[R] coxme with frailty--variance of random effect?

Terry Therneau therneau at mayo.edu
Mon Feb 6 13:56:57 CET 2012

In answer to the several questions:

1. Variance of the random effect:  Your example is not reproducable
since you didn't give the random number seed.  Instead I'll use one of
the data sets that comes with the survival package.
> library(coxme)
> fit <- coxme(Surv(tstart, tstop, status) ~ treat + (1|center), cgd)
> VarCorr(fit)$center

> var(ranef(fit)$center)
[1] 0.06261608

 Yes, it is true that for a random effects model, the estimated variance
of the random effect is not equal to var(estimated per center effects).
Exactly the same is true of a linear mixed effects model: try the same
with lmer
	> library(lme4)
	> lfit(status ~ treat + (1|center), cgd)
	> VarCorr(lfit)$center
	> var(ranef(lfit)$center)

Why? It's a statistical insight that took me a while, so I don't think I
can explain it over email.  Find someone familiar with mixed efffects
models and have a chat.

2. coxph(.... +frailty(center)) and coxme give different results.
 Read the documentation.  One of them is fitting a gamma distribution
for the random effect, the other a Gaussian.

Terry Therneau

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