Stat 491 Chapter 3--Probability

# why would the probability be so low in 1 while the

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Unformatted text preview: in the region, roughly 2 people [.002 .997 1000 = 1.994] would have HIV and the test would give positive result. Approximately, the test gives positive results for roughly 17[(.002 .997 + .015 .998) 1000 = 16.964] people. The test gives positive results for 15 more than actually are. Hence, the probability that the person have HIV given a positive test result is 1.994/16.949 = 11.7543%. 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... The two lessons to be learnt from this example are 1 2 The patient must be told his likelihood in addition to the specificity and sensitivity of the test, NOT just the readout. The prevalence information is very important in determining the person's likelihood. The best course of action may be to do a more accurate (Western Blot Procedure) test if a positive readout is met. The combination of these two procedures is highly accurate. In the previous calculation, we updated the person's prior probability of infection in light of the test result to get the person's posterior probability of infection. This is a special cases of the general class of inference known us Bayesian Inference. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Generalization of Bayes' Rule Let B1 , B2 , . . . , Bm be a set of mutually exclusive and exhaustive disease states. Let A be the presence of a symptom or set of symptoms. Then P(Bi |A) = P(A|Bi ) P(Bi ) m . P(A|Bj ) P(Bj ) j=1 Read Example 3.27 in the textbook. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Summary Defined Probability Addition and multiplication laws Independent and dependent events Conditional Probability and Relative Risks to quantify the dependence between events. Accuracy of screening tests defined as an application of conditional probabilities. Application of Bayes' rule for computing PV + and PV - when only sensitivity, specificity and prevalence are known. This is a special case of Bayesian Inference. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Homework Problems 3.49, 3.50, 3.75, 3.83, 3.84 Chapter 3: Probability Stat 491: Biostatistics...
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