Contributor
Posts: 30

PHREG output statement question

In phreg, using the output statement with survival=
option, what is the formula to recreate the survival= calculation?  I cannot recreate it.

Thank you very much!

Posts: 2,655

Re: PHREG output statement question

There are a number of survivor functions available, and the calculations are available for each type in the documentation under Details: PHREG Procedure>Survivor Function Estimators.  There is a Breslow estimator, Flemin-Harrington estimator, and the product-limit estimator.

You should be able to check the calculation based on the formulas provided.

Steve Denham

Contributor
Posts: 30

Re: PHREG output statement question

I'm trying to use the betas from the model, plug in the individual patient data into a formula with the betas and try to recreate the exact values that I get in the survival=

I think i would use this, but what do I plug in for alpha?

hi(t) = exp(α + β1xi1 + β2xik + ・ ・ ・+ βkxik)

Thoughts?

Super User
Posts: 20,781

Re: PHREG output statement question

I'm not sure, but here's what I'd try

The formula you have is the hazard function formula, h(t), not the survivor function.

The survivor is S(t)=S(baseline)(t)^exp(B1x.....)

from SAS docs.

You have your beta's from the output and you can get the baseline syntax in proc phreg

Baseline (out=)

I don't know if you'd need to set values for the covariates or not, but that's where I'd start.

Posts: 2,655

Re: PHREG output statement question

Expanding on Reeza's comment.

Some math thoughts: In exp(α + β1xi1 + β2xik + ・ ・ ・+ βkxik), the first term exp(α) is a constant that ends up as a multiplier of exp( β1xi1 + β2xik + ・ ・ ・+ βkxik), and is thus just part of S(baseline).  You do not need alpha to calculate survivor functions.

Steve Denham

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