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#1
11-29-2013
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A Complicated PPV Question!

A test yields 80% infected and 10% non-infected.....prevalence is 10%.
What is positive predictive value?

A. 47%
B. 54%
C. 75%
D. 25%

#2
11-29-2013
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A. 47%

Assuming total population of 100. 10% prevalence would mean total diseased number to be 10 out of which 80%(8) are ruled + by test. And so on. 8+9/17=0.47

Could you give the answer with possible explanation if I'm headed in the wrong direction.
#3
11-29-2013
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sure i will let you know answer with explanation..waiting for some more answers...
Can you please explain how you calculated specificity??

#4
11-29-2013
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Okay. 1. I think I calculated something else in previous reply so ignore that. 2. Could you please write the whole question because either you wrote the question wrong or the answer I'm getting from your given values is not any one of the options.
Thank you.
#5
11-30-2013
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Same here just as insomniac did. I also got a different answer somewhere around 80%
#6
11-30-2013
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New stool test for shigella infection yields postive results in 80% of infected patients and in 10% of uninfected patients ...prevalence of shigela in population is 10%..What is the probability that a patient who tests positive with the new test is infected with shigella ..

P.s: insomiac u were right BUT 8+9/17 = 0.47 .plz explain this equation.
#7
11-30-2013
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Quote:
 Originally Posted by medicalbiology Question: A test yields 80% infected and 10% noninfected.....prevalence is 10% ...what is positive predicted value ?? a.47% b.54% c.75% d.25%

very confusing question!

if i suppose 80% infected as sensitivity and 10% noninfected as specificity then with a prevalnce of 10% , the positive predictive value is 8%.

now,if the question is correctly asked then i must have misinterpreted it.

'test yields 80% infected' means all the positive results ( TP and FP included ), then 80% is not the sensitivity n our whole calculation collapses n i can't find the answer then without sensitivity n specificity.
#8
11-30-2013
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Quote:
 Originally Posted by medicalbiology New stool test for shigella infection yields postive results in 80% of infected patients and in 10% of uninfected patients ...prevalence of shigela in population is 10%..What is the probability that a patient who tests positive with the new test is infected with shigella .. P.s: insomiac u were right BUT 8+9/17 = 0.47 .plz explain this equation.
equation is simple, Insomniac has wrongly put 9 in the numerator.

with 80% sensitivity n 10% specificity, using 2 by 2 table,
TP=80 , FP=90
FN=20, TN=10

PPV = 80/80+90 = 80/170 = 47%
#9
11-30-2013
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Quote:
 Originally Posted by medicalbiology New stool test for shigella infection yields postive results in 80% of infected patients and in 10% of uninfected patients ...prevalence of shigela in population is 10%..What is the probability that a patient who tests positive with the new test is infected with shigella .. P.s: insomiac u were right BUT 8+9/17 = 0.47 .plz explain this equation.

i am using this formula only using sensitivity and specificity,not putting 10% prevalence in consideration.

if using 10% prevalence in the formula, i get a diferent answer!

plz xplain medicalbiology!
#10
11-30-2013
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Quote:
 Originally Posted by organo14 equation is simple, Insomniac has wrongly put 9 in the numerator. with 80% sensitivity n 10% specificity, using 2 by 2 table, TP=80 , FP=90 FN=20, TN=10 PPV = 80/80+90 = 80/170 = 47%
If this should b the case thn FP must equal to 10 not 90,
as q says test is positive in. 10 % who dnt hav disease
consequentlt equation become
80/80+10= 88%

If i m wrong correct me plz??
#11
11-30-2013
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organ14 i am also confused in specificty thing..... According to statement it should be 10% specificity .. I willl let u know uworld explanation soon but explanation is also not very helpful...
#12
11-30-2013
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Quote:
 Originally Posted by hardtime If this should b the case thn FP must equal to 10 not 90, as q says test is positive in. 10 % who dnt hav disease consequentlt equation become 80/80+10= 88% If i m wrong correct me plz??
Exactly hardtime FP should be 10 NOT 90..
#13
11-30-2013
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the question is wrongly put,

the specificity = 90%
sensitivity = 80%
prevalence of infection = 10%
suppose we have 1000 pts,
then

infected noninfected

test +ve 80 90 = 170
test -ve 20 890 = 910

100 900 = 1000

so PPV = 80/170 = 47%
 The above post was thanked by: devareddy (11-30-2013), dr mumble (09-12-2014), nsesereso (12-02-2013)
#14
11-30-2013
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Quote:
 Imagine that population consist of 100 patients .Since the disease prevalence is 10% that means 10 patients have disease and 90 do not ..Performing a test with with 80% sensiitivity on 10 diseased patients yields 8 TF . performing a test with 90% specificity on 90patients without disease yield 9 FP .. PPV = 8/(8+9) = 47%
BUT same question how specificity is 90% ?
#15
11-30-2013
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Quote:
 Originally Posted by medicalbiology Answer is: BUT same question how specificity is 90% ?
Got it

sensitivity = 80 %

FP as question mentioned = 10% = and we know that 1-specificity=FP r specificity = 1-FP rates

So putting values = 1 - .1 = .9 r 90/100

We make square

Disease present disease absent
test positive 8 (TP) 9 (FP)

test negitive 2 (FN) 81 (FN)

10 90 100

By putting values we get the ans

#16
11-30-2013
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Here's the explanation.

Seems like I guessed correctlywhat medicalbiology was trying to say in the first post.
Here's how I had gotten around it.
Attached Thumbnails

 The above post was thanked by: medicalbiology (12-01-2013), nsesereso (12-02-2013), Subuhi (12-02-2013)
#17
11-30-2013
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Quote:
 Originally Posted by Insomniac Seems like I guessed correctlywhat medicalbiology was trying to say in the first post. Here's how I had gotten around it.
but how do we know that 10 percent were labeled as false positive...
#18
11-30-2013
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Quote:
 Originally Posted by CisternaChyli but how do we know that 10 percent were labeled as false positive...
@CisternaChyli

It states that right in the question.
"New stool test for shigella infection yields postive results....."in 10% of uninfected patients""
#19
11-30-2013
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Quote:
 Originally Posted by Insomniac @CisternaChyli It states that right in the question. "New stool test for shigella infection yields postive results....."in 10% of uninfected patients""
whoops my bad, i didnt read carefully . It all makes sense now, just gotta read carefully. I get tripped up cause i forget to just assume the amount of patients.
#20
12-01-2013
 USMLE Forums Master Steps History: CS Only Posts: 557 Threads: 29 Thanked 296 Times in 186 Posts Reputation: 316

Quote:
 Originally Posted by medicalbiology A test yields 80% infected and 10% non-infected.....prevalence is 10%. What is positive predictive value? A. 47% B. 54% C. 75% D. 25%

It would be really helpful if you could tell us where this question is from, because if it is from NBME I won't look at it, same goes for uworld
Secondly, please just post the whole question next time.
The way you put it at first is so confusing, there is no way I could have known what this question is asking...
Please everyone who posts questions, lets try to do it the right way so that it helps us all!
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#21
12-01-2013
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I have a question...

what if the specificity and sensitivity is the same... ex. 45% and prevalence is 30%.

Then asked to calculate prevalence.. what would the prevalence be in this example?
#22
12-01-2013
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val7 itz from uworld....Actually it is not allowed to write whole question of copyright material..
#23
12-01-2013
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PPV = TP/(TP+FP). It was impossible to work out the TP or FP rate from the way the original question was worded.

Sky_blue2000, your question is confusing, If the prevalence is 30%, then the prevalence is 30%
#24
12-01-2013
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Oh sorry!!

I meant what would the PPV be if the prevalence is 30%

and specificity and sensitivity are both 45%
#25
12-01-2013
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Lets say sample size is 1000 patients

Prevalance = 30%

Therefore diseased = 300, non diseased = 700

We now need to work out our TP and FP numbers

Sensitivity = 45% In other words this test will give a positive result in 45% of the people with the disease (ie its rubbish!)

So the True Positive rate = 300 x 45% = 135.

This means that the False Negative rate, which is all the patients our test missed, is 300 - 135 = 165

Now, specificity = 45%

This means that, out of all the 700 patients without disease, our test will give a truly negative result only 45% of the time

So our True Negative rate = 700 x 45% = 315

This means that the False Positive rate, which is all the patients without disease that our test gave a positive result for, is 700 - 315 = 385

We now have all the numbers needed to make a 4x4 table and work out anything else.

The PPV = TP/(TP+FP) = 135/(135+385) = 26%

So the test is worse than simply tossing a coin...
 The above post was thanked by: Doc889 (01-23-2014), medicalbiology (12-01-2013), sky_blue2000 (12-01-2013)

#26
12-01-2013
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Quote:
 Originally Posted by USMLEUK. Lets say sample size is 1000 patients Prevalance = 30% Therefore diseased = 300, non diseased = 700 We now need to work out our TP and FP numbers Sensitivity = 45% In other words this test will give a positive result in 45% of the people with the disease (ie its rubbish!) So the True Positive rate = 300 x 45% = 135. This means that the False Negative rate, which is all the patients our test missed, is 300 - 135 = 165 Now, specificity = 45% This means that, out of all the 700 patients without disease, our test will give a truly negative result only 45% of the time So our True Negative rate = 700 x 45% = 315 This means that the False Positive rate, which is all the patients without disease that our test gave a positive result for, is 700 - 315 = 385 We now have all the numbers needed to make a 4x4 table and work out anything else. The PPV = TP/(TP+FP) = 135/(135+385) = 26% So the test is worse than simply tossing a coin...

Thank you soo much!! Great explanation
#27
12-01-2013
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Waoh!, that was a pain.:p

Quote:
 Originally Posted by sky_blue2000 Oh sorry!! I meant what would the PPV be if the prevalence is 30% and specificity and sensitivity are both 45%

Applying Bayes Theorem:

PPV = Sensitivity x Prevalence/ [ (Sensitivity x Prevalence) + (1-Specificity)(1-Prevalence)]

Plug in those values and you get ~26% PPV
 The above post was thanked by: Doc889 (01-23-2014), USMLEUK. (12-01-2013)
#28
12-01-2013
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Ha, i remember seeing that on uworld and clearly totally didnt take it in...
#29
12-01-2013
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confusion..

Quote:
 Originally Posted by USMLEUK. Lets say sample size is 1000 patients Prevalance = 30% Therefore diseased = 300, non diseased = 700 We now need to work out our TP and FP numbers Sensitivity = 45% In other words this test will give a positive result in 45% of the people with the disease (ie its rubbish!) So the True Positive rate = 300 x 45% = 135. This means that the False Negative rate, which is all the patients our test missed, is 300 - 135 = 165 Now, specificity = 45% This means that, out of all the 700 patients without disease, our test will give a truly negative result only 45% of the time So our True Negative rate = 700 x 45% = 315 This means that the False Positive rate, which is all the patients without disease that our test gave a positive result for, is 700 - 315 = 385 We now have all the numbers needed to make a 4x4 table and work out anything else. The PPV = TP/(TP+FP) = 135/(135+385) = 26% So the test is worse than simply tossing a coin...
u xplained it really well but i have 1 confusion.. in calculating the TP u did 300 x 45% .. thn did u divide it by 100 to get rid of the % ??

i knw my ques is lame but jst want to b sure.. weak in maths :/

thanks..
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#30
12-02-2013
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yep, multiplying something by 45% (per-cent) just means multiplying by "45 per 100" ie 45/100, or 0.45
#31
12-02-2013
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This same question was discussed in the beh science vedio of Kaplan. The answer is 47%. Insomnia's photograph explanation is correct!
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