2 questions in statistic: help wanted
1.What are the odds of rolling a seven using two, standard, fair dice?
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)
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?
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