[R] Survival analysis with no events in one treatment group

[Daniel Malter]

Hi John,

to me it still seems that you have two "problems", given your first email.
The first one, if I am correct, is that you have NO admissions in one of the
groups. That is, you have Treat A, B, C, D and for one of these treatments
there is not a single admission. Then you cannot estimate a survival
function for this group because nobody died (got hospitalized). I think you
have to exclude this group because your survival rate is 100% and your
hazard rate 0%. But more proficient people may have better advice with that.

That subject 2 did not get hospitalized is not a problem though. The
observation is censored at 12 months. Since there are more patients in his
treatment group (subject 1) who had an event, the survival function can be
estimated. 

To the multiple admissions problem: To account for the fact that some have
more than one event you may create a "number of events" variable, say
numEvents, and include that in a strata() argument to your regression call:

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

Use strata if you think that your baseline hazard is different in the
different strata (in your case: if you think that the baseline hazard of
having an event differs with having had prior event(s)). At the same time
you assume that your treatment effect  - the beta on your Treat variable -
is the same across all strata. If you have reason to assume that the effect
of your treatment varies (interacts) with the number of prior events, then
it is not the correct approach. In addition you may include the
cluster(Subject) or frailty(Subject) commands.

Instead of strata you might also consider using a dummy variable, coding the
number of prior events (if the maximum number admissions per patient is
reasonably small and the number of cell frequencies reasonably large).

Finally, you may want to consult Terry Thernau and Patricia Grambsch's book
"Modeling survival data". It shows how to apply the techniques in R/S-Plus.
I find it invaluable.

Does that help you?

Daniel


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

-----Ursprüngliche Nachricht-----
Von: John Field [mailto:JohnField at ozemail.com.au] 
Gesendet: Sunday, December 30, 2007 10:14 PM
An: Daniel Malter; R-help at r-project.org
Betreff: Re: AW: [R] Survival analysis with no events in one treatment group

Hi Daniel,

Sorry, it may have been clearer if I had used "subjects" instead of
"patients".  The treatments were administered to all subjects, and then in
the succeeding 12 months, some were hospitalised and some were not.  Hence
only about 25% of the subjects were hospitalised.

The start of the data:
subj    time1   time2   event Treat
1       0       6.2     1       A
1       6.2     12      0       A
2       0       12      0       A

so subject 1 was hospitalised at 6.2 months, subject 2 not at all.

Hope this makes it clearer.
Regards,
John





.At 12:59 PM 31/12/2007, Daniel Malter wrote:
>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
>-------------------------
>
>-----Ursprüngliche 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
>
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