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 lognormal,loglogistic and weibull.

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

data(ovarian)
## 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)