[R] Apparently Conflicting Results with coxph

[Peter Dalgaard]

Kevin E. Thorpe wrote:
> Dear List:
>
> I have a data frame prepared in the couting process style for including
> a binary time-dependent covariate.  The first few rows look like this.
>
>     PtNo Start    End Status Imp
> 1      1     0  608.0      0   0
> 2      2     0  513.0      0   0
> 3      2   513  887.0      0   1
> 4      3     0   57.0      0   0
> 5      3    57  604.0      0   1
> 6      4     0  150.0      1   0
>
>
> The outcome is mortality and the covariate is for an implantable
> defibrillator, so it is expected that the implant would reduce the
> risk of death.  The results of fitting coxph (survival package) are:
>
> Call:
> coxph(formula = Surv(Start, End, Status) ~ Imp, data = nina.excl)
>
>
>      coef exp(coef) se(coef)     z    p
> Imp 0.163      1.18    0.485 0.337 0.74
>
> Likelihood ratio test=0.11  on 1 df, p=0.738  n= 335
>
> Since this was unexpected, I created a non-counting process data
> frame with an indicator variable representing received an implant
> or not.  Here are the results:
>
> Call:
> coxph(formula = Surv(Days, Dead) ~ Implant, data = nina.excl0)
>
>
>          coef exp(coef) se(coef)     z       p
> Implant -1.77     0.171    0.426 -4.15 3.3e-05
>
> Likelihood ratio test=19.1  on 1 df, p=1.21e-05  n= 197
>
> I found this degree of discrepancy surprising, especially the point
> estimate of the coefficient.  I have verified the data frames are
> set up correctly.
>
> Here is what I have tried to understand what is going on.
>
> I tried fitting models adjusted for other covariates that I have in
> the data frame.  This did not appreciably affect the coefficients
> for the implant variable.
>
> I ran cox.zph on the two models shown above and plotted the results.
> In both cases, the point estimate of Beta(t) is sort of parabolic
> in that the curves are monotonically increasing to a local maximum
> after which they are monotonically decreasing (the CIs are a bit
> more wiggly).
>
> I would interpret this to mean that the effect of implant is probably
> time-dependent.  If so, how do I actually get a "proper" estimate of
> beta(t) for a variable like this?
>
> Are there some other things I should look at to understand what's
> going on?
>
>   
If you want to play with time-dependent regression coefficients have a
look at the timereg package and the book that it supports.

However, first you need to consider the possibility of selection effects
that can take place even with non-varying effects. In the case at hand I
would suspect a bias created by the fact that you don't implant devices
into people who are already dead.

> Here is my sessionInfo.
> R version 2.5.0 (2007-04-23)
> i686-pc-linux-gnu
>
> locale:
> LC_CTYPE=en_US.UTF-8;LC_NUMERIC=C;LC_TIME=en_US.UTF-8;LC_COLLATE=en_US.UTF-8;LC_MONETARY=en_US.UTF-8;LC_MESSAGES=en_US.UTF-8;LC_PAPER=en_US.UTF-8;LC_NAME=C;LC_ADDRESS=C;LC_TELEPHONE=C;LC_MEASUREMENT=en_US.UTF-8;LC_IDENTIFICATION=C
>
> attached base packages:
> [1] "splines"   "stats"     "graphics"  "grDevices" "utils"     "datasets"
> [7] "methods"   "base"
>
> other attached packages:
>   cmprsk survival
>  "2.1-7"   "2.31"
>
>
>   


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907