The frailty function allows one to add a simple random effects term to a Cox or survreg 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"), ...)
- the variable to be entered as a random effect. It is always treated as a factor.
- either the
tdistribution may be specified. The routines
frailty.tdo the actual work.
- Arguments for specific distribution, including (but not limited to)
- cutoff for using a sparse coding of the data matrix. If the total number of levels of
xis larger than this value, then a sparse matrix approximation is used. The correct cutoff is still a matter of exploration: if the number of levels is very large (thousands) then the non-sparse calculation may not be feasable in terms of both memory and compute time. Likewise, the accuracy of the sparse approximation appears to be related to the maximum proportion of subjects in any one class, being best when no one class has a large membership.
- 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
- if specified, this fixes the degrees of freedom for the random effect. Specifying this implies
method='df'. Only one of
dfshould be specified.
- the method used to select a solution for theta, the variance of the random effect. The
fixedcorresponds to a user-specified value, and no iteration is done. The
dfselects the variance such that the degrees of freedom for the random effect matches a user specified value. The
aicmethod seeks to maximize Akiake's information criteria 2*(partial likelihood - df). The
remlmethods are specific to Cox models with gamma and gaussian random effects, respectively. Please see further discussion below.
- the degrees of freedom for the t-distribution.
- convergence critera for the iteration on theta.
frailty plugs into the general penalized modeling framework provided by the
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
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.
coxme package has superseded this method. It is faster, more stable, and more flexible.
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 <- survreg(Surv(time, status) ~ rx + frailty.gaussian(litter, df=13, sparse=FALSE), rats ) rfit2b <- survreg(Surv(time, status) ~ rx + frailty.gaussian(litter, df=13, sparse=TRUE), rats )
Documentation reproduced from package survival, version 2.37-4. License: LGPL (>= 2)