Cox regression relates the hazard (instantaneous risk of the event) to several predictors, without assuming a particular shape for survival over time.
Why it matters
It is the standard way to adjust survival comparisons for age, sex, stage and other factors.
Key ideas
- h(t) = h0(t) × exp(b1·X1 + …)
- exp(b) = hazard ratio (HR)
- Proportional hazards: the HR stays about the same over time
- Handles censoring
- Check PH assumption (Schoenfeld residuals)
- Need enough events: about 10 per predictor
Real-life research example
Death hazard after surgery modelled by age, tumour stage and treatment.
When to use
- Time-to-event outcome with covariates
When NOT to use
- Don't ignore a clear violation of proportional hazards
- Don't fit many predictors with few events
Quick takeaway
Cox gives adjusted hazard ratios without needing a survival-curve formula.
Try it yourself
A study has 30 events. How many predictors could you reasonably include? Write the rule and the answer.
Model answer
About 10 events per predictor, so roughly 3 predictors. Fitting more risks unstable estimates.