Simulate data for PHREG Cox Model

[openatom]

I am trying to do a simple simulation where I create several different replication datasets (replicating a known dataset I have).   I'm using SAS 9.4 and here is the code I'm trying to use for simulation (found on: http://sas-and-r.blogspot.com/2010/03/example-730-simulate-censored-survival.html😞

data simcox;
  beta1 = 2;
  lambdat = 0.002; *baseline hazard;
  lambdac = 0.004; *censoring hazard;
  do i = 1 to 1000;
    x1 = rand("Bernoulli",0.5);
    linpred = exp(-beta1*x1);
    t = rand("WEIBULL", 1, lambdaT * linpred);
    * time of event;
    c = rand("WEIBULL", 1, lambdaC);
           * time of censoring;
    time = min(t, c);    * which came first?;
    censored = (c lt t);
    output;
  end;
run;

I am having trouble figuring out the values to use (bold in red).  How do I know what to specify beta and lambdas as? Is there a way to find estimates of these values by running a Cox model on my known data, then using these estimated values of beta and lambdas for my simulation? If so, please explain in detail how to find these.

Thank you.

[Rick_SAS]

I'm away from my reference materials (in my office), but I believe the answer is that you can run PROC LIFEREG and use the DIST=WEIBULL option to get these values. One of them (possibly lambdat) is estimated by exp(Intercept) and the other (lambdac?) by 1/shape (look for "Weibull Shape" in the output. If 1/shape doesn't work, try just shape.... it depends on how you parameterize the Weibull survival model.

HTH

[openatom]

Thank you, this is helpful.  I noticed that LIFEREG will also output something it calls "shape" and "scale," but they appear to be inverses and not directly related to the Weibull PDF in SAS (https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.5&docsetId=fedsqlref&docsetTarget=p1...) where a=shape and lambda=scale.

In LIFEREG, I assume that the "scale" is lambda? 

(shape) a = exp(Intercept) ?

(scale) lambda = lambdac ?

Does this seem correct?

[Rick_SAS]

Yes. I thought it was lambdac = 1/lambda, but I could be wrong. As I said, it depends on the parameterization of the distribution. Some use scale and others use rate (=1/scale).

Since your goal is a simulation, it should be easy to check. In your simulation, set the scale parameter in your simulation to 4 and generate a large data set (like, 5,000 observations). LIFEREG will either report scale=4 or scale=0.25. If it reports 4, then the formulas in your simulation match those in the PROC. If it reports 0.25, then in your simulation you need to replace the scale parameter by (1/scale) in order to match the parameterization in the PROC. Then rerun to make sure.