st: RE: generating data from AFT survival models with frailty

["Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>]

Albert - 

The gamma frailty model says that the hazard function is multiplied by a gamma-distributed random variable with shape and scale parameter both equal to 1 for each value of the "subject" (i.e. group) variable. Let h(t) be the hazard function for an "average" subject (frailty = 1) and H(t) be the integral of h(u) from 0 to t. Then if G_i is a gamma-distributed frailty for the ith "subject", the actual hazard for that subject is G_i*h(t) and the integrated hazard is H_i(t) = G_i*H(t). Since the survival function is S_i(t) = exp(-H_i(t)) you can generate random values of "t" by its inverse function S-1_i(U) where U ~ uniform(0,1). Once you have these values of "t", you can censor them as you wish. ALso, of course h(t) can depend on covariates in whatever way you wish and the G_i have to be generated so that they are the same for all repeated observations pertaining to the i-th subject.

The actual form of h(t) depends on the AFT model (see documentation under -streg-).



Al Feiveson


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Albert Navarro
Sent: Tuesday, March 15, 2011 3:55 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: AFT survival models with frailty

Dear all,

I would like to simulate survival data with gamma frailty in a AFT parametric model (exponential, weibull, lognormal and loglogistic). I would be grateful if you could give me some reference about it, I only found documents about the use of frailties in PH models.

Thanks in advance!!!

Albert Navarro




      

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