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Re: st: Frailty gamma or inv gaussian distribution

From   Maarten Buis <>
Subject   Re: st: Frailty gamma or inv gaussian distribution
Date   Wed, 12 Sep 2012 09:35:47 +0200

On Tue, Sep 11, 2012 at 9:25 PM, Alexander James wrote:
> I am trying to run a survival model. I am facing an issue regarding how I should set the frailty. When I use gamma distribution I get very significant, but when I try to run it with inverter Gaussian distribution the level of significance of my main explanatory variable reduces substantially. I could not find any test to indicate which of them is more appropriate or a reference to explain why I am observing the chance in significance level. Would someone have a suggestion for this question?
> ps. I am using an exponential model

Conceptually, a model with gamma frailty or inverse Gaussian frailty
are very similar. So if they give very different results, than the
conclusion is that your models aren't robust enough to draw meaningful
conclusions. So rather than trying to select one of these models a the
"best", you should try to make your model more robust(*).

In this case, I suspect your problem is the form of the baseline
hazard that you have chosen by specifying an exponential model. Within
an exponential model, you assume that the baseline hazard is constant
over time. With frailty the baseline hazard will decline: the frail
are selected out early, so at later points in time the more hardy
remain. For more on that see: (Vaupel and Yashin 1985). If your model
is wrong and the baseline hazard net of frailty is not constant over
time, your model will try to assign all those changes in the baseline
hazard to the frailty component, which can easily lead to an unstable
model like the one you have. The solution is to try different baseline
hazard functions, so try different distributions in the
-distribution()- option of -streg- or try -stcox-.

Hope this helps,

(*) Despite the name, you are not going to achieve that by adding the
-robust- or -vce(robust)- options: These refer to a completely
different type of robustness.

James W. Vaupel and Anatoli I. Yashin (1985) Heterogeneity's Ruses:
Some Surprising Effects of Selection on Population Dynamics. The
American Statistician, 39(3): 176--185 .

Maarten L. Buis
Reichpietschufer 50
10785 Berlin

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