# Sensitivity and Specificity in Biostatistics

Sensitivity is defined as the ability of a test to detect the presence of a disease in those who truly have the disease. It is calculated as the number of people with a disease who test positive (true positive) divided by the total number of people who have the disease (true positive + false negative). In this case, sensitivity equals the number of people with HIV antibody who test positive (100) divided by the total number of people who have HIV antibody (120). This yields 100/120 = 83% (not a very sensitive test).

11% (choice A) corresponds to the prevalence of the disease in the tested population, which in this case equals the total number of people with HIV antibody (true positive + false negative = 100 + 20 = 120) divided by the total number of people tested (100 + 20 + 50 + 950 = 1120). This yields 120/1120 = 11%.

67% (choice B) corresponds to the positive predictive value of the test, which equals the number of people with the disease who test positive (true positives = 100) divided by the total number of people testing positive (all positives = 50). This yields 100/150 = 67%.

95% (choice D) corresponds to the specificity of the test, which equals the number of people without HIV antibody who test negative (950) divided by the total number of people without HIV antibody (1000). This yields 950/1000 = 95%.

98% (choice E) corresponds to the negative predictive value of the test, which equals the number of people without HIV antibody who test negative (950) divided by the total number of people testing negative (970). This yields 950/970 = 98%.
An easy way to remember these concepts is:

Sensitivity = true positives/all diseased
Specificity = true negatives/all normal
PPV = true positives/all positives
NPV = true negatives/all negatives
Prevalence = all diseased/total population

If you prefer charts and formulas:

(Diseased) (Normal)
People with HIV antibody People without HIV antibody

Positive test a, true pos. b, false pos.
Negative test c, false neg d, true neg.

Sensitivity = a/(a + c)
Specificity = d/(b + d)
PPV = a/(a + b)
NPV = d/(c + d)
Prevalence = (a + c)/(a + b + c + d)

Choose your favorite approach. Just make sure you know this stuff, as it is almost always tested and gains you easy points once you have mastered the concepts.

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### POST COMMENT

DrRao said...
10/29/2008 7:50 AM

Excellant presentation. Very helpful for study

DrRao said...
10/29/2008 7:52 AM

Excellent presentation, very helpful for studies

Dr.Vishaal Bhat said...
10/29/2008 8:22 AM

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