Biostats Equation Q

[loveoforganic2]

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My 8th grade math is failing me hard.

If you're given a sensitive, specificity, and prevalence, how do you calculate PPV and NPV?

Say, 90% specificity, 75% sensitivity, 10% prevalence, PPV = ? NPV = ?

 

[addo]

90% specificity, 75% sensitivity, 10% prevalence, PPV = ? NPV = ?

To make the numbers easy, say you run 1000 tests... there is a 10% prevalence so you know there are going to be 100 cases of whatever youre testing for.
Out of those 100 cases, 75 are going to be True Positives, and 25 are going to be False Negatives, because sensitivity=75%
Out of the 900 negative cases, 810 are going to be True Negatives and 90 are going to be False Positives

Positive predictive value=True Positives/True Positives+False Positives=75/(75+90)=.45 or 45%
NPV=TN/TN+FN=810/(810+25)=.97 or 97%
So as you can see the more rare the disease and the higher the sensitivity the higher the NPV. LIkewise, the rarer the disease and the lower the specificity the lower the PPV
Thats why you want high sensitivity to rule disease out and high specificity to rule disease in

 

[projectlogic]

Make the 2x2 table.

Use a number like 1000 for population size.

100 people will have the disease. 900 people will not.


75% of 100 = 75 (sensitivity) = TP
100 - 75 =25 = FN

90% of 900 = 810 (specificity) = TN
900 - 810 = 90 = FP

Now you have all the numbers in your 2x2 to calculate PPV and NPV.

PPV = 75/(75+90)
NPV = 810/(810+25)

 

[loveoforganic2]

Thank you both. For some reason whenever I've gone to make the 2x2 table, I trip myself up, but that all makes sense. I'll try setting up some more random numbers for myself