R help - Feb 2010 - Accelerated failure time interpretation of coefficients

I have one more conceptual question though, it would be fantastic if 
someone could graciously help out:

I am using an accelerated failure time model with time-varying 
covariates because I assume that my independent variables have a 
different impact on the chance for a failure at different points in 
lifetime. For example: High temperature has a different impact on 
failure in earlier years than in later years (for whatever reason). 
So far so good (hopefully).

But: From my regression I only get one coefficient for each 
independent variable and I am wondering how this "one" variable 
reflects the above mentioned time-dependent impact of my variable. 
Shouldn't I be getting a coefficient for each year of lifetime, 
which tells me exactly what impact a variable has in a given year?

I'm pretty sure I am totally mixing things up here, but I really 
couldn't find any helpful information, so any help is highly 
appreciated!!

Thank you very much!
Best
Philipp

On 2/23/2010 3:37 PM, Philipp Rappold wrote:
> I have one more conceptual question though, it would be fantastic if
> someone could graciously help out:
>
> I am using an accelerated failure time model with time-varying
> covariates because I assume that my independent variables have a
> different impact on the chance for a failure at different points in
> lifetime. For example: High temperature has a different impact on
> failure in earlier years than in later years (for whatever reason). So
> far so good (hopefully).
well, if by 'chance for a failure' you mean the hazard, then you could 
first graphically test that indeed you have a time-varying effect. This 
you can do by first fitting a Cox model assuming time-independent effect 
for temperature, and then use (transformations) of the scaled Schoenfeld 
residuals that are implemented in cox.zph().

Note, that unless you're using the Weibull model (and its special the 
exponential), then any other standard choice for a parametric AFT model 
does not assume PH.

Now, if you need to go to time-varying effects, then you can do that 
under both AFT and PH models. In the former including time-dependent 
covariates is a bit more tricky you can find more information, e.g., in 
Section 5.2 of Cox & Oakes (1984), Analysis of Survival Data, Chapman & 
Hall. For the latter it is a bit more easier and you can have a look in 
standard texts for survival analysis, e.g., Therneau & Grambsch (2000). 
Modeling Survival Data: Extending the Cox Model, Springer.


I hope it helps.

Best,
Dimitris
> But: From my regression I only get one coefficient for each independent
> variable and I am wondering how this "one" variable reflects the
above
> mentioned time-dependent impact of my variable. Shouldn't I be getting
a
> coefficient for each year of lifetime, which tells me exactly what
> impact a variable has in a given year?
>
> I'm pretty sure I am totally mixing things up here, but I really
> couldn't find any helpful information, so any help is highly
appreciated!!
>
> Thank you very much!
> Best
> Philipp
>
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-- 
Dimitris Rizopoulos
Assistant Professor
Department of Biostatistics
Erasmus University Medical Center

Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
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