R: Regression for a Parametric Survival Model

survreg {survival} | R Documentation

## Regression for a Parametric Survival Model

### Description

Fit a parametric survival regression model. These are location-scale models for an arbitrary transform of the time variable; the most common cases use a log transformation, leading to accelerated failure time models.

### Usage

    survreg(formula, data, weights, subset,
            na.action, dist="weibull", init=NULL, scale=0,
            control,parms=NULL,model=FALSE, x=FALSE,
            y=TRUE, robust=FALSE, cluster, score=FALSE, ...)

### Arguments

`formula` | a formula expression as for other regression models. The response is usually a survival object as returned by the `Surv` function. See the documentation for `Surv`, `lm` and `formula` for details.
`data` | a data frame in which to interpret the variables named in the `formula`, `weights` or the `subset` arguments.
`weights` | optional vector of case weights
`subset` | subset of the observations to be used in the fit
`na.action` | a missing-data filter function, applied to the model.frame, after any `subset` argument has been used. Default is `options()\$na.action`.
`dist` | assumed distribution for y variable. If the argument is a character string, then it is assumed to name an element from `survreg.distributions`. These include `"weibull"`, `"exponential"`, `"gaussian"`, `"logistic"`,`"lognormal"` and `"loglogistic"`. Otherwise, it is assumed to be a user defined list conforming to the format described in `survreg.distributions`.
`parms` | a list of fixed parameters. For the t-distribution for instance this is the degrees of freedom; most of the distributions have no parameters.
`init` | optional vector of initial values for the parameters.
`scale` | optional fixed value for the scale. If set to <=0 then the scale is estimated.
`control` | a list of control values, in the format produced by `survreg.control`. The default value is `survreg.control()`
`model,x,y` | flags to control what is returned. If any of these is true, then the model frame, the model matrix, and/or the vector of response times will be returned as components of the final result, with the same names as the flag arguments.
`score` | return the score vector. (This is expected to be zero upon successful convergence.)
`robust` | Use robust sandwich error instead of the asymptotic formula. Defaults to TRUE if there is a `cluster` argument.
`cluster` | Optional variable that identifies groups of subjects, used in computing the robust variance. Like `model` variables, this is searched for in the dataset pointed to by the `data` argument.
`...` | other arguments which will be passed to `survreg.control`.

### Details

All the distributions are cast into a location-scale framework, based on chapter 2.2 of Kalbfleisch and Prentice. The resulting parameterization of the distributions is sometimes (e.g. gaussian) identical to the usual form found in statistics textbooks, but other times (e.g. Weibull) it is not. See the book for detailed formulas.

### Value

an object of class `survreg` is returned.

### References

Kalbfleisch, J. D. and Prentice, R. L., The statistical analysis of failure time data, Wiley, 2002.

### See Also

`survreg.object`, `survreg.distributions`, `pspline`, `frailty`, `ridge`

### Examples

    # Fit an exponential model: the two fits are the same
    survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='weibull',
                                        scale=1)
    survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian,
            dist="exponential")

    #
    # A model with different baseline survival shapes for two groups, i.e.,
    #   two different scale parameters
    survreg(Surv(time, status) ~ ph.ecog + age + strata(sex), lung)

    # There are multiple ways to parameterize a Weibull distribution. The survreg
    # function embeds it in a general location-scale family, which is a
    # different parameterization than the rweibull function, and often leads
    # to confusion.
    #   survreg's scale  =    1/(rweibull shape)
    #   survreg's intercept = log(rweibull scale)
    #   For the log-likelihood all parameterizations lead to the same value.
    y <- rweibull(1000, shape=2, scale=5)
    survreg(Surv(y)~1, dist="weibull")

    # Economists fit a model called `tobit regression', which is a standard
    # linear regression with Gaussian errors, and left censored data.
    tobinfit <- survreg(Surv(durable, durable>0, type='left') ~ age + quant,
    	            data=tobin, dist='gaussian')

[Package survival version 3.2-7 Index]