# Statistic: 2 questions

1.      A new diagnostic test has been developed to Diagnose Disease Y. The new test was compared to the standard diagnostic test (â€œthe gold standardâ€) on the same set of patients, and the following data were obtained:

Number of patients diagnosed by the new test as having Disease Y, who actually had Disease Y = 3,252

Number of patients in the group who were diagnosed by the standard test as having Disease Y = 4,579

Number of patients diagnosed by the new test as not having Disease Y = 4, 737

Number of patients diagnosed by the new test as having Disease Y, who actually do not have Disease Y= 784

The standard diagnostic test is a tissue biopsy, and therefore, is considered to be 100% sensitive for diagnosing Disease Y.

a.       Create the 2×2 table that shows this data

b.      Calculate:

i.      The sensitivity of the new test

ii.      The specificity of the new test

iii.      The false positive rate of the new test

iv.      The false negative rate of the new test

v.      The positive predictive value of the new test

vi.      The negative predictive value of the new test

vii.      The likelihood ratio positive for the new test

viii.      The likelihood ratio negative for the new test

2.      Two new tests have been developed to diagnose Condition Z. One test (Test A) measures a metabolite â€œMetabolite Aâ€ in the serum. The other test (Test B) measures a different metabolite, â€œMetabolite Bâ€ in the urine. After appropriate preliminary testing, human trials are conducted. Following informed consent, the two tests were run on a group of patients with each patient getting both tests, as well as the â€œgold standardâ€ test for diagnosing Condition Z. The following data were obtained:

Important!!!! Since some answers depend on the results you obtained in previous sections of the problem, it is important for you that you show *all* work, since I will give partial credit if your analysis and set up are correct, even if your numerical result is incorrect.

Serum level (metabolite A)     # of patients                Disease positive                      Disease negative

(mg / ml)                                                                      (by gold standard)      (by gold standard)

0 â€“ 1.99                                                 25                                22                                3

2.0 â€“ 3.99                                273                              201                              72

4.0 â€“ 5.99                                584                              572                              12

6.0 â€“ 7.99                                538                              529                                9

8.0 â€“ 9.99                                175                              170                                5

>10.0                                         14                                14                                0

Urine level (metabolite B)

(ng/ml)

0 â€“ 2.99                                                 30                                  5                              25

3.0 â€“ 5.99                                245                                46                                         199

6.0 â€“ 8.99                                423                              400                              23

9.0 â€“ 11.99                              628                              620                                8

12.0 â€“ 14.99                            175                              169                                6

15.0 â€“ 17.99                              99                                95                                4

>18.0                                           9                                  9                                0

a)      For test A, a cutoff value of 4.0 mg / ml of metabolite A is chosen as the boundary between a negative and a positive test result (i.e., values below 4.0 mg / ml  are considered â€œnegativeâ€ and values of 4.0 mg / ml or greater are considered â€œpositiveâ€).

For test B, a cutoff value of 6.0 ng / ml for metabolite B is chosen as the boundary between a negative and a positive test result (i.e., values below 6.0 ng / ml are considered â€œnegativeâ€ and values of 6.0 ng / ml or greater are considered â€œpositiveâ€).

i.      Create a fully labeled 2 x 2 table for test A

ii.      Create a fully labeled 2 x 2 table for test B

iii.      Which test is the more sensitive at diagnosing Condition Z?

iv.      Which test is the more specific at diagnosing Condition Z?

b)      What is the post-test probability of disease being present in a patient with a positive test result for test A if the pre-test probability of Condition Z is 8%, and the cutoff value of 4.0 mg/ml is chosen?