ethanjohnsons

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# Sensitivity & Specificity Confusion

By definition, Sensitivity & Specificity are:

Test Result

Negative Positive

absent 8660 (a) 960(b)

disease present 40 (c) 340 (d)

Sensitivity

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.

Specificity

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,

Pathological diagnosis

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??

Test Result

Negative Positive

absent 8660 (a) 960(b)

disease present 40 (c) 340 (d)

Sensitivity

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.

Specificity

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,

Pathological diagnosis

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??

ASKER CERTIFIED SOLUTION

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ASKER

Sensitivity = d/(c+d)

Specificity = a/(a+b)

Pathological diagnosis

Clinical diagnosis Alzheimer’s disease Other causes of dementia

Alzheimer’s disease 1643 (d) 190 (b)

Other causes of dementia 127 (c) 228 (a)

So, I got it. I didn't think that the table structure different for this....