Stat 491 Chapter 3--Probability

Suppose the ethnic distribution in houston tx is 30

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Unformatted text preview: s and 5% Asian American. What is the overall probability of type II DM among 40 to 59 year-old in Houston? Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Total Probability Rule: Example cont'd... Let A1 = {Caucasian}, A2 = {African American}, A3 = {Hispanics}, A4 = {Asian American} and B = {Having Type II DM}. Then, P(B) = P(B|A1 ) P(A1 ) + P(B|A2 ) P(A2 ) + P(B|A3 ) P(A3 ) + P(B|A4 ) P(A4 ) = (.07)(.3) + (.1)(.25) + (.12)(.4) + (.05)(.05) = 0.0965. Therefore, the overall probability of type II DM among 40 to 59 year-old in Houston is 0.0965. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Generalized Multiplication Rule Let A1 , A2 , . . . , Am be arbitrary set of events, not necessarily mutually independent. P(A1 A2 Am ) = P(A1 ) P(A2 |A1 ) P(A3 |A2 A1 ) P(Am |A1 A2 Am-1 ) This is a direct consequence of definition of conditional probability. The rule reduces to the multiplication law discussed before if the events A1 , A2 , . . . , Am are mutually independent. Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability Conditional Probability Bayes' Rule and Screening Tests Predictive Value, Sensitivity and Specificity Predictive Value Positive of a screening test PV + = P(disease|test+ ) Predictive Value Negative of a screening test PV - = P(no disease|test- ) Sensitivity of a screening test Sensitivity = P(test+ |disease) Specificity of a screening test Specificity = P(test- |no disease) Question: Which of the above information do you think can be directly measured by clinicians? Chapter 3: Probability Stat 491: Biostatistics Probability and Inference Definitions and Properties Event Relations Laws of Probability...
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