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A disease has a prevalence of 11%. A diagnosis has 85% probability of correctly identifying the disease. This is called Sensitivity. The test also has a 20% probability of wrongly labeling a subject as positive. (In other words, Specificity is 80%). Estimate the probability that person who is tested negative has the disease?

A disease has a prevalence of 11%. A diagnosis has 85% probability of correctly identifying the disease. This is called Sensitivity. The test also has a 20% probability of wrongly labeling a subject as positive. (In other words, Specificity is 80%). Estimate the probability that person who is tested negative has the disease?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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A disease has a prevalence of 11%. A diagnosis has 85% probability of correctly identifying the disease. This is called Sensitivity. The test also has a 20% probability of wrongly labeling a subject as positive. (In other words, Specificity is 80%). Estimate the probability that person who is tested negative has the disease?
Transcribed Image Text:A disease has a prevalence of 11%. A diagnosis has 85% probability of correctly identifying the disease. This is called Sensitivity. The test also has a 20% probability of wrongly labeling a subject as positive. (In other words, Specificity is 80%). Estimate the probability that person who is tested negative has the disease?
Expert Solution
Step 1

Let D=The Person has the disease.

Dc=The person doesn't have the disease.

P=The person is tested positive.

N=The person is tested negative.

Given,

P(D)=11%=0.11

P(Dc)=1-P(D)=1-0.11=0.89

P(P|D)=85%=0.85

P(N|D)=1-P(P|D)=1-.85=0.15

P(P|Dc)=20%=0.2

P(N|Dc)=80%=0.8

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