Question

1. The screening was repeated using the 130mg of blood glucose per 100ml cut-off point in a population with an 8% prevalence of diabetes, as contrasted to the 5% prevalence in question 2, above. Calculate the sensitivity, specificity, PPV, and NPV. How do the sensitivity and specificity compare to what they were in the 5% diabetic population in question 2? How does the increased prevalence of diabetes affect the PPV?

	"Gold-Standard" Test
Screening	Disease	No Disease	Total
Positive	263	64	327
Negative	537	9136	9673
Total	800	9200	10000

Sensitivity =

Specificity =

PPV =

NPV =

Answer 1

a) The sensitivity of the test is defined as the probability of correctly identifying the people with the disease. It is computed here using Bayes theorem as:

P( + | Disease) = P(+ and disease) / P(disease) = 263 / 800 = 0.32875
Therefore 0.32875 is the required sensitivity of the test here.

b) The specificity of the test is defined as the probability of correctly identifying the people with no disease. Here it is computed as:
P( - | no disease) = P(- and no disease) / P(no disease) = 9136 / 9200 = 0.9930
Therefore 0.9930 is the required specificity here.

c) The PPV is obtained as the probability that a person with positive test actually have the disease. It is therefore computed as:
P( disease | +) = P(+ and disease) / P( + ) = 263 / 327 = 0.8043
Therefore 0.8043 is the required proportion here.

d) The NPV is computed here as:
P( no disease | -) = P(- and no disease) / P(-) = 9136 / 9673 = 0.9445
Therefore 0.9445 is the required proportion here.