Healthcare

1. A new blood serum test has been developed to diagnose hyperporcelainemia. After the appropriate animal tests, a large human trial was conducted on patients, suspected of having elevated serum porcelain levels. Informed consent was obtained, and all patients in the study underwent the new blood test as well as a confirmatory “gold standard” test. Assume, for this problem, that the results of the gold standard test reflect the true disease state of the patient.

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

The following data were obtained:

Serum porcelain level # of patients Disease positive Disease negative

(mcg / ml) (by gold standard) (by gold standard)

0 – 1.99 274 71 203

2.0 – 3.99 325 120 205

4.0 – 5.99 478 303 175

6.0 – 7.99 819 708 111

8.0 – 9.99 423 402 21

>10.0 152 137 15

a. If a cutoff value of 2.0 mcg / ml is chosen as the boundary between a negative and a positive test result for the new test (i.e., values below 2.0 mcg / ml are considered “negative” and values of 2.0 mcg / ml or greater are considered “positive”), create the 2x2 table for this data.

b. Calculate:

i. The sensitivity of the test –

ii. The specificity of the test –

c. If, on the other hand, a cutoff value of 4.0 mcg / ml is chosen as the boundary between a negative and a positive test result for the new test (i.e., values below 4.0 mcg / ml are considered “negative” and values of 4.0 mcg / ml or greater are considered “positive”), create the 2x2 table for this data:

d. Calculate:

i. The sensitivity of the test –

ii. The specificity of the test –

d. If the pre-test probability of hyperporcelainemia in this group is 12%, what is the post-test probability of disease being present in a patient with a positive test result if a cutoff value of 4.0 is chosen?

2. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of 12 to 15 there are both normal and diseased individuals), how does changing the cutoff value (moving it more toward the normal (lower end of the scale, in this case) vs moving it toward the diseased (upper end of the scale, in this case) affect the true positive, true negative, false positive, and false negative numbers and how does moving the cutoff value affect the sensitivity and specificity of the test? Choose the correct answer for each statement.

a. Moving the cutoff value toward the normal population (lower numbers in this example)

i. True positive numbers ____________increase / decrease ____________

ii. True negative numbers ___________increase / decrease ____________

iii. False positive numbers __________increase / decrease _____________

iv. False negative numbers __________increase / decrease ____________

v. Sensitivity _______________increases / decreases ________________

vi. Specificity _______________increases / decreases ________________

3. What does it mean if two curves that are plotted on an ROC curve cross each other?

4. A mathematical technique (algorithm) for reducing the number of bits needed to store digital data (or an image) but which results in loss of information is known as ____________________________. Be specific!