Sensitivity and Specificity

The table below shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients with known TB status. Use it to answer the questions below. Test for TB TB absent TB present Negative 1739 8 Positive 51 22 Use this table to calculate the sensitivity and specificity of the test. Suppose that you have the knowledge that the prevalence of TB in a population is P(D) = 0.001, use the previously calculated sensitivity and specificity to answer the following questions about testing a patient from the population (not those used in the study in the table.) 1. Using the law of total probability, calculate P(Pos}, the probability that a randomly chosen person from the population tests positive for the disease and P(Neg), the probability that a randomly chosen person tests negative for the disease. 2. Using Bayes\" formula, find the probability that a patient who tested positive has the disease P(D | Pos) and the probability that a patient who tested negative is healthy P(H | Neg). 3. If the disease prevalence were P(D) =0.5, repeat the calculations to nd the new P(D ] P05} and P(H [ Neg)