# R: (Approximate) Frailty models

frailty {survival} | R Documentation

## (Approximate) Frailty models

### Description

When included in a coxph or survreg, fits by penalised likelihood a random effects (frailty) model. `frailty` is generic, with methods for t, Gaussian and Gamma distributions.

### Usage

    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"), ...)

### Arguments

`x` | group indicator
`distribution` | frailty distribution
`...` | Arguments for specific distribution, including (but not limited to)
`sparse` | Use sparse Newton-Raphson algorithm
`df` | Approximate degrees of freedom
`theta` | Penalty
`eps` | Accuracy of `df`
`method` | maximisation algorithm
`tdf` | df of t-distribution

### Details

The penalised likelihood method is equivalent to maximum (partial) likelihood for the gamma frailty but not for the others.

The sparse algorithm uses the diagonal of the information matrix for the random effects, which saves a lot of space.

The frailty distributions are really the log-t and lognormal: t and Gaussian are random effects on the scale of the linear predictor.

### Value

An object of class `coxph.penalty` containing a factor with attributes specifying the control functions.

### References

Therneau TM, Grambsch PM, Pankratz VS (2003) "Penalized survival models and frailty" Journal of Computational and Graphical Statistics 12, 1: 156-175

### See Also

`coxph`,`survreg`,`ridge`,`pspline`

### Examples

    kfit <- coxph(Surv(time, status)~ age + sex + disease + frailty(id), kidney)
    kfit0 <- coxph(Surv(time, status)~ age + sex + disease, kidney)
    kfitm1 <- coxph(Surv(time,status) ~ age + sex + disease +
                    frailty(id, dist='gauss'), kidney)
    coxph(Surv(time, status) ~ age + sex + frailty(id, dist='gauss', method='aic',caic=TRUE), kidney)
    # uncorrected aic
    coxph(Surv(time, status) ~ age + sex + frailty(id, method='aic', caic=FALSE), kidney)

    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 )
    rfit2a
    rfit2b

[Package survival version 2.32 Index]