Logistic Regression

Lead Author(s): Jeff Martin, MD

Definition of Logistic Regression

Logistic regression is the method of multivariable analysis used most often in cross-sectional and case-control studies.

In logistic regression the log odds of the outcome is modeled with the linear equation:

Log odds (called the logit, hence logistic regression) are used because

They extend from minus to plus infinity and therefore do not constrain the prediction of the linear model
Unlike directly modeling the probability, which has a minimum of 0 and a maximum of 1,
Unlike the odds, which has a minimum of 0.

Prediction in a linear model isn’t constrained to a 0 minimum or a 1 maximum,

So exponentiating the b from a logistic equation returns an odds for one unit of change in the variable x.

In the case of a dichotomous variable x, the b is comparing the odds for the variable = 1 versus the variable = 0.
In other words, exponentiating b gives the odds ratio for the two values of x.
In the case of a continuous variable x, exponentiating b gives the odds ratio for a one unit difference in the value of x