R help - Dec 2007 - Survival analysis with no events in one treatment group

I'm trying to fit a Cox proportional hazards model to some hospital 
admission data.  About 25% of the patients have had at least one 
admission, and of these, 40% have had two admissions within the 12 
month period of the study.  Each patients has had one of 4 
treatments, and one of the treatment groups has had no admissions for 
the period.  I used:

surv.obj<-Surv(time=time1,time2=time2,event=event,type="counting")
model<-coxph(surv.obj~Treatment+cluster(Subject))

and, as explained in the coxph help page, I get a warning message 
about convergence because the MLE of one of the coefficients is 
infinite since there are no admissions in one group.

I'm looking for suggestions about how to proceed with an analysis of 
these data.  I'd prefer not to ignore the fact that there are 
multiple admissions, but any alternative ideas I have at the moment do this.

Many thanks,
John Field
================================Faculty of Health Sciences Statistical Support
Service
The University of Adelaide, Australia 5005

Hi John,

I am on the slow side - can you provide sample code. How can one treatment
group have no admissions? 

Let's say there are treatments W, X, Y, Z. Do you mean that NONE of the
patients who got admitted the first time and, say, received treatment X
during the first admission, have ever had a second admission (in your data).
And for the other treatments W, Y, and Z some of those who got admitted the
first time came in a second time?

Cheers and a happy new year's eve,
Daniel

-------------------------
cuncta stricte discussurus
-------------------------

-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von John Field
Gesendet: Sunday, December 30, 2007 9:16 PM
An: R-help at r-project.org
Betreff: [R] Survival analysis with no events in one treatment group

I'm trying to fit a Cox proportional hazards model to some hospital
admission data.  About 25% of the patients have had at least one admission,
and of these, 40% have had two admissions within the 12 month period of the
study.  Each patients has had one of 4 treatments, and one of the treatment
groups has had no admissions for the period.  I used:

surv.obj<-Surv(time=time1,time2=time2,event=event,type="counting")
model<-coxph(surv.obj~Treatment+cluster(Subject))

and, as explained in the coxph help page, I get a warning message about
convergence because the MLE of one of the coefficients is infinite since
there are no admissions in one group.

I'm looking for suggestions about how to proceed with an analysis of these
data.  I'd prefer not to ignore the fact that there are multiple admissions,
but any alternative ideas I have at the moment do this.

Many thanks,
John Field
================================Faculty of Health Sciences Statistical Support
Service The University of
Adelaide, Australia 5005

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Hi again,

I meant some rows of sample data, rather than sample code. Sorry about that.

Daniel 


-------------------------
cuncta stricte discussurus
-------------------------

-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von John Field
Gesendet: Sunday, December 30, 2007 9:16 PM
An: R-help at r-project.org
Betreff: [R] Survival analysis with no events in one treatment group

I'm trying to fit a Cox proportional hazards model to some hospital
admission data.  About 25% of the patients have had at least one admission,
and of these, 40% have had two admissions within the 12 month period of the
study.  Each patients has had one of 4 treatments, and one of the treatment
groups has had no admissions for the period.  I used:

surv.obj<-Surv(time=time1,time2=time2,event=event,type="counting")
model<-coxph(surv.obj~Treatment+cluster(Subject))

and, as explained in the coxph help page, I get a warning message about
convergence because the MLE of one of the coefficients is infinite since
there are no admissions in one group.

I'm looking for suggestions about how to proceed with an analysis of these
data.  I'd prefer not to ignore the fact that there are multiple admissions,
but any alternative ideas I have at the moment do this.

Many thanks,
John Field
================================Faculty of Health Sciences Statistical Support
Service The University of
Adelaide, Australia 5005

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

John,
   The key issue with a data set that has no events in one group is that the 
usual Wald tests, i.e., beta/se(beta), do not work.  They is based on a Taylor 
series argument of the usual type: f(x) = f(x0) + a polynomial in (x-x0), and 
for infinite beta "x" and "x0" are so far apart that the
approximation isn't
even close.  The score and likelihood ratio statistics are just fine, however. 
So if you completely ignore any printout that involves the "infinite
beta"
columns of the estimated variance matrix all should be well.
   
   In your case, a second issue is that the likelihood ratio test is not valid 
for data sets with multiple events per subject. You have to account for the 
within subject correlation in some way, either by moving to a random effects 
model or a gee type variance.  You have done the latter by adding
"cluster" to
your coxph call.  Thus, only the "robust score test" line of your
final output
is reliable.  The LR test is tainted by multiple events, and the robust Wald by 
the infinite beta.  Use summary() to print all the test statistics.
   
  Assume you have variables x1 and x2 in a model, and want to test the 
importance of adding x3.  Stepwise regression programs often use score tests for
this, but most users have never done it and don't know how. 
   	> fit1 <- coxph(Surv(time1, time2, event) ~ x1 + x2 +
cluster(subject),
   		               subset= (!is.na(x3)))
   	> fit2 <- coxph(Surv(time1, time2, event) ~ x1 + x2 + x3 + 
   		              cluster(subject), init=c(coef(fit1), 0))
   		              
Now the "robust score test" in fit2 is a test of (coef1, coef2, 0) [no
need for
x3] vs the model with x3.  If you have no missing values you can skip the subset
argument, but make sure that the two fits are actually on the same data set: 
always check that the "n=" part of the printout matches.

	Terry Therneau
	Mayo Clinic