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Old 07-04-2011
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Stats Calculating the Positive Predictive Value?

There is a epidemiology question in Kaplan Lecture Notes - CK that says
A 55 yrs old man visits a doctor with a urinary complaint. exam reveals 1 cm nodule on the prostate. The doctor orders PSA test. By common standard PSA more than 4 is abnormal. this test has sensitivity of 80%and specificity of 90%. a recent article found that in a cross sectional study 10% of men this age have prostate ca. The result of the man PSA is 7. What is the best estimate of the likelihood that this patient has prostate carcinoma.

A. 13%
B. 25%
C. 36%
D. 47%
E. 58%
F. 81%

THE CORRECT ANSWER GIVEN IS D 47%..what i want to know is that are they asking us to calculate the positive predictive value??..n how they arrived at the answer of 47%.pls explain in clarity.anyone.thnks
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Old 07-04-2011
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Check this out

http://en.wikipedia.org/wiki/Positive_predictive_value


They are using this equation



However I think we can't do this without a calculator, but I got the trick in this one:

The first step is making a 2 x 2 table with the data we have (ignore the dashes)

-----------------Disease
--------------(+)------(-)
Test------(+)--A-------B
----------------------------- <--- Don't ignore these dashes
----------(-)--C------- D


Sensitivity and specificity are values related to the TEST, the incidence and prevalence has nothing to do with them. So let's think that we have 200 patients in who we are screening prostate cancer, 100 have prostatic cancer and 100 does not have prostatic cancer (50% of prevalence)

-----------------Disease
----------------(+)-------(-)
Test------(+)---80-------10----->90 <-- this is the sum of this row
------------------------------------------
----------(-)----20-------90---->110 <-- this too

----------------100------100 <--- these is the sum of these columns

Do you remember that sensitivity is A/(A+C) ? and sensitivity is D/(B+D) ?
Check the table, you will realize that meets with the sensitivity and specificity of the question.

Now, we have the additional data about the 10% of prevalence of prostatic cancer. The positive predictive value is influenced by the prevalence. In the previous table we assumed that we had 50% of prevalence, so it is time to correct it by multiplying by 10 the patients who are negative to the disease:

-----------------Disease
----------------(+)-------(-)
Test------(+)---80-------100----->180 <-- this is the sum of this row
------------------------------------------
----------(-)----20-------900---->920 <-- this too

----------------100------1000--->>1100<<--- this is the total population (1100)

Now we have 100 who have prostatic cancer, and 1000 who don't. The prevalence is close (but not exactly) to 10% right? So now, you have to calculate the PPV which is A/(A+B) so we have now: 80 /(80+180) --> 80/180.
Now I admit that you have to do a little basic arithmetic calculation, and the answer is 0.44, which is close to 0.47, so you have the answer.

In this trick I showed you, the calculation doesn't has 0.47 as result because 100 is not the 10% of 1100, which is the total population, however the result is closer enough to pick a proper answer.

I hope this have helped you. Any questions are welcome

Last edited by Sadalssud; 07-04-2011 at 05:44 PM.
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Old 07-05-2011
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Quote:
Originally Posted by Sadalssud View Post
Check this out

http://en.wikipedia.org/wiki/Positive_predictive_value


They are using this equation



However I think we can't do this without a calculator, but I got the trick in this one:

The first step is making a 2 x 2 table with the data we have (ignore the dashes)

-----------------Disease
--------------(+)------(-)
Test------(+)--A-------B
----------------------------- <--- Don't ignore these dashes
----------(-)--C------- D


Sensitivity and specificity are values related to the TEST, the incidence and prevalence has nothing to do with them. So let's think that we have 200 patients in who we are screening prostate cancer, 100 have prostatic cancer and 100 does not have prostatic cancer (50% of prevalence)

-----------------Disease
----------------(+)-------(-)
Test------(+)---80-------10----->90 <-- this is the sum of this row
------------------------------------------
----------(-)----20-------90---->110 <-- this too

----------------100------100 <--- these is the sum of these columns

Do you remember that sensitivity is A/(A+C) ? and sensitivity is D/(B+D) ?
Check the table, you will realize that meets with the sensitivity and specificity of the question.

Now, we have the additional data about the 10% of prevalence of prostatic cancer. The positive predictive value is influenced by the prevalence. In the previous table we assumed that we had 50% of prevalence, so it is time to correct it by multiplying by 10 the patients who are negative to the disease:

-----------------Disease
----------------(+)-------(-)
Test------(+)---80-------100----->180 <-- this is the sum of this row
------------------------------------------
----------(-)----20-------900---->920 <-- this too

----------------100------1000--->>1100<<--- this is the total population (1100)

Now we have 100 who have prostatic cancer, and 1000 who don't. The prevalence is close (but not exactly) to 10% right? So now, you have to calculate the PPV which is A/(A+B) so we have now: 80 /(80+180) --> 80/180.
Now I admit that you have to do a little basic arithmetic calculation, and the answer is 0.44, which is close to 0.47, so you have the answer.

In this trick I showed you, the calculation doesn't has 0.47 as result because 100 is not the 10% of 1100, which is the total population, however the result is closer enough to pick a proper answer.

I hope this have helped you. Any questions are welcome
thnks aa lot for the answer.really appreciate ur help.i understoof the first half of the explanation.but could not understand about the prevalance being 50%before nthen how u calculate with 10%.sorry.still trying my best
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Old 07-05-2011
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Quote:
Originally Posted by samstar View Post
thnks aa lot for the answer.really appreciate ur help.i understoof the first half of the explanation.but could not understand about the prevalance being 50%before nthen how u calculate with 10%.sorry.still trying my best
Well, it is simple: When you have a sensitivity or specificity, they are showed as % right? in this case 80% and 90%, the easiest way to express this is using multiples of 10, such as 100 or 1000, so the calculations that we have to do will be easier and quicker.

I used that data to make the first table assuming that 100 were people with cancer and 100 were healthy, that is why I was saying that is 50% prevalence, because the total population in that table is 200, so 100 is the 50%. You can see that the sensitivity and specificity are 80% and 90% in this table.

Now, In order to build the another table, you have the data which says that the prevalence is 10%, so you must INCREASE the number of people who is in C and D, who are HEALTHY to decrease the incidence from 50% to 10% and make it match with the question. You can see that the sensitivity and specificity remains the same, 80% and 90%

Keep in mind that sensitivity and specificity are related only to the test.
Positive predictive value and negative predictive value depend on the prevalence of certain disease in a population.
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Old 09-10-2013
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Perfectly explained, understood it clearly, but one question please:
why do you multiply the 10% with the whole column of the SPECIFICITY, please explain, thanks in advance
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Old 10-12-2013
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i think always try to construct a 2/2 table before answering these questions. its simple and straight forward then. prevalence is needed to compute predictive values, we all know that .lets walk through this question together
1. if population size is not given, assume its 1000 (its nice round no and big enough for easy calculations)
2. as prevalence is 10% meaning out of 1000 population 100 are diseased and 900 are healthy.
3. sensitivity is 80 % meaning out of 100 diseased it will pick 80. meaning true positive = 80 and 20 will be false negative.
4. specificity is 90 % meaning out of 900 healthy 810 will be picked as healthy by the test i.e true negative = 810 and 90 will be false positive.
5.now u got all the values . put values in formula and there is answer

6. TP/ TP+FP = ppv
7. 80/ 80+90 = 80/170 = 0.47


i hope that helps
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6. TP/ TP+FP = ppv
7. 80/ 80+90 = 80/170 = 0.4
Good job.. I am also use 2x2 table always to calculate this type of qs.. 2x2 make it clear and easy.. Key point on this qs is 10%- if u get how to use it then u will get correct answer
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