2. A given population of 100,000 individuals shows a prevalence for Disease A of

Question

2. A given population of 100,000 individuals shows a prevalence for Disease A of 60%. A particular test for Disease A shows a sensitivity of 75% and a specificity of 50%. A. How many individuals in the population have Disease A? B. Draw the contingency table filling in the values for a, b, c and d (as shown on slide 109) in the appropriate boxes and showing your calculations in each casc. C. What is the diagnostic accuracy of the test? D. If the test is given to every individual in the population, how many individuals will be falsely identified as having the disease?

Explanation / Answer

A. Prevalence is the total number of the diseased individual (true positive and false negative) out of the total population.

prevelance = Tdisease /total x 100

This is given as 60% , that means out of 100.000 people , 60,000 people have the disease.

B.To form the table , we must first deduce the values of a,b,c and d .

we know

We also know total diseased individuals (A + C) are 60,000

putting the values in the equation, we get ,

A= 75 x 60,000 / 100 = 45000

therefore, C = 60000-45000 = 15000

Now,

Specificity: D/(D+B) × 100

We know the individuals with no disease will be D + B = 100,000 - 60,000 =40000

Therefore , D = 50 x 40,000 / 100 = 20000.

and B = 20,000.

now we put all the values in the table as belows

C. Out of the 100,000 people , test could determine 45,000 person as true negative and 40,000 people as healthy cases ,

Therefore the accuracy = 45000 + 40000 / 100000 = 85%.

D. Here the false positive cases are asked , which means individuals that doesnt have the disease still shows positive on test.

It is simply the value of b, which is 20,000.

disease no disease total Positive 45000 a 20000 b Ttest positive = 65000 Negative 15000 c 20000 d Ttest negative = 35000 Tdisease =60,000 Tnon disease = 40,000 100,00

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