What is the Cox proportional hazards assumption, and how can you assess it?

• A. Requires equal group sizes; assess with t-tests
• B. Assumes hazard ratios are constant over time; assess with Schoenfeld residuals, time-dependent covariates, graphical checks
• C. Requires no censoring; assess with Kaplan-Meier
• D. Requires normal distribution of covariates; assess with Q-Q plots

Answer: (B)

The key idea is that the Cox model assumes the hazard ratio between groups stays the same over the entire follow-up period. In other words, a covariate’s effect on the hazard is multiplicative and does not change with time, even if the baseline hazards differ between groups.

You can assess this in several ways. One common approach uses Schoenfeld residuals: after fitting the model, you examine residuals for each covariate against time. A systematic pattern or a significant slope suggests the covariate’s effect changes over time, indicating a violation of proportional hazards; a formal Grambsch–Therneau style test can provide a global or per-covariate p-value.

Another method is to include time-dependent covariates: add an interaction between a covariate and a function of time (or time itself) in the model. If that interaction is statistically significant, the hazard ratio for that covariate changes over time, signaling non-proportional hazards.

Graphical checks are also informative. Plotting log(-log(survival)) versus time for different groups should yield roughly parallel curves if the proportional hazards assumption holds; departures from parallelism point to time-varying effects.

If proportional hazards don’t hold, consider alternatives like stratified Cox models (which allow baseline hazards to differ by strata) or models with time-varying coefficients to capture changing effects over time.