Question

Suppose a medical manufacturer designed two, new, screening tests to rapidly diagnose syphilis, which is caused by the bacteria Treponema pallidum. The company tested both screening tests in a high risk population. The ‘gold standard’ test was a lab culture and identification. The data for both tests are below.

	Culture (Gold Standard)
New Test 1	Disease (+)	Disease (-)
(+)	65	86
(-)	8	600

	Culture (Gold Standard)
New Test 2	Disease (+)	Disease (-)
(+)	91	80
(-)	8	700

A- Calculate the sensitivity and specificity for each test.

Answer 1

For the New test 1

True positive=65

False negative=8

True negative=86

False positive=600

Sensitivity is a probability where test indicate disease among those with the disease

Sensitivity=True Positive(A)/True Positive+false negative(A+C)*100

65/65+8*100=89%

New Test 1 has a senstivity of 89%

Specificity is the fraction of those without the disease and they will have negative test results.

Specificity=True negative (D)/True negative+false positive(D+B)*100

86/86+600=12%

New test 1 has specificity of 12%

New test 2

Senstivity=True Positive/True Positive+false negative*100

True positive=91

False negative=8

Sensitivity=91/91+8*100=91.9%

For test number 2 senstivity is 91.9%

Specificity=True negative/true negative+false positive*100

True negative=80

False positive=700

Specificity=80/80+700*100=10.2%

In test number 2 specificity is 10.2%