survreg.distributions {survival} | R Documentation

## Parametric Survival Distributions

### Description

List of distributions for accelerated failure models. These are location-scale families for some transformation of time. The entry describes the cdf F and density f of a canonical member of the family.

### Usage

    survreg.distributions

### Format

There are three basic formats; only the first two are used in the built-in distributions

name: | name of distribution
variance: | Variance
init(x,weights,...): | Function returning an initial
mean and | variance
deviance(y,scale,parms): | Function returning the deviance
density(x,parms): | Function returning F,
| 1-F,f,f'/f,f''/f
quantile(p,parms): | Quantile function
scale: | Optional fixed value for scale parameter

and for transformations of the time variable

name: | name of distribution
dist: | name of transformed distribution
trans: | transformation (eg log)
dtrans: | derivative of transformation
itrans: | inverse of transformation
scale: | Optional fixed value for scale parameter

For transformations of user-defined families use

name: | name of distribution
dist: | transformed distribution in first format
trans: | transformation (eg log)
dtrans: | derivative of transformation
itrans: | inverse of transformation
scale: | Optional fixed value for scale parameter

### Details

There are four basic distributions:`extreme`, `gaussian`, `logistic` and `t`. The last three are parametrised in the same way as the distributions already present in R. The extreme value cdf is

F=1-e^{-e^t}.

When the logarithm of survival time has one of the first three distributions we obtain respectively `weibull`, `lognormal`, and `loglogistic`. The Weibull distribution is not parameterised the same way as in `rweibull`.

The other predefined distributions are defined in terms of these. The `exponential` and `rayleigh` distributions are Weibull distributions with fixed `scale` of 1 and 0.5 respectively, and `loggaussian` is a synonym for `lognormal`.

Parts of the built-in distributions are hardcoded in C, so the elements of `survreg.distributions` in the first format above must not be changed and new ones must not be added. The examples show how to specify user-defined distributions to `survreg`.

### See Also

`survreg`, `pnorm`,`plogis`, `pt`

### Examples

    ## not a good fit, but a useful example
    survreg(Surv(futime,fustat)~ecog.ps+rx,data=ovarian,dist='extreme')
    ##
    my.extreme<-survreg.distributions$extreme
    my.extreme$name<-"Xtreme"
    survreg(Surv(futime,fustat)~ecog.ps+rx,data=ovarian,dist=my.extreme)

    ## time transformation
    survreg(Surv(futime,fustat)~ecog.ps+rx,data=ovarian,dist='weibull',scale=1)
    my.weibull<-survreg.distributions$weibull
    my.weibull$dist<-my.extreme
    survreg(Surv(futime,fustat)~ecog.ps+rx,data=ovarian,dist=my.weibull,scale=1)

    ## change the transformation to work in years
    ## intercept changes by log(365), other coefficients stay the same
    my.weibull$trans<-function(y) log(y/365)
    my.weibull$itrans<-function(y) exp(365*y)
    survreg(Surv(futime,fustat)~ecog.ps+rx,data=ovarian,dist=my.weibull,scale=1)

    ## Weibull parametrisation
    y<-rweibull(1000, shape=2, scale=5)
    survreg(Surv(y)~1, dist="weibull")
    ## survreg reports scale=1/2, intercept=log(5)

[Package survival version 2.18 Index]