Random effects terms
The frailty function allows one to add a simple random effects term to a Cox model.
frailty(x, distribution="gamma", ...)
frailty.gamma(x, sparse = (nclass > 5), theta, df, eps = 1e-05,
method = c("em","aic", "df", "fixed"), ...)
frailty.gaussian(x, sparse = (nclass > 5), theta, df,
method =c("reml","aic", "df", "fixed"), ...)
frailty.t(x, sparse = (nclass > 5), theta, df, eps = 1e-05, tdf = 5,
method = c("aic", "df", "fixed"), ...)x |
the variable to be entered as a random effect. It is always treated as a factor. |
distribution |
either the |
... |
Arguments for specific distribution, including (but not limited to) |
sparse |
cutoff for using a sparse coding of the data matrix.
If the total number of levels of |
theta |
if specified, this fixes the variance of the random effect.
If not, the variance is a parameter, and a best solution is sought.
Specifying this implies |
df |
if specified, this fixes the degrees of freedom for the random effect.
Specifying this implies |
method |
the method used to select a solution for theta, the variance of the
random effect.
The |
tdf |
the degrees of freedom for the t-distribution. |
eps |
convergence criteria for the iteration on theta. |
The frailty plugs into the general penalized
modeling framework provided by the coxph
and survreg routines.
This framework deals with likelihood, penalties, and degrees of freedom;
these aspects work well with either parent routine.
Therneau, Grambsch, and Pankratz show how maximum likelihood estimation for
the Cox model with a gamma frailty can be accomplished using a general
penalized routine, and Ripatti and Palmgren work through a similar argument
for the Cox model with a gaussian frailty. Both of these are specific to
the Cox model.
Use of gamma/ml or gaussian/reml with
survreg does not lead to valid results.
The extensible structure of the penalized methods is such that the penalty
function, such as frailty or
pspine, is completely separate from the modeling
routine. The strength of this is that a user can plug in any penalization
routine they choose. A weakness is that it is very difficult for the
modeling routine to know whether a sensible penalty routine has been
supplied.
Note that use of a frailty term implies a mixed effects model and use of a cluster term implies a GEE approach; these cannot be mixed.
The coxme package has superseded
this method. It is faster, more stable, and more flexible.
this function is used in the model statement of either
coxph or survreg.
It's results are used internally.
S Ripatti and J Palmgren, Estimation of multivariate frailty models using penalized partial likelihood, Biometrics, 56:1016-1022, 2000.
T Therneau, P Grambsch and VS Pankratz, Penalized survival models and frailty, J Computational and Graphical Statistics, 12:156-175, 2003.
# Random institutional effect
coxph(Surv(time, status) ~ age + frailty(inst, df=4), lung)
# Litter effects for the rats data
rfit2a <- coxph(Surv(time, status) ~ rx +
frailty.gaussian(litter, df=13, sparse=FALSE), rats,
subset= (sex=='f'))
rfit2b <- coxph(Surv(time, status) ~ rx +
frailty.gaussian(litter, df=13, sparse=TRUE), rats,
subset= (sex=='f'))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.