Tuesday, April 21, 2009

Brain teaser

The tiger riddle was a warm up-

1% of men at age forty who participate in routine screening have testicular cancer. 80% of men with testicular cancer will get a positive result. 8.2% of men without testicular cancer will also get a positive test result. A man in this age group had a positive test in a routine screening. What is the probability that he actually has testicular cancer?

Again no googling please. To avoid spoilers do not look at the comments. If you want more than one shot send me the answer and I'll tell you if it's correct (peterharv@gmail.com) so you can avoid the comments.


Mike said...

I should be excluded because I have a final on this on Monday, but oh well. The question is asking about the test's positive predictive value; what is the chance that this patient who tested positive for disease X, actually has disease X?

The equation basically puts all 'true positives' over the sum of 'true positives' and 'false positives'. So, in this case if we started with 1,000 men, and 1% had cancer, we would have 10 men with cancer, of which only 8 would be caught by the test given the 80% sensitivity (our 'true positives').

On the other side we would have 990 without cancer, 81 of which (8.2%) the test would say did have cancer (our false positives).


8/(8+81) = 0.089, or 8.9% positive predictive value.

But this is strange. Only 8.9% chance that someone who tests positive for testicular cancer actually has testicular cancer?

I think so... because its prevalence in the population is so low, the PPP is lowered (don't ask why).

Anyway, is this correct. I think this is correct. Could you let me know by Monday?

Peter H of Lebo said...

Correct nice job, Sorry a little late-hope you did well on your final- If this problem is any indication you probable rock it.

Mike said...

Yeah. I think it went well. Kinda' bombed the midterm so hopefully it will salvage my grade. (Many parts of this question were actually on the test. Good timing.)