Given a test result comes back positive/negative, what is the likelihood that the patient in fact has/does not have the disease?

This is the data that you may use if you need number sets.

Assume that a patient with a T4 value of 7 or less is considered to be hypothyroid, i.e., set the cut point equal to 7. Using the data below that number of patients who are classified TN, FP, TP, and FN are

TN = 79 FP =18

TP = 25

FN = 2

Problem: A patient underwent a diagnostic test for hypothyroidism. The diagnostic test correctly identifies patients who in fact have the disease in 93% of the cases and correctly labels healthy patients as healthy in 81% of the cases. Assume that about 4% of all patients have the disease and the test for this particular patient comes back positive (i.e., the test indicates that the patient has the disease).

(a) Determine the sensitivity and the specificity of the test.

(b) If a randomly picked individual from the population undergoes this test and the test result is positive, what is the probability that this person in fact has the disease?

Additional Questions for your group. You are to answer all. Each group will be asked to present a different questions during the informal presentations next week.

Produce a graph where P(Disease|Test Positive) is on the vertical axis and prevalence is on the horizontal axis for a diagnostic test that correctly identifies patients who in fact have the disease in 93% of the cases and correctly labels healthy patients as healthy in 81% of the cases. What does this graph tell you about random testing for a relatively uncommon disease?

You work at a diagnostic lab. Last year, the lab was asked by a local clinic to perform a certain diagnostic medical test 1347 times. If the test of a patient came back positive, the clinic treated the patient for the disease. You wish to determine the number of patients that were treated unnecessarily based on the testing done at your lab. What information would you need to determine this number and how would you go about calculating this number?

Assume that there is a tradeoff between sensitivity and specificity: a test with a higher sensitivity has a lower specificity and vice versa. If your goal is to minimize the number of patients who are treated unnecessarily, should you maximize sensitivity or specificity? What about if your goal is to minimize the number of patients that are missed by the test?