[R] Apparently Conflicting Results with coxph
P.Dalgaard at biostat.ku.dk
Mon Oct 1 15:48:43 CEST 2007
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:
> 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:
> 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)
> attached base packages:
>  "splines" "stats" "graphics" "grDevices" "utils" "datasets"
>  "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
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