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Date:         Tue, 2 Sep 2008 00:35:59 -0700
Reply-To:     Oliver.Kuss@MEDIZIN.UNI-HALLE.DE
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Oliver.Kuss@MEDIZIN.UNI-HALLE.DE
Organization: http://groups.google.com
Subject:      Re: Person-period data set with gamma heterogeneity
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=windows-1252

On 31 Aug., 16:34, stefan.p...@ISH.DE (Stefan Pohl) wrote: > Hi list, > > I have a person-period 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 Person-period 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, 156163.). 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


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