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#1
03-25-2012
 USMLE Forums Veteran Steps History: 1+CK+CS Posts: 257 Threads: 49 Thanked 75 Times in 50 Posts
Specificity Sensitivity Question!

Assuming that mammography has a sensitivity of 90% and a specificity of 98% and that consecutive tests are independent, what is the probability that a woman with breast cancer will have a negative yearly screening mammogram for
two consecutive years?
a. 1/10
b. 2/10
c. 4/10
d. 1/100
e. 4/100

#2
03-25-2012
 USMLE Forums Guru Steps History: Step 1 Only Posts: 452 Threads: 11 Thanked 354 Times in 197 Posts Reputation: 364

D.........
#3
03-25-2012
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 529 Threads: 57 Thanked 284 Times in 152 Posts Reputation: 294
D

They are asking about the probability of FALSE NEGATIVE results of mammogram for 2 consecutive events. FALSE NEGATIVE RATE = 1-seNsitivity = 1-0.9 = 0.1

Now the probability of having 2 false negative results in 2 consecutive yrs are independent events so u multiply the probabilities 0.1*0.1 or 1/10*1/10 =1/100 (option d)
 The above post was thanked by: Dr. Mexito (03-25-2012), excellence (05-18-2014), Hope2Pass (03-26-2012), Kruno (03-15-2016), taher (11-16-2013)

#4
03-26-2012
 USMLE Forums Veteran Steps History: 1+CK+CS Posts: 257 Threads: 49 Thanked 75 Times in 50 Posts

yup the answer is D
#5
11-16-2013
 USMLE Forums Scout Steps History: Not yet Posts: 65 Threads: 9 Thanked 14 Times in 9 Posts Reputation: 24

Guys, I donot understand why do we have to multiply 1/10 of the first year with the 1/10 of next year as those two tests are independent. Why the answer is not just 1/10. Please explain?

If sensitivity is 90% means, out of 100 diseased 90 were correctly identified as diseased (True Positives) and 10% were missed (False negatives) &

If the specificity is 98% means, out of 100 healthy people 98 were correctly identified as normal (True negatives) and 2 were missed (False positives)

False Negative rate = False negatives/ No. of diseased = 10/100 = 1/10. I can get this far. But the multiplying thing. Elaborate please..........
#6
08-10-2016
 USMLE Forums Newbie Steps History: Not yet Posts: 3 Threads: 0 Thanked 0 Times in 0 Posts Reputation: 10

Quote:
 Originally Posted by devareddy Guys, I donot understand why do we have to multiply 1/10 of the first year with the 1/10 of next year as those two tests are independent. Why the answer is not just 1/10. Please explain? If sensitivity is 90% means, out of 100 diseased 90 were correctly identified as diseased (True Positives) and 10% were missed (False negatives) & If the specificity is 98% means, out of 100 healthy people 98 were correctly identified as normal (True negatives) and 2 were missed (False positives) False Negative rate = False negatives/ No. of diseased = 10/100 = 1/10. I can get this far. But the multiplying thing. Elaborate please..........

You have to multiply because we have to find the <probability that a woman with breast cancer will have a negative yearly screening mammogram for two consecutive year>. So she has to have 2 negative yearly screening mammograms for 2 consecutive years.
This type of probability is called COMPOUND PROBABILITY and it can be calculated by multiplying the porbabilities of each independent event.

So we have two independets events with a probability of 1/10 each one; we multiply 1/10*1/10 and we find 1/100 (answer D).

 Tags Biostatistics-Epidemiology, Step-1-Questions

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