9.1 Graphical checks

For a categorical covariate, proportional hazards means \(H_g(t) = c_gH_1(t)\), so the curves of \(\log \hat H_g(t) = \log (-\log \hat S_g(t))\) for the groups should be parallel when plotted against \(\log t\) (the problem on proportional hazards in the section on the Nelson–Aalen estimator). Curves that converge, diverge or cross suggest that the hazard ratio changes with time; crossing Kaplan–Meier curves, as for the veteran regimens (Figure 6), always mean crossing hazards. These plots work for a few groups but not for continuous covariates or for several covariates at once, for which residuals are used.

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