chemamr
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A 55 year old man visits his primary care physician with a complaint of urinary infrequency. Examination finds a 1 cm nodule on his prostate gland. The physician orders a PSA. By common standards, a PSA level greater than 4 ng/ml is considered abnormal. Using this standard this test has a sensitivity of 80% and a specifitity of 90%. A recently published epidemiologic article found that in a cross sectional study, 10% of men of this age have prostate cancer. The result on the patientīs PSA is 7 ng/ml. What is your best estimate of the likelihood that this man actually has prostate cancer???
A. 13%
B. 25%
C. 36%
D. 47%
E. 58%
F. 69%
G. 72%
H. 81%
I read this question in kaplan lectures notes, i know the answer but I HAVE NO IDEA WHY, PLEASE EXPLAIN ME HOW DO YOU GET THIS. THANK YOU FOR ALL YOUR INPUTS. 
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| phuluong2k
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The simple way to answer this q is to make the 2X2 table
I suppose the population is 1000 x n, so prevalence = 100n
The 2x2 table
------------------------------ Cancer---------------- Non cancer ---------------- Total
PSA positive---------------- 80n = 80%x 100 n------- 90 n-------------------- 170n
PSA negative--------------- 20n------------------------810n = 90%x900n---- 830n
Total-------------------------100n---------------------- 900n------------------ 1000n
the likelihood that this man actually has prostate cancer = Positive predictive value
= 80n/170n = 47%
To symplify, you can eliminate n, suppose the population is 1000, ( you guess which number that help you to calculate easily, 100 is so small, 10.000 or more is so big )
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| chemamr
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WOW, excellent Luong Nguyen, i understand now. Thank you so much !
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| phuluong2k
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You are wellcome 
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| guayoman
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I was going to post the same Q Chema did. Then I found this thread by coincidence. Great explanation Phuluong. Thanx
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| mac007
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hey phuluong2k
q says specificity to be90% which is equal to TN/TN+FP so why u taking 810 as PSA negative, i guess it shd be 90 since this is true negative value ..............please explain phuluong or chemamr
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| phuluong2k
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specificity = True negative/ true negative + false positive
------------= True negative/ number of non - cancer = 90%
so True negative = 90%x 900 = 810.
90 is PSA positive, but non-cancer, so it is palse positive
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| mac007
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thanks phuloung2k i got it now
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| mayday
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Hi phuluong2k, do you think the "10% of men of this age have prostate cancer" is an extra info and not useful in calculation?
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| mayday
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Oh, nevermind, I got it
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| alenka
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Hi,guys!
let me give you my view on this question-it took me 2 days to figure it out,lol.
i guess in q like this you can't avoid N-you have to pick N-so 1000 is good enough.
then-they give you prevalence-10%,so that means that out of those 1000 people 10% will actually have cancer,which is 100 men.then they give them(THIS 100 MEN) this test-it took me a while to figure out that to determine sensitivity you have to run the test on men thet YOU ALREADY KNOW HAVE THE DISEASE.so 80% of the tests will come back positive-true positive since you already know that all this 100 people have cancer.the other 20% or 20 people will have negative test-you already know-false negative.
the second part-to figure out the specificity.Ok,we've started with 1000 people 100 of which have cancer,so we are left with 900,who are healthy and we know that for sure.now we run the test on them and 90% which is about 810 peope-comes back negative.and we know it's true negative since all 900 men are healthy.so the rest 10% or 90 people-are false positive.
now we are ready
cancer |non-cancer
test + | 80 | 90
test --- | 20 | 810
they want to know how sure you are if this patient with positive test really has cancer-PPV.
PPV -it's all about positive TEST=TP/TP+FP=80/80+90=47 %.
HOPE IT WILL HELP SOMEBODY.
GOOD LUCK.
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| frank100
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great thanks
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