[R] survreg vs. aftreg (eha) - the relationship between fitted coefficients?

[Göran Broström]

On Fri, Dec 10, 2010 at 5:21 PM, Eleni Rapsomaniki
<er339 at medschl.cam.ac.uk> wrote:
> Dear R-users,
>
> I need to use the aftreg function in package 'eha' to estimate failure times for left truncated survival data.

Be careful! This is only possible under strong assumptions about the
(unobserved) covariate vector. This is not (yet) reflected on the help
page for aftreg, but has been discussed here earlier.

 Apparently, survreg still cannot fit such models. Both functions
should be fitting the accelerated failure time (Weibull) model.
However, as Göran Broström points out in the help file for aftreg, the
parameterisation is different giving rise to different coefficients.
The betas for adjusted covariates are opposite in sign but otherwise
identical, whereas the intercept is quite different in a non-obvious
way. The log-likelihoods are similar also, but not identical. I would
like to find out how I can convert one set of coefficients to the
other so as to obtain the same linear predictors using either model.
Any ideas???

Yes. Since you work with Weibull data, try 'phreg' instead. You will
have to change sign of estimated coefficients, and divide them by
estimated shape, see the help page for 'weibreg', to compare to
parameters from survreg, but they are directly comparable with those
from coxph and coxreg.

Göran


>
> #the example below uses right-censored data for simplicity (the principle should be the same with left truncation I hope)
> library(survival)
> library(eha)
>
> #  COMPARE coefs between survreg ('survival' pkg) and aftreg ('eha' pkg)
> #Fitting NULL models (no covariates) results in (approximately) the same coefs (which is good!)
>
> m1_NULL=survreg(Surv(futime/365, status==1) ~ 1, data=pbcseq)
> m2_NULL=aftreg(Surv(futime/365, status==1) ~ 1, data=pbcseq)
>
> c(m1_NULL$coef, 1/m1_NULL$scale) #--> intercept= 3.878656  ,  shape = 1.478177
> c(m2_NULL$coef[1], exp(m2_NULL$coef[2])) #--> intercept= 3.878859 ,  shape=1.478150
>
>
> # NOW I adjust for covariates
>
> m1=survreg(Surv(futime/365, status==1) ~ chol+stage, data=pbcseq)
> m2= aftreg(Surv(futime/365, status==1) ~ chol+stage, data=pbcseq)
>
> ###      m2  #######
> #Coefficients:
> # (Intercept)         chol        stage
> # 5.944641913 -0.001692574 -0.470861324
>
> #Scale= 0.6416744
>
> #Loglik(model)= -483.9   Loglik(intercept only)= -506.8
> #        Chisq= 45.91 on 2 degrees of freedom, p= 1.1e-10
> #n=1124 (821 observations deleted due to missingness)
>
> ###      m2  #######
>
> #Covariate          W.mean      Coef Exp(Coef)  se(Coef)    Wald p
> #chol              303.777     0.002     1.002     0.000     0.000
> #stage               3.298     0.460     1.584     0.119     0.000
> #
> #log(scale)                    5.029   152.807     0.477     0.000
> #log(shape)                    0.467     1.595     0.095     0.000
> #
> #Events                    92
> #Total time at risk          9017
> #Max. log. likelihood      -484.31
> #LR test statistic         45.0
> #Degrees of freedom        2
> #Overall p-value           1.64669e-10
>
> Many thanks for any help you may be able to provide.
>
> Eleni Rapsomaniki
> Research Associate
> University of Cambridge
> Institute of Primary and Public Health
>
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>



-- 
Göran Broström