LIFEREG: hazard function with SAS exponential distribution is not flat?

Occasional Contributor
Posts: 8

LIFEREG: hazard function with SAS exponential distribution is not flat?

[ Edited ]

Hi Community,

I'm trying to understand the parameterization that SAS uses for the exponential distribution in LIFEREG procedure.

I went directly to PROC LIFEREG User's Guide and found in page 3038 the parameterization that LIFEREG uses for this distribution. What I don't understand here is the shape of the hazard function, that is supposed to be h(w)=f(w)/S(w), and should be by definition of the exponential distribution, non time dependent.

With the expression given by SAS user's guide we have:

h(w) = exp(w-mu),

where w=log(t) and exp(-mu)=alpha. So it is time dependent.

Could anyone explain which is the mistake I'm commiting in the interpretation of this?

Thank you very much!

SAS Employee
Posts: 340

Re: LIFEREG: hazard function with SAS exponential distribution is not flat?

With the notation found in LIFEREG documentation: h(t) = g(t)/G(t) = alpha (constant).

Note, that other literature (for example Wikipedia) might use f(t) and S(t) for the untransformed pdf and survival functions.

Occasional Contributor
Posts: 8

Re: LIFEREG: hazard function with SAS exponential distribution is not flat?

Hi gergely_batho,

First of all, thank you for your response.

I already knew that the untransformed functions worked well, maybe I should have mentioned that. What I'm trying to understand here is how did they apply the transformation to the functions, and if they are not commiting a mistake when doing it.

Thank you very much!

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