Date: Tue, 2 Sep 2008 00:35:59 0700
ReplyTo: Oliver.Kuss@MEDIZIN.UNIHALLE.DE
Sender: "SAS(r) Discussion" <SASL@LISTSERV.UGA.EDU>
From: Oliver.Kuss@MEDIZIN.UNIHALLE.DE
Organization: http://groups.google.com
Subject: Re: Personperiod data set with gamma heterogeneity
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On 31 Aug., 16:34, stefan.p...@ISH.DE (Stefan Pohl) wrote:
> Hi list,
>
> I have a personperiod data set and I want to know if there is unobserved
> heterogenity in my data.
> First of all, I simply estimated PROC logistic with so much constants as
> periods and several covariantes, sex, premum paid... (varying over the
> periods).
>
> My data look like this. For 2 persons:
>
> Person Period event indicator premium
> 1 1 0 100
> 1 2 0 110
> 1 3 1 130
> 2 . . .
> 2 . . .
> 2 3 0 250
> 2 4 0 230
> 2 5 0 220
> 2 6 0 210
> 2 7 0 190
> 2 8 0 180
>
> Person 1 is observed complete an has the event in period 3 (event
> indicator=1).
>
> Person 2 is in periods 1 and 2 left truncated: not under risk, I have no
> covariate information and in the estimation procedure this Personperiod is
> dropped out. Person 2 is also right censored, i.e. the event indicator = 0.
>
> What I want to know: Is there a very naive way to incorporate gamma frailty
> (with mean=1) by sampling values from the appropriate gamma distribution an
> deal the values as a separate covariate, like sex, premium. The gamma
> frailty term should be the same for each person.
>
> Is this a good idea?
>
> Best Stefan.
Dear Stefan,
if you are willing to accept an exponential survival distribution in
periods you can interpret your model as a Poisson model with a
specific offset, sometimes also called a piecewise exponential model.
This equivalence between survival and Poisson models has been shown by
Aitkin and Clayton (The fitting of exponential, Weibull and extreme
value distributions to complex censored data using GLIM. Applied
Statistics 29, 156–163.).
As such you can code your model with PROC GENMOD or PROC GLMMIX and
account for the person effect via GEE (GENMOD) or incorporating a
random effect (GLIMMIX). Please note that in the random effect case
you will have a normal (not a gamma) distribution for the random
effect.
However, I am not sure if this adjusts adequatly for your left
truncated data ...
Hope that helps,
Oliver
