Statistical models for categorical responses Logistic Regression Analysis

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Statistical models for categorical responses Logistic Regression Analysis 2 by 2 Contingency Tables •

Statistical models for categorical responses Logistic Regression Analysis 2 by 2 Contingency Tables • Odd Ratios • Risk Ratios • Mantel-Haenszel Test Survival Analysis

2 by 2 Contingency Tables • Risk of disease: p 1 or p 2

2 by 2 Contingency Tables • Risk of disease: p 1 or p 2 Est: a/(a+b) and c/(c+d) • Risk Ratios: p 1/p 2 Est: a/(a+b) c/(c+d) • Odd Ratios: a/b or ad c/d cb

2 Mantel-Haenszel Tests Suppose we have k strata producing k tables such as: •

2 Mantel-Haenszel Tests Suppose we have k strata producing k tables such as: • Mantel-Haenszel Test for association in stratified 2 x 2 tables O = a 1+…+ak E = (a 1+b 1) (a 1+c 1)/n 1 +…+ (ak+bk) (ak+ck)/nk M-H = (|O-E|-0. 5)2/V • Mantel-Haenszel Test for common OR in stratified 2 x 2 tables

Dataset EAR Column Variable Format or Code --------------------------1 -3 ID 5 Clearance by 14

Dataset EAR Column Variable Format or Code --------------------------1 -3 ID 5 Clearance by 14 days 1=yes/0=no 7 Antibiotic 1=CEF/2=AMO 9 Age 1=<2 yrs/2=2 -5 yrs/3=6+ yrs 11 Ear 1=1 st ear/2=2 nd ear --------------------------

Logistic Regression Analysis When to Use it: • Response is categorical • Several Confounding

Logistic Regression Analysis When to Use it: • Response is categorical • Several Confounding factors or Numeric Covariates Logistic Regression model: Logit(p) = log(p/(1 -p))= + 1 x 1+…+ kxk

Logistic curves Slope=2 Slope=1 Slope=0. 5 Slope=0. 1

Logistic curves Slope=2 Slope=1 Slope=0. 5 Slope=0. 1

Odds Ratio: Assume that x 1 is a binary factor. B is the group

Odds Ratio: Assume that x 1 is a binary factor. B is the group x 1=0 A is the group x 1=1 Then the odds ratio OR = p. A(1 - p. A)/(p. B(1 - p. B)) = exp{ 1}