R help - Jun 2011 - cluster() or frailty() in coxph

Dear List,

Can anyone please explain the difference between cluster() and
frailty() in a coxph? I am a bit puzzled about it. Would appreciate
any useful reference or direction.

cheers,

Ehsan


> marginal.model <- coxph(Surv(time, status) ~ rx + cluster(litter), rats)
> frailty.model  <- coxph(Surv(time, status) ~ rx + frailty(litter), rats)
> marginal.model
Call:
coxph(formula = Surv(time, status) ~ rx + cluster(litter), data = rats)


    coef exp(coef) se(coef) robust se    z      p
rx 0.905      2.47    0.318     0.303 2.99 0.0028

Likelihood ratio test=7.98  on 1 df, p=0.00474  n= 150
> frailty.model
Call:
coxph(formula = Surv(time, status) ~ rx + frailty(litter), data = rats)

                coef  se(coef) se2   Chisq DF   p
rx              0.914 0.323    0.319  8.01  1.0 0.0046
frailty(litter)                      17.69 14.4 0.2400

Iterations: 6 outer, 24 Newton-Raphson
     Variance of random effect= 0.499   I-likelihood = -180.8
Degrees of freedom for terms=  1.0 14.4
Likelihood ratio test=37.6  on 15.4 df, p=0.00124  n= 150

Hi Ehsan,

My understanding (hopefully someone will jump in if this is wrong) is
that cluster() identifies a variable that is an indicator for
correlated observations (rats in a litter, children in a classroom,
etc.).  The relative risk from treatment (rx) is for a random sample
of rats.

frailty() estimates the relative risk from treatment (rx) within
litters.  Also, by default, it (frailty) uses a gamma distribution and
estimates the scale parameter unless specified by theta (or df).

There is an entire chapter devoted to frailty models in Therneau &
Grambsch book on the cox model (the title is something like Survival
Data Analysis).

HTH,

Josh

On Sat, Jun 25, 2011 at 3:48 PM, Ehsan Karim <wildscop at hotmail.com>
wrote:
> Dear List,
>
> Can anyone please explain the difference between cluster() and
> frailty() in a coxph? I am a bit puzzled about it. Would appreciate
> any useful reference or direction.
>
> cheers,
>
> Ehsan
>
>
>
>> marginal.model <- coxph(Surv(time, status) ~ rx + cluster(litter),
rats)
>> frailty.model ?<- coxph(Surv(time, status) ~ rx + frailty(litter),
rats)
>> marginal.model
> Call:
> coxph(formula = Surv(time, status) ~ rx + cluster(litter), data = rats)
>
>
> ? ?coef exp(coef) se(coef) robust se ? ?z ? ? ?p
> rx 0.905 ? ? ?2.47 ? ?0.318 ? ? 0.303 2.99 0.0028
>
> Likelihood ratio test=7.98 ?on 1 df, p=0.00474 ?n= 150
>> frailty.model
> Call:
> coxph(formula = Surv(time, status) ~ rx + frailty(litter), data = rats)
>
> ? ? ? ? ? ? ? ?coef ?se(coef) se2 ? Chisq DF ? p
> rx ? ? ? ? ? ? ?0.914 0.323 ? ?0.319 ?8.01 ?1.0 0.0046
> frailty(litter) ? ? ? ? ? ? ? ? ? ? ?17.69 14.4 0.2400
>
> Iterations: 6 outer, 24 Newton-Raphson
> ? ? Variance of random effect= 0.499 ? I-likelihood = -180.8
> Degrees of freedom for terms= ?1.0 14.4
> Likelihood ratio test=37.6 ?on 15.4 df, p=0.00124 ?n= 150
>
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-- 
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/

Addition of a cluster() term fits a Generalized Estimating Equations
(GEE) type of model, addition of frailty() fits a random effects  model
(Mixed Effect or ME).  In glm analysis (linear regression, logistic
regression, etc) the arguments about the advantages/disadvantages of GEE
ve ME would easily fill a volume.  Most of this argument carries over to
the coxph case; I find both approaches useful.  

Caveats:
  1. Coxph with cluster() only allows the "working independence"
variance structure.  The details for other variance structures were
worked out by Alicia Z in her Iowa State PhD thesis, but I've never
gotton around to implementing it.
  2. For random effects, the coxme function is preferred.
  3. In comparing GEE and ME one part of the arguement is that the
former model is "marginal" and the second "conditional", and
thus the
coefficients from the models mean different things.  I take this with a
grain of salt.  Remember that ALL models are wrong.

Terry Therneau