Diagnostic test - speciicity when multiple testing - clever statistician needed!

#1
During validation of a diagnostic test a false positive event is observed in 1 out of 60 occasions leading to a specificity of 98.3% when testing for a single event. If 30 events are looked for using this test at a single time point and detection of a single event is considered a positive result, then would we expect the specificity of this test to be 50%, since there is a 30 x 1/60 probability of detecting a false positive event?If we increase the threshold for what we consider a positive result to the detection of 2 events then would we expect the specificity to be 99.2% i.e. a 30 x (1/60 x 1/60) probability of detecting two false positive events

I wonder if this may be more complicated than above and whether specificity can be predicted in this fashion.

Many thanks!
 
Last edited:
#2
As I understand your post the specificity is the chance of not getting a false positive.
Your reasoning is plausible but, alas, incorrect. By that reasoning if 60 tests were done the specificity would be 0 but in fact there is quite a good chance of getting no false positive in 60 tests so the specificity can't be 0.
If you do 30 tests at once and define a false positive as getting one (or presumably more than one) positive result, the question is what is the probability of getting 30 negatives out of 30 tests given the probability of each is 59/60. You can get the answer to this in Excel =BINOMDIST(30,30,59/60,0) = 60%

If you do 30 tests at once and define a false positive as getting two (or presumably more than two) positive results, then the question is what is the probability of getting 29 or 30 negatives out of 30 given the probability of each is 59/60. You can get the answer to this in Excel by adding the extra probability =BINOMDIST(30,30,59/60,0)+BINOMDIST(29,30,59/60,0).
kat