# [R] Accelerated failure time interpretation of coefficients

Philipp Rappold philipp.rappold at gmail.com
Tue Feb 23 17:10:53 CET 2010

```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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