, right? But what happens when we use this test to screen for a rare disease that affects only 1 in 1,000 people? The answer might surprise you! Let's explore this counterintuitive phenomenon using probability theory and Bayes' Theorem. Medical tests have two key accuracy measures: If you HAVE the disease, 99% chance the test is positive If you DON'T have the disease, 99% chance the test is negative Let's test a population and see what happens. Adjust the sliders to explore how disease prevalence and test accuracy affect results. How common is the disease in the population? True positive rate (detects disease when present) True negative rate (correctly identifies healthy people) Testing Population of 10,000 People Bayes' Theorem: The Key to Understanding What we really want to know is: If the test is positive, what's the probability the person actually has the disease? P(Disease | Positive) = Probability of having disease given positive test P(Positive | Disease) = Sensitivity (true positive rate) P(Disease) = Disease prevalence in population P(Positive) = Total probability of testing positive Let's calculate with the default values: 99% sensitivity, 99% specificity, 0.1% prevalence. Step 1: How many actually have the disease?

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