[R] A question on time-dependent covariates in the Cox model.

[Jacob Etches]

This is a question about time-varying effects rather than time-varying 
covariates, even if the SAS method tests for the former by using the 
latter.  SAS evaluates the line

>> dosetime=time*dose;

for all observations at each event time as it estimates the model, such 
that you are not using future information.  It has the effect of 
testing for a linear change in the magnitude of the effect of dose over 
time.  I believe Paul Allison's survival book recommends this as a 
quick and dirty test for constancy of effect.  Had you put that line in 
a datastep prior to PHREG, rather than in PHREG, you'd get a completely 
different (and uninformative) result (probably the same as R is giving 
you), because each observation's total survival time would be used to 
create a single value for the interaction term.  You could manually 
replicate SAS's behaviour in R if you wanted, but every observation 
would have to start a new time interval whenever any other observation 
has an event, as Peter explained below.

You might also want to look at Aalen's additive survival model for 
non-linear changes in effect over time:
http://www.med.uio.no/imb/stat/addreg/

hope that helps,
Jacob Etches


On 2005/06/22, at 06:34, Peter Dalgaard wrote:

> "Marianne dk" <m_323stat at hotmail.com> writes:
>
>> I have a dataset with
>>
>> event=death
>> time (from medical examination until death/censoring)
>> dose (given at examination time)
>>
>> Two groups are considered, a non-exposed group (dose=0), an exposed 
>> group
>> (dose between 5 and 60).
>>
>> For some reason there is a theory of the dose increasing its effect 
>> over
>> time (however it was only given (and measured) once = at the time of
>> examination).
>>
>> I tested a model:
>>
>> coxph(Surv(time,dod)~dose + dose:time)
>>
>> Previously I tested the model in SAS:
>>
>> proc phreg data=test;
>> 	model time*dod(0)=dose dosetime /rl ties=efron;
>> 	dosetime=time*dose;
>> 	run;
>>
>> Without the interaction terms I get the same results for the two 
>> models. By
>> including the interaction terms I do not. The model in R gives a 
>> negative
>> coefficient for the interaction term which is expected to be positive 
>> (and
>> is so in SAS). The LRTs are also completely different.
>>
>> TWO QUESTIONS:
>>
>> 1) Is it reasonable to bring in an interaction term when dose is only
>> measured once?
>>
>> 2) If yes, can anyone give a hint on explaining the difference 
>> between the
>> models in R and SAS?
>
> I don't know what SAS does, maybe it second-guesses your intentions,
> but R will definitely get it completely wrong. If you use time as a
> covariate, the same time (of death/censoring) will be applied at all
> death times. Pretty obviously, long observation times tend to be
> associated with low mortalities! With interactions you get, er,
> similarly incorrect effects.
>
> To do coxph with time-dependent variables, you need to split data
> into little time segments, according to the death time of every death,
> inserting a new variable (ntime, say) which is the time of the
> endpoint of the interval.
>
> -- 
>    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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