Model diagnostics · Implementation

Proportional-Hazards Diagnostic (log–log & Schoenfeld)

The standard check that a Cox model's proportional-hazards assumption holds: parallel log–log survival curves and flat, time-independent scaled Schoenfeld residuals.

Download SVG Open code and full worked example

When to use it

After fitting any Cox model and before trusting its hazard ratio. If hazards are non-proportional, a single HR is a time-averaged summary that can mislead; switch to time-varying effects, RMST, or stratification.

How to read it

Log–log curves that stay parallel (do not cross) support PH; a sloped or curved Schoenfeld residual trend (or a small global test p-value) indicates a time-varying effect for that covariate.

Worked example

A two-arm Cox model is checked two ways: log(−log S(t)) is plotted against log(time) for each arm, and the scaled Schoenfeld residuals for the treatment indicator are plotted against time with a smoother.

Same two-arm survival data as the Kaplan–Meier example; residuals from the fitted Cox model for the treatment term.

Result: The two log–log curves are roughly parallel and the residual smoother is flat around zero (global cox.zph p ≈ 0.4), so the proportional-hazards assumption is reasonable and the reported hazard ratio is interpretable as a constant effect.

Produced by

Cox proportional-hazards regression

Reference: Gatto NM, Wang SV, Murk W, et al. Visualizations throughout pharmacoepidemiology study planning, implementation, and reporting. Pharmacoepidemiol Drug Saf. 2022;31(11):1140-1152.