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`.

`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 2.20 Index]