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I have to draw a survival probability plot with three different surviuval estimates using the phreg, lifereg and the lifetest procedure with sas for make a confrontation

the models:

   proc phreg data=data;
   class trt;
      model time*event(0)=trt / rl;
   run;

   proc lifereg data=data;
      model time*event(0) = trt   / dist=weibull;
   run;

   proc lifetest data =data METHOD=KM;
      time time*event(0);
   run; 

i know that for the lifetest it's possible to draw the survival probability plot by using "plots = (s)" and for the phreg by using "plot(overlay)=survival", but i don't know how to draw this plot type with the lifereg and how to draw an unique plot with the three survival curves for make the confrontation

thank you in advance

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  • $\begingroup$ Quick comment: the KM is but one way to estimate the survival function, and it is the only one which can be fully summarized by a plot. The KM curve is but an estimate of survival, not THE survival function. Parametric survival regression estimates the survival as a strict function of the model parameters; the Cox model doesn't estimate the survival at all. The omission of survival plots was deliberate in both cases, as the coefficients alone summarize what is important, when it is important at all. $\endgroup$ – AdamO Dec 14 '17 at 17:11
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Parametric survival regression uniquely determines the survival curve. For the Weibull model, you can simply extract the coefficient estimates, transform them as needed, then plug them in as parameters to the Weibull survival function: $\exp(-(x/\lambda)^k))$.

Cox models, in general, are not so straightforward. Their main strength, and weakness, is the use of an arbitrary baseline hazard function. You can use a density smoothed estimate of the Schoenfeld residuals to come up with an estimate of the baseline hazard function, or use the Breslow cumulative hazard estimator relevant post here.

The simplest approach, and the one I see most often, is to use the empirical Survival estimate, the Kaplan Meier, in the relevant strata of the Cox model. Assuming treatment is two levels, you can print the KM curves for either treatment group, and overlay the Cox model output. Inference from the Cox model is in fact asymptotically equivalent to the log-rank test.

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