Question

1) Scientists have developed an inexpensive new test that can rapidly diagnose COVID-19 infections, a timely advance that comes as clinicians and public health officials are scrambling to cope with testing backlogs while the number of cases continues to climb. The new test – officially named the “SARS-CoV-2 DETECTR” – is easy to implement and to interpret, and requires no specialized equipment, which is likely to make the test more widely available than the current COVID-19 test kits.

To examine the effectiveness of the new COVID-19 screening test in County A. Participants were assigned to the new “SARS-CoV-2 DETECTR” screening test or the current test. The three months study period produced these results:

           

		Current test
New test result		Confirmed	Not confirmed	Total
	Positive	150	850	1000
	Negative	50	19,150	19200
	Total	200	20,000	20,200

1. i. Calculate the sensitivity of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

2. i. Calculate the specificity of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

3. i. Calculate the predictive value positive of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

4. i. Calculate the predictive value negative of the “SARS-CoV-2 DETECTR” screening test.. (2pts)

ii. Interpret your results (0.5pt):

Answer 1

The table gives the number of individuals in each of the four groups as follows-

	Confirmed (Has the condition)	Not confirmed (Does not have the condition)	Total
Positive	150 (a)	850 (b)	1000
Negative	50 (c)	19,150 (d)	19,200
Total	200	20,000	20,200

Cell a = Positive and Confirmed = True positive = 150

Cell b = Positive and Not confirmed = False positive = 850

Cell c = Negative and Confirmed = False negative = 50

Cell d = Negative and Not confirmed = True negative = 19,150

• Sensitivity = [a/(a+c)]*100 = [ 150 / (150+50) ]*100 = 75%

Sensitivity is the ability of a screening to detect a true positive, reflecting a test's ability to correctly identify all the individuals who have the condition. It is the screening test's probability of correctly identifying, solely from among people who are known to have the condition, all those who do indeed have the condition. The Sensitivity of the “SARS-CoV-2 DETECTR” screening test is 75% which implies that out of a 100 cases who are known to have the condition this test can correctly identify 75 times that they do indeed have the condition or the probability that a person from among those who are known to have the condition who tested positive do indeed have the condition is 0.75

• Specificity = [d/(b+d)]*100 = [ 19150 / (850+19150) ]*100 = 95.75%

Specificity is the ability of a screening to detect a true negative, reflecting a test's ability to correctly identify all the individuals who do not have the condition. It is the screening test's probability of correctly identifying, solely from among people who are known not to have the condition, all those who do indeed not have the condition. The Specificity of the “SARS-CoV-2 DETECTR” screening test is 95.75% which implies that out of a 100 cases who are known not to have the condition this test can correctly identify almost 96 times that they indeed do not have the condition or the probability that a person from among those who are known not to have the condition who tested negative indeed do not have the condition is 0.96.

• Predictive value positive = [a/(a+b)]*100 =  [ 150 / (150+850) ]*100 = 15%

The Predictive value positive helps to establish whether people who tested positive on the screening test do or do not actually have the condition of interest. This measure focuses on the practical usefulness of the test in clinical practice. It refers to the accuracy of the positive results as given by the screening test. PPV is the probability of correctly identifying from among people who might or might not have the condition, all those people who do actually have the condition. Here, PPV is 15% which implies that the probability that people with a positive screening test result indeed do have the condition of interest is 0.15

• Predictive value negative = [d/(c+d)]*100 =  [ 19150 / (50+19150) ]*100 = 99.74%

The Predictive value negative refers to the accuracy of negative results produced by the screening test. NPV is the probability of correctly identifying from among people who might or might not have the condition, all those people who do not actually have the condition. Here, NPV is 99.74% which implies that the probability that people with a negative screening test result indeed do not have the condition of interest is almost 1.

These four tests are used to describe the characteristics of a screening test.