For a diagnostic test of a certain disease, 1 denotes the probability that the diagnosis is
Question:
For a diagnostic test of a certain disease, π1 denotes the probability that the diagnosis is positive given that a subject has the disease, and π2 denotes the probability that the diagnosis is positive given that a subject does not have it. Let ρ denote the probability that a subject does have the disease.
a. Given that the diagnosis is positive, show that the probability that a subject does have the disease is π1 ρ/[π1 ρ + π2(1 – ρ)].
b. Suppose that a diagnostic test for HIV+ status has both sensitivity and specificity equal to 0.95, and ρ = 0.005. Find the probability that a subject is truly HIV+ , given that the diagnostic test is positive. To better understand this answer, find the joint probabilities relating diagnosis to actual disease status, and discuss their relative sizes.
Step by Step Answer:
a Let pos denote positive diagnosis dis denote subject has disease b 9500595005 05...View the full answer
