Stat 491 Chapter 3--Probability

# Stat 491 Chapter 3-Probability

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Unformatted text preview: al Probability Bayes' Rule and Screening Tests Bayes' Rule Let A = Symptom and B = disease. P(B) = is the probability of the disease in the reference population. P(B) is also known as the prevalence of the disease in the reference population. The prevalence information can be combined with the specificity and sensitivity information to get PV + and PV - . Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Bayes' Rule Cont'd... Bayes' Rule says that the Predictive Value Positive is given by PV + = P(A|B) P(B) P(A|B) P(B) + P(A|B) P(B) Sensitivity Prevalence = Sensitivity Prevalence + (1 - Specificity) (1 - Prevalence) Similarly, the Predictive Value Negative is given by PV - = P(A|B) P(B) B) P(B) + P(A|B) P(B) P(A| Specificity (1 - Prevalence) = Specificity (1 - Prevalence) + (1 - Sensitivity) Prevalence Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Bayes' Rule: Example It is known that Enzyme-Linked Immunosorbent Assay (ELISA) test for HIV infection has 99.7% sensitivity and 98.5% specificity. What is the likelihood that a person has been infected with HIV if he or she had a positive test readout given that 1 2 the prevalence of HIV infection in the region where the patient is from is 0.2%? the patients decision to come for a test resulted from his or her concern of high-risk behavior and the prevalence of HIV infection among high-risk groups in the person's region is 20%. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Bayes' Rule: Example Cont'd... Why would the probability be so low in (1) while the tests are very accurate? This is easy to explain. The test has high false positive rate compared to the prevalence HIV. Of 1000 people...
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## This note was uploaded on 10/30/2013 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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