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

2. 2 by 2 Contingency Tables Risk of disease: p1 or p2
Est: a/(a+b) and c/(c+d)
Risk Ratios: p1/p2
Est: a/(a+b)
c/(c+d)
Odd Ratios:
a/b or ad
c/d cb

3. 2 Mantel-Haenszel Tests
Suppose we have k strata producing k tables such as:
Mantel-Haenszel Test for association in stratified 2x2 tables
O = a1+…+ak
E = (a1+b1) (a1+c1)/n1 +…+ (ak+bk) (ak+ck)/nk
M-H = (|O-E|-0.5)2/V
Mantel-Haenszel Test for common OR in stratified 2x2 tables

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

5. Logistic Regression model:
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))= +1x1+…+ kxk

6. Slope=0.1
Slope=0.5
Slope=1
Slope=2
Logistic curves

7. Odds Ratio:
Assume that x1 is a binary factor.
B is the group x1=0
A is the group x1=1
Then the odds ratio
OR = pA(1- pA)/(pB(1- pB)) = exp{1}