[R] Accelerated failure time interpretation of coefficients

[Göran Broström]

Philipp Rappold wrote:
> 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).

You could try to split data in separate "age windows", fit separate 
models, and compare coefficient estimates. Create the "windows" with 
"age.window" in 'eha'. E.g.,

 > dat1 <- age.window(dat, c(0, 10), surv = c"start", "stop", "cens"))
 > dat2 <- age.window(dat, c(10, 20), surv = c"start", "stop", "cens"))
 > dat3 <- age.window(dat, c(20, 100), surv = c"start", "stop", "cens"))

Then  fit the same model to the three data frames.

Göran

> 
> 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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>>