Question 1 David is extremely bored one day. He goes through his previous 200 em

Question

Question 1

David is extremely bored one day. He goes through his previous 200 emails, including his spam folder, to determine which emails should have truly been marked as spam or not. He obtains the following results:

(a) What is the prevalence of spam?

(b) What is the sensitivity of the spam filter?

(c) What is the specificity of the spam filter?

(d) What is the positive predictive value of the spam filter?

(e) What is the negative predictive value of the spam filter?

Question 2

It is known that there are a number of possible genetic risk factors for Alzheimer’s disease. Certain alleles on the gene APOE are the most well known. Alzheimer’s is thought to effect 11% of poeople over the age of 65 in the United States. There are currently a large number of tests for Alzheimer’s. Consider a (fictitious) test that when administered to individuals over 65 years old:

Detects Alzheimer’s 94% of the time when it is present.

Detects Alzheimer’s 7% of the time when it is not present.

(a) What is the prevalence of Alzheimer’s in the population? (Those aged 65 years or more living in the United States.)

(b) What is the sensitivity of the test?

(c) What is the specificity of the test?

(d) What is the positive predictive value of the test?

(e) What is the negative predictive value of the test?

Explanation / Answer

1.

a)

P = (24+1)/200 = 0.125 [ANSWER]

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b)

P(MS|TS) = 24/(24+1) = 0.96 [ANSWER]

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c)

P(MNS|NS) = 165/(165+10) = 0.942857143 [ANSWER]

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d)

P(TS|MS) = 24/(24+10) = 0.705882353 [ANSWER]

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e)

P(NS|MNS) = 165/(165+1) = 0.993975904 [ANSWER]

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