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

Eleni Rapsomaniki er339 at medschl.cam.ac.uk
Fri Dec 10 17:21:29 CET 2010

```Dear R-users,

I need to use the aftreg function in package 'eha' to estimate failure times for left truncated survival data. 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???

#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, exp(m2_NULL\$coef)) #--> 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