Question

A new test is being assessed as a rapid screening tool for HIV+ status. In a sample of 483 persons, 50 are HIV+ as defined by traditional assays. Of these 50, the new screening test was positive for 40 persons. Of those HIV- (as defined by traditional assays), the new screening test was negative for 416 persons.

Fill in the table (5 points)

                                                    Gold Std- Traditional

Test	HIV +	HIV-	total
+
-

Total                                                                                                                        

a. What is the prevalence of HIV+ status in the study sample? (1 point)

1. 4%
2. 10%
3. 15%
4. 27%

b. What is the sensitivity of the new test? (1 point)

1. 70%
2. 75%
3. 80%
4. 90%

c. What is the specificity of the new test? (1 point)

1. 86%
2. 88%
3. 92%
4. 96%

d. What is the positive predictive value (PPV) of the new test? (1 point)

1. 50%
2. 60%
3. 70%
4. 80%

e. What is the negative predictive value (NPV) of the new test? (1 point)

1. 80%
2. 72%
3. 94%
4. 98%

QUESTION 3 (15 points)

Suppose that your company has just developed a new screening test for a disease and you are in charge of testing its validity and feasibility. You decide to evaluate the test on 1000 individuals and compare the results of the new test to the gold standard. You know the prevalence of disease in your population is 30%. The screening test gave a positive result for 292 individuals. Two hundred eighty-five (285) of these individuals actually had the disease on the basis of the gold standard determination.

1. Fill in all cells of the two by two table. (5 points)

		Gold Standard Determination of Disease		Total
Results of Screening Test		Yes	No
	Positive
	Negative
	Total

b. Calculate and interpret the predictive value of a positive test. (5 points)

c. What would happen to the predictive value positive if this test were administered in a population with a disease prevalence of 1% instead of 30%? (Note that the sensitivity and specificity of the test remain the same.) Would it remain the same? Increase? Decrease? (5 points)

Answer 1

Following is the completed table:

Gold Std- Traditional
Test	HIV +	HIV-	total
+	40	17	57
-	10	416	426
Total	50	433	483

(a)

Out of 483 persons, 50 are HIV+ so

P(HIV+) = 50 /483 = 0.10

Answer: correct option is b.

(b)

The sensitivity is

Pr(positive test| HIV) = (True positive number of cases) / (Number of cases have HIV) = 40 / 50= 0.80

Answer: correct option is c.

(c)

The specificity is

Pr(negative test| no HIV) = (True negative number of cases) / (Number of cases do not have HIV) = 416 / 433 = 0.96

Answer: correct option is d.

(d)

Positive predictive value given the probability that a person actually have diseases among those for whom test gives positive result. SO required value is

Positive predictive value= P(HIV | Positive) = 40 / 57= 0.70

Answer: correct option is c.

(e)

Negative predictive value given the probability that a person actually do not have diseases among those for whom test gives negative result. So required value is

Negative predictive value= P(no HIV | negative) = 416 / 426 = 0.98

Answer: correct option is d.