By definition, Sensitivity & Specificity are:
absent 8660 (a) 960(b)
disease present 40 (c) 340 (d)
the probability that a symptom is present (or screening test is positive) given that the person has the disease d/(c+d) 340 / (40+340) = .895. This is also know as the true positive rate.
the probability that a symptom is not present (or screening test is negative) given that the person does not have the disease a/(a + b) 8660 / (8660 + 960) = .90. This is also known as true negative rate.
But, in this case,
Clinical diagnosis Alzheimer’s disease Other causes of dementia
Alzheimer’s disease 1643 190
Other causes of dementia 127 228
If the clinical diagnosis is considered a screening test for Alzheimer’s disease,
then the sensitivity of this test would be:
Pr (screen test is present | person has the disease)
= 1643/(1643+127) = 0.928
and the specificity of this test would be:
Pr (screening test is negative | the person does not have the disease)
= 228/(190+228) = 0.545
What I am confused is whay these two have different formula to get sensivitiy and specificity?
Am I missing something here??