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st: Re: Interpreting Theta with gompertzhet

From (Roberto G. Gutierrez, StataCorp.)
Subject   st: Re: Interpreting Theta with gompertzhet
Date   Mon, 07 Oct 2002 11:07:05 -0500

A. A. Siyam <> asks:

> A colleague of mine is asking about how to best interpret the "theta" value
> following the estimation of a "gompertzhet" model.

> As an example, we have the following model:

> xi:gompertzhet time i.tenureg i.newcohort i.marstat i.nmm i.socg
> i.educ i.bathg i.carg i.urind i.pob, dead(outcome) frailty(gamma) robust hr

[output omitted]

> We found a great deal of help in understanding the gompertz model from the
> book "Introduction to Survival Analysis Using Stata" by Cleves,Gould and
> Gutierrez. But, there seems to be very little explanation of how to use and
> interpret the "theta" coeffi cient estimated by the model.

First of all, the equivalent way to fit your model using the more modern 
-streg- is

    . stset time, failure(outcome)
    . xi: streg i.tenureg i.newcohort i.marstat i.nmm i.socg /*
    	  */ i.educ i.bathg i.carg i.urind i.pob, dist(gompertz) /*
	  */ frailty(gamma) robust

That being said, you'll find the discussion of the frailty variance, theta,
estimated by -streg, frailty()- in Section 15.3 of the aforementioned text

Namely, theta is the estimated frailty variance.  If significantly different
from zero (in the case of robust no formal likelihood-ratio test is available,
so merely compare the parameter estimate to its standard error), this
indicates significant heterogeneity.  This heterogeneity can be thought of as
arising from some unobserved observation-specific effect, or frailty.  Theta
measures the variability of these frailties.  If close to zero, then the
frailties are virtually non-existent, and you can get by with the standard
Gompertz model.

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