R help - Oct 2007 - X matrix deemed to be singular in counting process coxph

Dear all,

I have a question  with respect to counting process formulation of the 
coxph(survival) model.
I have two groups of observations for which I have partitioned each 
observation into two distinct time intervals, namely, entry day till day 13, 
and day 13 till death or censorship day (of course the latter only for the 
observations that survived the first 13 day interval), and added a dummy
't'
representing the first and second interval [0,1]. The reason I want this is 
because the groups have crossing survival curves and I happen to know that 
the change in hazard ratio between the groups occurs at day 13.

I try the following:
> coxph(Surv(Start,Stop,event)~group*t+cluster(nr),data=dat4)
Call:
coxph(formula = Surv(Start, Stop, event) ~ group * t + cluster(nr),
    data = dat4)

which results in  :

         coef exp(coef) se(coef) robust se      z       p
group     0.336     1.400   0.0409    0.0408   8.24 1.1e-16
t         NA        NA   0.0000    0.0000     NA      NA
group:t -0.689     0.502   0.0530    0.0530 -13.02 0.0e+00

Likelihood ratio test=180  on 2 df, p=0  n= 13244
Warning message:
X matrix deemed to be singular; variable 2 in: coxph(Surv(Start, Stop, 
event) ~ group * t + cluster(nr),

deleting all terms apart from 't' still results in the same warning.
I seem to have been stuck on this one. Does anyone known or have any 
suggestions why t can't be estimated?
I haven't been able to find any help on the RSiteSearch.


Many thanks in advance.

Caspar

PS: I could send a some of this dataset if anyone interested for a tryout

Caspar Hallmann
MSc Student WUR
The Netherlands

What you have is a slightly more subtle variant of the following:

   library(survival)
   data(lung)	
   mydata <- cbind(lung, newvar =2)
   coxph(Surv(time, status) ~ ph.karno + newvar,  mydata)

                coef exp(coef) se(coef)     z     p
    ph.karno -0.0164     0.984  0.00585 -2.81 0.005
    newvar        NA        NA  0.00000    NA    NA


 You have created a data set where at all times <13 the variable t=0, and at
all
times >13 the variable t=1.  The Cox model compares the values of the
covariates
of each subject who died to the values of those who did not die, using the 
current covariate values AT THAT TIME.  Since the value of your "t" is
always a
constant within the set, the variable contains no information for discriminating
the events from the non-events.  Zero information --> a coefficient of NA.
 
 	Terry Therneau   
 	Mayo Clinic