8.5 Adjusted survival curves

A fitted Cox model with the Breslow baseline gives a predicted survival curve for any covariate pattern, \(\hat S(t \mid x) = \hat S_0(t)^{\exp (\hat \beta ^{\mathsf T}x)}\). Plotting curves for chosen patterns shows the size of effects in terms patients and clinicians understand (Figure 8). For a patient with a squamous tumour on the standard regimen, the predicted median survival is \(92\) days with a Karnofsky score of \(40\), \(144\) days with \(60\), and \(283\) days with \(80\); the predicted six-month survival is \(19\%\), \(41\%\) and \(62\%\).

dS1234560001KKKaˆ000000...aaay(t00000025575rrrs|nnnxofofof)skskskyyy864000::: m m mededediiiananan21984234days — Figure 8: Predicted survival curves from the Cox model with treatment, cell type and Karnofsky score, for a patient with a squamous-cell tumour on the standard regimen and three performance scores. The curves are powers of one another, \(\hat S_0(t)^{e^{\hat \beta ^{\mathsf T}x}}\), as proportional hazards requires; the medians are where they cross the dashed line.

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