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Re: st: Write a parametric survival model in the hazard notation


From   Steve Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Write a parametric survival model in the hazard notation
Date   Sun, 5 Sep 2010 10:28:35 -0400

--

Florian Christ:

While it is true that any survival model can be written in hazard
notation, it is _not_ true that the coefficients will necessarily have
an interpretation in terms of altering hazard ratios. The generalized
gamma model is what is known as an accelerated failure time model, and
the effect of the regression variables is to multiply time, not the
hazard. No transformation of coefficients will remedy this, and a
rewrite of the likelihood equation will not help.

You _can_ plot hazard functions from the generalized gamma with
-stcurve-. Use a bootstrap to get get CIs for the difference or ratio
over a range of time points. As an aside: the BIC comparisons don't
actually show that the model fit the data well, and residual checks
and plots will still be necessary.

Bit this is a long way around. To get easier interpretations in terms
of hazard ratios, I suggest that you fit -stcox-  and add interactions
of covariates and time. Also consider -stpm2- (from SSC) for flexible
parametric hazard models.

Steve

Steven J. Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

On Sun, Sep 5, 2010 at 6:46 AM, Christ, Florian <Florian.Christ@whu.edu> wrote:
> Dear statalisters,
>
> I am new to statalist and would greatly appreciate your help with regard to my 'rookie' event-history problem.
>
> I am reporting coefficients from a parametric survival model (Generalized gamma distribution; following the AIC and BIC criterion) for my research project. However, as I am examining employee turnover as dependent variable interpretation of coefficients would be easier, if they would equal the hazard notation rather than the survival notation (e.g., positive coefficients should mean that the predictor increases the hazard). E.g., Cleves et al. mention in their great book on p.20 that "any parametric survival model can be written in the hazard notation".
>
> So I was wondering if and how I can practically write my survival model (generalized gamma distribution) in the hazard notation? Do I have to write an own maximum likelihood estimator for this? If so, how? Alternatively I may probably just transform the coefficients so that they reflect the hazard logic (probably with estout; transform). If there are other solutions to this problem I would also greatly appreciate your help.
>
> Thanks so much in advance for your help and support.
>
> Best regards,
>
> Florian
>
>
>
> Florian Christ
>
> WHU – Otto Beisheim School of Management
> Doctoral Research Fellow
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