1. Introduction to Logistic Regression
Coronary Heart Disease (CHD)
Baseline: CAT, ECG
Age: potential confounder or modifier

2. Definitions p = probability of CHD
C = catecholamine level (0=low, 1=high)
E = ECG (0=normal,1=abnormal)
A = age (in years)
p/(1-p) = odds of CHD
logit(p) = log(p/(1-p))

3. Logistic Model
The log of the odds of CHD as a linear combination C, E and A
Graphical Interpretation: 4 lines – log(odds) versus age; for each of the 4 C/E groups
No interactions

5. Estimates: So the estimates are:
logit chd cat ecg age
Logit estimates Number of obs =
LR chi2(3) =
Prob > chi2 =
Log likelihood = Pseudo R =
chd | Coef. Std. Err z P>|z| [95% Conf. Interval]
cat |
ecg |
age |
_cons |
So the estimates are:
This model assumes that the rate of change of the log of the odds of CHD per year of age does not depend on CAT or ECG and is estimated to be
There is another assumption here. See the graphs.

6. CAT effect & ECG effect
This model assumes that the effect of CAT on the log of the odds of CHD does not depend on ECG or age. It is estimated by:
This model assumes that the effect of ECG on the log of the odds of CHD does not depend on CAT or age. It is estimated by
…sound familiar?
Study the graphs to see this clearly
The dependent variable has changed. Instead of studying changes in expected values, we study changes in logarithms of odds.