Cox proportional hazards regression
What question does this help answer?
“How does the instantaneous event rate over follow-up differ between groups or across predictors?”
When to use it
Use Cox regression when the outcome is time-to-event, participants have different follow-up durations, censoring occurs, and a relative hazard is a meaningful effect measure.
When not to use it
A simple Cox model may be unsuitable when proportional hazards is strongly violated, recurrent events or competing risks dominate the problem, or the scientific target is an absolute risk at a particular time rather than a hazard ratio alone.
How it works in plain language
The model compares event hazards between participants with different predictor values without requiring a parametric form for the baseline hazard. Participants who have not experienced the event by their last observation can contribute censored follow-up.
Why Mallard may recommend it
Mallard may recommend Cox regression when the plan asks about time to death, recurrence, hospitalization, treatment discontinuation, or another event and follow-up varies.
Key assumptions
- The proportional-hazards assumption is appropriate for modeled covariates or addressed with extensions.
- Censoring is handled under assumptions appropriate to the analysis.
- Time origin and risk-set entry are defined correctly.
- Time-varying exposures or confounders are handled appropriately when present.
What to watch out for
Hazard ratios are not risk ratios. A single hazard ratio can obscure changing effects over time. Always examine whether proportional hazards is plausible and consider absolute risks or survival probabilities for interpretation.
Clinical example
Compare time to cardiovascular event among treatment groups while adjusting for baseline age and comorbidity.
How to interpret it
A hazard ratio of 0.75 indicates an estimated 25% lower hazard at a given time for the exposed group, under the proportional-hazards interpretation; it does not directly mean 25% fewer events by the end of follow-up.
The curves a hazard ratio summarises
- Survival analysis-part 2: Cox proportional hazards model (opens in a new tab) · Indian J Thorac Cardiovasc Surg · doi 10.1007/s12055-020-01108-7
- Survival Analysis and Interpretation of Time-to-Event Data: The Tortoise and the Hare (opens in a new tab) · Anesth Analg · doi 10.1213/ANE.0000000000003653