---- Steinar Fossedal wrote:
> I have fitted an exponential survival model with gamma frailty, and now
> find myself in a pickle trying to interpret and apply the predictive
> results. Specifically I'm getting predictions of individual hazard that
> exceeds one. Such estimates are, of course, problematic to use in the
> next step of my analysis.
Actually you have no problem. Hazards are not the same as probabilities,
and can range between 0 and +infinity. The interpretation of a hazard is
the number of times in a unit time that you can on average be expected
to experience the event. Say the event is experiencing a cold. My hazard
for experiencing a cold when time is measured in months is probably less
than 1, but if time is measured in centuries it will clearly be larger
than one (until someone invents the cure for the common cold).
> I reason that this is caused by the multiplicative effect of the frailty
> parameter on the hazard, and that the model only ensures the validity of
> the population hazard values - not the unobserved individual's. With
> validity I mean restrictions that ensure the hazard stays between zero
> and one. To me, this seems like an inherent weakness in frailty models.
> This may not matter much when investigating hazard ratios and
> differences between populations, but it does pose a problem when making
> individual predictions
Actually the model without frailty component (possibly with robust
standard errors) is the model that correctly looks at population values
of the hazard, while the model with frailty component captures the hazards
at the individual level (if you believe your model, i.e. the unobserved
component of your model is gamma distributed, uncorrelated with your
observed variables, the effects of the observed variables are correctly
specified, etc. etc. It is no coincidence that robust standard errors are
called robust, thus implying that other models are less robust. (However,
I still think that the name robust suggests more robustness than it can
deliver. But that is another issue))
Hope this helps,
Maarten
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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