I have following data from experiment to assess accuracy of test in patients with and without disease:
Where T stands for test and D stands for disease.
I want to get probability of (D+|T+) with prevalence of disease at 0.9 (90%)
I used formula:
P(D+|T+) = P(T+|D+) * P(D+) / P(T+) P(T+|D+) = 80/100 = 0.8 (from table) P(T+) = 90/200 = 0.45 (from table) P(D+) = 0.9 (given for actual population) Hence: P(D+|T+) = 0.8 * 0.9 / 0.45 = 1.6
However, how can probability be > 1
Where is the error in my calculations ?