A new screening test for a certain disease is being developed. The test was admi

Question

A new screening test for a certain disease is being developed. The test was administered to 780 persons, 120 of whom are known to have the disease. The new test was found to be positive in 100 of the 120 people with the disease, as well as in 30 people who do not have the disease: What is the sensitivity of the test? (Show your work) _____ What is the specificity of the test? (Show your work) _____ Assume that the sensitivity and specificity of the test remained the same but the prevalence of disease increased by 66%: How many false positives would there be? _____ How many false negatives would there be? _____

Explanation / Answer

1) a)Since 120 people have the disease, we have true positive=100, false negative=20

Sensitivity= true positives/(true positive + false negative)

=100/(100+20)

=100/120

=10/12

=0.8333

b) True negative =780-120=660 and false negative=120-100=20

Specificity=true negatives/(true negative + false positives)

=660/(660+20)=660/680=0.97059

2) a) Since, the prevalence of disease is increase by 66%, the true positive and false negative will increase by same amount. Thus,

true positive=100+100*66/100=166

b) False negative=20+20*66/100=20+13.2=33.2=33

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