What is the proportional hazards assumption in Cox models?

• A. It assumes hazards are proportional to baseline risk.
• B. It assumes the hazard ratio between groups is constant over time; violation may require time-varying coefficients or alternative models.
• C. It assumes no censoring.
• D. It assumes the outcome is rare.

Answer: (B)

The essential idea is that, in Cox models, the effect of covariates on the hazard is multiplicative and does not change over time. This means the hazard for someone with a given set of covariates x is h(t|x) = h0(t) exp(β'x), where h0(t) is the baseline hazard. The hazard ratio between two groups (or two covariate profiles) is constant across all times: HR = exp(β'(x1 − x0)) and does not depend on how long you follow people.

If the hazard ratio stays the same over time, the proportional hazards assumption holds. If the HR changes with time—say a treatment has a strong early effect that weakens later—the assumption is violated. In that case you’d use time-varying coefficients or another modeling approach, such as a stratified Cox model or an alternative survival model.

The other statements don’t describe this assumption: censoring can occur and is handled in Cox models, the outcome being rare is not a requirement, and the hazard being proportional to baseline risk isn’t the proportional hazards idea.