Survivor Functions, Hazard Functions and Pictures

Unfamiliar jargon like Kaplan-Meier curves, PROC PHREG, right-censored and hazard functions can be daunting to the newcomer. Survival analysis is really quite straightforward; it is simply a set of statistical techniques used when the focus is “time to event”. The event can be death, divorce, arrest, substance abuse or literally anything else. You’ve been wanting survival analysis if you have ever asked any of these questions:

  • “How long can the average person with X be expected to survive before the event occurs?”
  • “Given that a person has made it up to this point, how much longer can she be expected to survive?”
  • “Are chances of survival higher for people in group A or group B?”

So, I was thinking today, why not just show pictures to calm people down and begin introducing concepts in survival analysis. Everybody likes pictures, right?

Let’s imagine a picture of a survivor function. It looks like this. In the beginning we are all alive and in the long-run we are all dead.

Survival plot









To get this curve, I used the following SAS code

ods graphics on ;
LIBNAME in "C:\Users\AnnMaria\Documents\survive" ;
TIME survt*status(0) ;
WHERE clinic = 1;

Now let’s compare some survival curves from actual data. These are from the addicts data set in David Kleinbaum’s book on survival analysis. Here we have two clinics and we want to know whether one clinic has a higher probability of patients surviving the treatment than the other. In this case survival means not dropping out of the treatment.









If you look at the curves above, you’ll see that Clinic 2 clearly had a better survival rate than did Clinic 1. That’s nice and all but what about the possibility that Clinic 1 had “tougher customers” ? Is Clinic 2 still superior when controlling for possible pre-existing differences?

That, my dears, is an adjusted survival curve, which is  a picture for another day.

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