1. Logistic regression
One of the most common types of modeling in the biomedical literature
Especially case-control studies
Used when the outcome is binary (yes/no)
Produces (functions of) odds ratios
Can be simple (one predictor) or multiple (two or more predictors)

2. Logistics of logistic regression
ln(odds) = β0 + β1X1 + β2X2 +…+ ε
(Which is similar to the equation for linear regression:
Y = β0 + β1X1 + β2X2 +…+ ε)
Why ln(odds)?
Probability can only be between 0 and 1 (severely non-normal).
Odds can only be between 0 and infinity (not normal)
“Log odds” can take on any value and is normal-ish enough.

3. Logistic regression example
From Lesko SM et al. JAMA 1993;269:
Where does this odds ratio come from?

4. From Lesko SM et al. JAMA 1993;269:998-1003
Where does OR come from?
From Lesko SM et al. JAMA 1993;269:
ln(odds) = β *[level 4 baldness(y/n)] + β2*age + β3*race + β4*religion + β5*education + β6*BMI + β7*alcohol + more βs)

5. Interpretation of ORs Odds ratios represent
The ratio of the odds of getting the outcome comparing exposed to unexposed
The multiplicative increase in odds of getting the outcome for each one-unit change in the exposure
ln(odds of MI) = β0 + β1(height [in]), where β1 = 0.15
This means that for each 1-inch increase in height, the odds of getting a MI increases by a factor of exp(0.15), or 16%

6. Things we talked about Correlation analysis (Pearson’s r)
Compared linear regression and correlation
Linear regression set up and interpretation
Distinction between linear and logistic regression
Multivariate regression and confounding
Logistic regression set up and interpretation