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
Accelerated failure time interpretation of coefficients
4 messages · Philipp Rappold, Dimitris Rizopoulos, Göran Broström
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
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Dimitris Rizopoulos Assistant Professor Department of Biostatistics Erasmus University Medical Center Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands Tel: +31/(0)10/7043478 Fax: +31/(0)10/7043014
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
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
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. G?ran
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
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.