Dimitris, thanks for your detailled answer and the literature
recommendation.
However, I'm still wondering about the interpretation of
coefficients in the AFT model with time-varying covariates. The
precise question is: How can I interpret a "single" coefficient if
my assumption is that an effect will vary over time (for example:
coeff = 0 in the beginning, then rising to >0, then slowly
decreasing back to 0).
Sure I will fetch Cox&Oakes (1984) from the library asap, but it's
still crazy that there's hardly any online information available on
the topic these days (or at least I can't find it). I realize this
is all a bit OT for r-help though...
Dimitris Rizopoulos wrote:
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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