survreg.distributions        package: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)

