[R] Repeated measures Cox regression ??coxph??

Fri Aug 16 17:03:42 CEST 2013

Sorry I'm late with this.

On 07/26/2013 02:02 PM, Terry Therneau wrote:
> Two choices. If this were a linear model, do you like the GEE
> approach or a mixed effects approach? Assume that "subject" is a
> variable containing a per-subject identifier.
>
> GEE approach: add "+ cluster(subject)" to the model statement in
> coxph Mixed models approach: Add " + (1|subject)" to the model
> statment in coxme.

Note that the 'cluster' approach ignores the clustering regarding the 
regression parameter estimates. It tries to correct the optimistic 
variance estimate given by ignoring the clustering, but it does nothing 
about the bias that may be introduced.

> When only a very few subjects have multiple events, the mixed model
> (random effect) approach may not be reliable, however.  Multiple
> events per group are the fuel for estimation of the variance of the
> random effect, and with few of these the profile likelihood of the
> random effect will be very flat.  You can get esssentially a random
> estimate of the variance of the "subject effect".  I'm still getting
> my arms around this issue, and it has taken me a long time.

John had exactly two observations per subject, and given that a frailty 
model is reasonable, the bias may be substantial if ignoring it. I made 
a small simulation study to convince myself: frailty variance = 1, one 
binary covariate (constant within subjects) and beta coefficient = 1. 
With 20 subjects, the bias for coxme was -0.004, for coxph (with 
'cluster', but it doesn't matter) -0.294 (based on 1000 replicates). 
(The bias for the frailty standard deviation was -0.108, but who cares 
when we regard it as just a nuisance?)

Of course this doesn't prove anything, but it makes me worried; it is 
easy to understand the frailty model, but what is the 'GEE' model in 
this survival case? Why should it be used in John's case?

> "Frailty" is an alternate label for "random effects when all we have
> is a random intercept".  Multiple labels for the same idea adds
> confusion, but nothing else.

The term "frailty" was (to my knowledge) coined by Vaupel, Manton & 
Stallard in a 1979 paper in 'Demography'. They used it to describe 
heterogeneity in demographic data, and what could happen if it was 
ignored. Just for the record.

Göran

> Terry Therneau
>
> On 07/25/2013 08:14 PM, Marc Schwartz wrote:
>> On Jul 25, 2013, at 4:45 PM, David
>> Winsemius<dwinsemius at comcast.net>  wrote:
>>
>>> On Jul 25, 2013, at 12:27 PM, Marc Schwartz wrote:
>>>
>>>> On Jul 25, 2013, at 2:11 PM, John
>>>> Sorkin<jsorkin at grecc.umaryland.edu>  wrote:
>>>>
>>>>> Colleagues, Is there any R package that will allow one to
>>>>> perform a repeated measures Cox Proportional Hazards
>>>>> regression? I don't think coxph is set up to handle this type
>>>>> of problem, but I would be happy to know that I am not
>>>>> correct. I am doing a study of time to hip joint replacement.
>>>>> As each person has two hips, a given person can appear in the
>>>>> dataset twice, once for the left hip and once for the right
>>>>> hip, and I need to account for the correlation of data from a
>>>>> single individual. Thank you, John
>>>>
>>>>
>>>> John,
>>>>
>>>> See Terry's 'coxme' package:
>>>>
>>>> http://cran.r-project.org/web/packages/coxme/index.html
>>>>
>>> When I looked over the description of coxme, I was concerned it
>>> was not really designed with this in mind. Looking at Therneau
>>> and Grambsch, I thought section 8.4.2 in the 'Multiple Events per
>>> Subject' Chapter fit the analysis question well. There they
>>> compared the use of coxph( ...+cluster(ID),,...)  withcoxph(
>>> ...+strata(ID),,...). Unfortunately I could not tell for sure
>>> which one was being described as superio but I think it was the
>>> cluster() alternative. I seem to remember there are discussions
>>> in the archives.
>>
>> David,
>>
>> I think that you raise a good point. The example in the book (I had
>> to wait to get home to read it) is potentially different however,
>> in that the subject's eye's were randomized to treatment or
>> control, which would seem to suggest comparable baseline
>> characteristics for each pair of eyes, as well as an active
>> intervention on one side where a difference in treatment effect
>> between each eye is being analyzed.
>>
>> It is not clear from John's description above if there is one hip
>> that will be treated versus one as a control and whether the extent
>> of disease at baseline is similar in each pair of hips. Presumably
>> the timing of hip replacements will be staggered at some level,
>> even if there is comparable disease, simply due to post-op recovery
>> time and surgical risk. In cases where the disease between each hip
>> is materially different, that would be another factor to consider,
>> however I would defer to orthopaedic physicians/surgeons from a
>> subject matter expertise consideration. It is possible that the
>> bilateral hip replacement data might be more of a parallel to
>> bilateral breast cancer data, if each breast were to be tracked
>> separately.
>>
>> I have cc'd Terry here, hoping that he might jump in and offer some
>> insights into the pros/cons of using coxme versus coxph with either
>> a cluster or strata based approach, or perhaps even a frailty based
>> approach as in 9.4.1 in the book.
>>
>> Regards,
>>
>> Marc
>>
>>
>>> -- David.
>>>> You also might find the following of interest:
>>>>
>>>> http://bjo.bmj.com/content/71/9/645.full.pdf
>>>>
>>>> http://www.ncbi.nlm.nih.gov/pubmed/22226885
>>>>
>>>> http://www.ncbi.nlm.nih.gov/pubmed/22078901
>>>>
>>>>
>>>>
>>>> Regards,
>>>>
>>>> Marc Schwartz
>>>>
>>>> ______________________________________________
>>>> 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.
>>> David Winsemius Alameda, CA, USA
>>>
>>> ______________________________________________
>>> 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.
>
> ______________________________________________ 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.
>