a thousand men in a cohort for which prostate cancer prevalence is 2.2%. The test we're using for prostate cancer has a sensitivity of 0.6 (gets the diagnosis right 60% of the time if a patient has prostate cancer) specificity of 0.95 (gets the diagnosis right 95% of the time if a patient does not have prostate cancer) Fill in the tree with the correct number of patients in each cell, and give the probability that a man actually has prostate cancer, given a positive test result.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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There are a thousand men in a cohort for which prostate cancer prevalence is 2.2%.

The test we're using for prostate cancer has a

  • sensitivity of 0.6 (gets the diagnosis right 60% of the time if a patient has prostate cancer)
  • specificity of 0.95 (gets the diagnosis right 95% of the time if a patient does not have prostate cancer)

Fill in the tree with the correct number of patients in each cell, and give the probability that a man actually has prostate cancer, given a positive test result.

Probability =    

1000
B+
B
Preview
Preview
T+
T
T
Preview
Preview
Preview
Preview
Transcribed Image Text:1000 B+ B Preview Preview T+ T T Preview Preview Preview Preview
Expert Solution
Step 1

Given:

B+ denotes prostate cancer, B- denotes no prostate cancer, 

T+ denotes positive result, T- denotes negative result.

P(B+) = 0.022

P(right diagnosis | B+) = 0.60

P(right diagnosis |  B-) = 0.95

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