Practical application

Population A

• ELISA test is applied to a million people where 1% are infected with HIV. Of the million people, 10,000 would be infected with HIV among whom the test detected 9,990 to be positive. Of the 1 million people in this population, 990,000 are not infected, among whom the test had detected 990 individuals be positive by the ELISA.

• Calculate the following:• Sensitivity and specificity• Positive Predictive Value• Negative Predictive Value

Sensitivity = a/(a+c)= 9990/(9990+10)= 99.9%Specificity= b/(b+d)= 989,000/(990+989,010)= 99.9%

ELISA test HIV infected Not infected Total

Positive 9990 990

Negative 10 989,010

10000 990,000 1,000,000

• Positive Predictive Value= a/(a+b)= 9990/(9990+990)=91%• Negative Predictive Value= d/(c+d)

=989,010/(10+989,010)= 99.9%

The effects of prevalence on the predictive value of test results in two different

populations.

Population B• Blood donors have already been screened

for HIV risk factors before they are allowed to donate blood, so that the HIV sero-prevalence in this population is closer to 0.1% instead of 1%. For every 1,000,000 blood donors, 1,000 are HIV positive.

Sensitivity= 99.9%Specificity= 99.9%PPV=a/(a+b)=50%

NPV= d/(c+d)=99.999%

ELISA HIV infected Not infected Total

+ ve 990 990 1,998

- ve 1 998,001 998,002

Total 1000 999,000 1000000

• With a sensitivity of 99.9%, the ELISA would pick up 999 of those thousand, but would fail to pick up one HIV sero-positive individual. Of the 999,000 uninfected individuals, the test would label 998,001 individuals assero-negative (true negatives). The ELISA would, however, falsely label 999 individuals as sero-positive (false-positives). Testing the blood donor pool results in as many false positive as true positive results.

Population C

• The second population consists of former IV drug users attending drug rehabilitation units, with a prevalence of 10% . For a million of these individuals, 100,000 would be HIV-infected and 900,000 would be HIV negative.

Sensitivity= 99.9%Specificity= 99.9%PPV=a/(a+b)=99%

NPP= d/(c+d)=99.999

ELISA HIV infected Not infected Total

+ ve 999,00 900 100,800

- ve 100 899,100 899,200

Total 100,000 900,000 1000000

• The HIV ELISA would yield 99,900 true positives and 100 false negatives. Of the 900,000 HIV negative individuals, the ELISA will find 899,100 to be negative but falsely label 900 as positive.

Summary of example

• The sensitivity and specificity of the test has not changed. It is just that the predictive value of the test has changed depending on the population being tested.

• The PPV is how many of the test-positives truly have the disease.

• In Pop. A 1% sero-positive rate, the ELISA has a PPV of 0.91 (91%).

• In blood donor with a 0.1% sero-prevalence, the PPV is only 0.5 (50%)

• In the high- prevalence population of intravenous drug users, the PPV is 0.99 (99%).

• Although the sensitivity of the ELISA does not change between populations, the PPV changes drastically from only half the people that tested positive being truly positive in a low- incidence population to 99% of the people testing positive being truly positive in the high- prevalence population.

• The NPV of the ELISA also changes depending on the prevalence of the disease.

• False positive results produced by high sensitivity of the screening test can easily be excluded by a confirmatory test with high specificity.

• Information on the possibility of false positive results and subsequent action should be provided to individuals prior to being screened (see informed consent).