Logistic Regression

Stratified analysis can be used to adjust for confounding, but the results can be difficult to adjust multiple confounders. If we have too many strata, we could end up with very small tables or 0 counts for some cells. WE can instead use Logistic Regression when the following situation exists:

• The design is cross-sectional, case-control, cohort, or clinical trial
• The outcome (D) is dichotomous
• Any type of exposure (continuous, categorical or ordinal)
• Confounders/covariates can be continuous, categorical or ordinal

Goals of Logistic Regression

• Association: Between an outcome and a set of independent variables
• Prediction: What do we expect the probability of outcome to be given the set of independent variables?
• Exploratory: What variables are associated with outcome?
• Adjustment for Confounding: Focus on a particular relationship; the other variables in the model are there for adjustment

Logistic Regression Model

We assume a linear relationship between the predictor variable(s) and the Log-odds of an event that Y = 1:

For risk p (if the design is appropriate: