Logistic regression
What question does this help answer?
“Which factors are associated with whether an event occurred, and what are the adjusted odds ratios?”
When to use it
Use binary logistic regression when the outcome has two states, such as readmission yes/no, disease present/absent, or treatment response yes/no.
When not to use it
If follow-up duration differs meaningfully and time-to-event information matters, survival analysis may be more appropriate. For common outcomes, odds ratios can differ substantially from risk ratios, so the estimand should be chosen deliberately.
How it works in plain language
The model relates predictors to the log odds of the outcome. Exponentiating a coefficient gives an odds ratio.
Why Mallard may recommend it
Mallard may recommend logistic regression when the plan has a binary primary outcome and adjustment for several predictors or confounders is needed.
Key assumptions
- Observations are independent unless dependence is explicitly modeled.
- Continuous predictors are modeled appropriately on the logit scale.
- Severe multicollinearity and complete or quasi-complete separation are addressed.
- The chosen predictors match the scientific objective.
- Sufficient outcome events exist for the intended model complexity.
What to watch out for
An odds ratio is not the same as a risk ratio. Logistic regression can support prediction or association analyses, but a regression coefficient is not automatically a causal effect.
Clinical example
Model 30-day readmission as a function of care setting, age, comorbidity burden, and prior utilization.
How to interpret it
An adjusted odds ratio of 1.35 means the estimated odds of the outcome are 35% higher for that predictor contrast, conditional on the variables in the model. It does not mean risk is 35% higher.
What adjusted odds ratios look like
- Primer on binary logistic regression (opens in a new tab) · Fam Med Community Health · doi 10.1136/fmch-2021-001290
- Statistics notes. The odds ratio (opens in a new tab) · BMJ · doi 10.1136/bmj.320.7247.1468