SOLUTION: A drug company is developing a new pregnancy-test kit for use on an outpatient basis. The company uses the pregnancy test on 100 women who are known to be pregnant, for whom 96 tes

Question 1018815: A drug company is developing a new pregnancy-test kit for use on an outpatient basis. The company uses the pregnancy test on 100 women who are known to be pregnant, for whom 96 test results are positive. The company uses the pregnancy test on 100 other women who are known to not be pregnant, of whom 99 test negative.
a) Calculate the sensitivity, specificity and predictive positive value of the test. Write the formula and show your work.

Found 2 solutions by mathmate, Boreal:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A drug company is developing a new pregnancy-test kit for use on an outpatient basis. The company uses the pregnancy test on 100 women who are known to be pregnant, for whom 96 test results are positive. The company uses the pregnancy test on 100 other women who are known to not be pregnant, of whom 99 test negative.
a) Calculate the sensitivity, specificity and predictive positive value of the test. Write the formula and show your work.

Solution:
Define the following events:
D=event of having the disease
~D=event of not having the disease
+=even of testing positive
~+=event of testing negative
and
p = prevalence of disease (pregnancy)
Then
P(+|D)= A =true positive = 0.96p
P(+|~D)= B = false positive = (1-0.99)(1-p)=0.01(1-p)
P(~+|D)= C = false negative = (1-0.96)p=0.04p
P(~+|~D)= D = true negative = 0.99(1-p)

Sensitivity
= probability of testing positive given patient has disease
= A/(A+C)
= 0.96p/(0.96p+0.04p)
= 0.96

Specificity
= probabiliy of testing negative given patient does not have disease
= D/(D+B)
= 0.99(1-p)/[(0.01+0.99)(1-p)]
= 0.99

Positive Predictive Value
= probability that patient has disease given he/she tests positive
= A/(A+B)
= 0.96p/(0.96p+0.01(1-p))
= 0.96p/(0.95p+0.01)
(value can be evaluated numerically once the prevalence of pregnancy is known for the population of the experiment)

For more information, read:
https://onlinecourses.science.psu.edu/stat507/node/71

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
====T+===T-===Total
P+==96===4=== 100 pregnant
P-== 1===99===100 not pregnant
T===97==103===200
Sensitivity is proportion of people pregnant who are correctly diagnosed.
P(T+|P+), given that they are pregnant, what is the probability they test positive.
Specificity is proportion of people not pregnant who are correctly diagnosed. Given that they are not pregnant, what is the probability they test negative
P(T-|P-)
Positive predictive value of the test is sum of true positives/TP+FP.
(96/97).
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