[R] Apparently Conflicting Results with coxph

[Kevin E. Thorpe]

Peter Dalgaard wrote:
> 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.
> 

Thanks.  The point in your last paragraph did cross my mind too.

-- 
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.6057