A screening test for COPD in women is being evaluated. Of the 100 women later confirmed to have COPD, 42 had a positive screen. Of the 150 women later determined to not have COPD, only 8 had a positive screen. Suppose in our population of interest, 20% of women have COPD. That is, P(COPD) = 0.20 in our population.

a) Fill in the frequency table from the information above.

COPD No COPD Positive Negative

Calculate the PPV of the test = P(COPD | Positive) for our population of interest. Remember that you can't calculate this directly from the conditional probability and must calculate it using Bayes rule.

What is the probability that a woman who does not have COPD will have a positive screen?