Suppose that the probability of a disease is 0.00369 in a population of unvaccin

Question

Suppose that the probability of a disease is 0.00369 in a population of unvaccinated subjects
and that the probability of the disease is 0.001 in a population of vaccinated subjects.
(a) What are the odds of disease without vaccine relative to the odds of disease with vaccine?
(b) How many people out of 100,000 would get the disease if they were not treated?
(c) How many people out of 100,000 would get the disease if they were vaccinated?
(d) What proportion of people out of 100,000 who would have gotten the disease would be
spared from it if all 100,000 were vaccinated? (This is called the protection rate.)
(e) Follow the steps in parts (a)–(d) to derive the odds ratio and the protection rate if the unvaccinated
probability of disease is 0.48052 and the vaccinated probability is 0.2. (The point is
that the odds ratio is the same in the two situations, but the total benefit of vaccination also
depends on the probabilities.)

Explanation / Answer

(a) Odds = 0.00369/0.001 = 3.69:1

(b) 100000 * 0.00369 = 369 people

(c) 100000 * 0.001 = 100 people

(d) Proportion = (0.001 + 0.00369)/1 = 0.00469

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