part15 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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Unformatted text preview: Public Health 6450 Fall 2011 Lynn Eberly and Andy Mugglin Division of Biostatistics School of Public Health University of Minnesota [email protected] Part 15 Review Contexts in Which Comparisons of Binomial Proportions Arise Risk Differences and Relative Risks for Binomial Proportions Odds Ratios for Binomial Proportions Where are we going? Previously: I One-sample hypothesis testing and CIs for H : p = p (Chapter 8.1) I Two-sample hypothesis testing and CIs for H : p 1- p 2 = 0 (Chapter 8.2) Current topics: I Two-by-two tables and study designs for comparing Binomial proportions (not in M,M &C) I Relative risks and odds ratios for comparing Binomial proportions (not in M,M &C) Eberly and Mugglin PubH 6450 Fall 2011 Part 15 2 / 41 Review Contexts in Which Comparisons of Binomial Proportions Arise Risk Differences and Relative Risks for Binomial Proportions Odds Ratios for Binomial Proportions Two-by-Two Tables The data from two-sample Binomial problems (such as those we’ve seen), with X 1 ∼ B ( n 1 , p 1 ) and X 2 ∼ B ( n 2 , p 2 ), can be summarized in a table: Success Group Yes No Total 1 X 1 ( a ) n 1- X 1 ( b ) n 1 2 X 2 ( c ) n 2- X 2 ( d ) n 2 We estimate p 1 and p 2 with I ˆ p 1 = X 1 / n 1 = a / ( a + b ) (The red letters are a switch in I ˆ p 2 = X 2 / n 2 = c / ( c + d ) . notation to match M,M &C) Eberly and Mugglin PubH 6450 Fall 2011 Part 15 3 / 41 Review Contexts in Which Comparisons of Binomial Proportions Arise Risk Differences and Relative Risks for Binomial Proportions Odds Ratios for Binomial Proportions Two-by-Two Tables (cont’d) I In many public health and medical contexts, we think of the rows as ‘exposure’ and the columns as ‘disease.’ I If the n 1 exposed individuals were randomly sampled from the population of exposed persons, and the n 2 unexposed individuals were randomly sampled from the population of unexposed persons, then p 1 = Pr(disease | exposed) estimated with ˆ p 1 p 2 = Pr(disease | unexposed) estimated with ˆ p 2 I The probability of having the disease is called the risk of disease. In what kinds of study designs do these tables arise? Eberly and Mugglin PubH 6450 Fall 2011 Part 15 4 / 41 Review Contexts in Which Comparisons of Binomial Proportions Arise Risk Differences and Relative Risks for Binomial Proportions Odds Ratios for Binomial Proportions Seat Belt Use and Fatal Accidents Records of accidents in 1998 by the Department of Highway Safety and Motor Vehicles in Florida: Safety Equipment Injury in Use Fatal Nonfatal Total None 1601 162,527 164,128 Seat belt 510 412,368 412,878 Total 2111 574,895 577,006 We are interested in Pr(disease | exposure), specifically in comparing Pr(fatal accident | no seat belt) to Pr(fatal accident | seat belt)....
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part15 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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