survfit               package:survival               R Documentation

Compute a Survival Curve for Censored Data

Description:

     Computes an estimate of a survival curve for censored data using
     either the Kaplan-Meier or the Fleming-Harrington method or
     computes the predicted survivor function for a Cox proportional
     hazards model.

Usage:

     survfit(formula, data, weights, subset, na.action, 
             newdata, individual=F, conf.int=.95, se.fit=T, 
             type=c("kaplan-meier","fleming-harrington", "fh2"),
             error=c("greenwood","tsiatis"),
             conf.type=c("log","log-log","plain","none"),
             conf.lower=c("usual", "peto", "modified"))
     ## S3 method for class 'survfit':
     x[...,drop=FALSE]
     basehaz(fit,centered=TRUE)

Arguments:

 formula: A formula object or a 'coxph' object. If a formula object is
          supplied it must have a 'Surv' object as the  response on the
          left of the '~' operator and, if desired, terms  separated by
          + operators on the right. One of the terms may be a 'strata'
          object.  For a single survival curve the '"~ 1"' part of the
          formula is not required. 

    data: a data frame in which to interpret the variables named in the
          formula, or in the 'subset' and the 'weights' argument. 

 weights: The weights must be nonnegative and it is strongly
          recommended that  they be strictly positive, since zero
          weights are ambiguous, compared to use of the 'subset'
          argument. 

  subset: expression saying that only a subset of the rows of the data
          should 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'. 

 newdata: a data frame with the same variable names as those that
          appear in the 'coxph' formula.  Only applicable when
          'formula' is a 'coxph' object. The curve(s) produced will be
          representative of a cohort who's covariates correspond to the
          values in 'newdata'. Default is the mean of the covariates
          used in the 'coxph' fit. 

individual: a logical value indicating whether the data frame
          represents different time epochs for only one individual (T),
          or whether multiple rows indicate multiple individuals (F,
          the default).  If the former only one curve will be produced;
          if the latter there will be one curve per row in 'newdata'. 

conf.int: the level for a two-sided confidence interval on  the
          survival curve(s). Default is 0.95. 

  se.fit: a logical value indicating whether standard errors should be
          computed.  Default is 'TRUE'. 

    type: a character string specifying the type of survival curve.
          Possible values are '"kaplan-meier"', '"fleming-harrington"'
          or '"fh2"' if a formula is given and '"aalen"' or
          '"kaplan-meier"' if the first argument is a 'coxph' object,
          (only the first two characters are necessary). The default is
          '"aalen"' when a 'coxph' object is given, and it is
          '"kaplan-meier"' otherwise. 

   error: either the string '"greenwood"' for the Greenwood formula or
          '"tsiatis"' for the Tsiatis formula, (only the first
          character is necessary).  The default is '"tsiatis"' when a
          'coxph' object is given, and it is '"greenwood"' otherwise. 

conf.type: One of '"none"', '"plain"', '"log"' (the default), or
          '"log-log"'.  Only enough of the string to uniquely identify
          it is necessary. The first option causes confidence intervals
          not to be generated.  The second causes the standard
          intervals 'curve +- k *se(curve)', where k is determined from
          'conf.int'.  The log option calculates intervals based on the
          cumulative hazard or log(survival). The last option bases
          intervals on the log hazard or log(-log(survival)).  These
          last will never extend past 0 or 1. 

conf.lower: controls modified lower limits to the curve, the upper
          limit remains unchanged.  The modified lower limit is based
          on an 'effective n' argument.  The confidence bands will
          agree with the usual calculation at each death time, but
          unlike the usual bands the confidence interval becomes wider
          at each censored observation.  The extra width is obtained by
          multiplying the usual variance by a factor m/n, where n is
          the number currently at risk and m is the number at risk at
          the last death time.  (The bands thus agree with the
          un-modified bands at each death time.) This is especially
          useful for survival curves with a long flat tail.

          The Peto lower limit is based on the same 'effective n'
          argument as the modified limit, but also replaces the usual
          Greenwood variance term with a simple approximation.  It is
          known to be conservative. 

       x: a 'survfit' object

     fit: a 'coxph' object

centered: Compute the baseline hazard at the covariate mean rather than
          at zero?

    drop: Only 'FALSE' is supported

     ...: Other arguments for future expansion

Details:

     Actually, the estimates used are the Kalbfleisch-Prentice
     (Kalbfleisch and Prentice, 1980, p.86) and the
     Tsiatis/Link/Breslow, which reduce to the Kaplan-Meier and
     Fleming-Harrington estimates, respectively, when the weights are
     unity.  When curves are fit for a Cox model, subject weights of
     'exp(sum(coef*(x-center)))' are used,  ignoring any value for
     'weights' input by the user.  There is also an extra term in the
     variance of the curve, due to the variance ofthe coefficients and
     hence variance in the computed weights.

     The Greenwood formula for the variance is a sum of terms
     d/(n*(n-m)), where d is the number of deaths at a given time
     point, n is the sum of 'weights' for all individuals still at risk
     at that time, and m is the sum of 'weights' for the deaths at that
     time.  The justification is based on a binomial argument when
     weights are all equal to one; extension to the weighted case is ad
     hoc.  Tsiatis (1981) proposes a sum of terms d/(n*n), based on a
     counting process argument which includes the weighted case.

     The two variants of the F-H estimate have to do with how ties are
     handled. If there were 3 deaths out of 10 at risk, then the first
     would increment the hazard by 3/10 and the second by 1/10 + 1/9 +
     1/8.  For curves created after a Cox model these correspond to the
     Breslow and Efron estimates, respectively, and the proper choice
     is made automatically. The 'fh2' method will give results closer
     to the Kaplan-Meier.

     Based on the work of Link (1984), the log transform is expected to
     produce the most accurate confidence intervals.  If there is heavy
     censoring, then based on the work of Dorey and Korn (1987) the
     modified estimate will give a more reliable confidence band for
     the tails of the curve.

Value:

     a 'survfit' object; see the help on 'survfit.object' for details.
     Methods defined for 'survfit' objects are provided for 'print',
     'plot', 'lines', and 'points'.

     For 'basehaz', a dataframe with the baseline hazard, times, and
     strata.

     The '"["' method returns a 'survfit' object giving survival for
     the selected groups.

References:

     Dorey, F. J. and Korn, E. L. (1987).  Effective sample sizes for
     confidence intervals for survival probabilities.  _Statistics in
     Medicine_ 6, 679-87.

     Fleming, T. H. and Harrington, D.P. (1984).  Nonparametric
     estimation of the survival distribution in censored data.  _Comm.
     in Statistics_ 13, 2469-86.

     Kalbfleisch, J. D. and Prentice, R. L. (1980).  _The Statistical
     Analysis of Failure Time Data._ Wiley, New York.

     Link, C. L. (1984). Confidence intervals for the survival function
     using Cox's proportional hazards model with  covariates. 
     _Biometrics_ 40, 601-610.

     Tsiatis, A. (1981). A large sample study of the estimate for the
     integrated hazard function in Cox's regression model for survival
     data. _Annals of Statistics_ 9, 93-108.

See Also:

     'print.survfit', 'plot.survfit', 'lines.survfit',
     'summary.survfit', 'survfit.object' 'coxph', 'Surv', 'strata'.

Examples:

     #fit a Kaplan-Meier and plot it
     fit <- survfit(Surv(time, status) ~ x, data=aml)
     plot(fit)
     # plot only 1 of the 2 curves from above
     plot(fit[1])
     ## the other line
     lines(fit[2], col="blue")

     #fit a cox proportional hazards model and plot the 
     #predicted survival curve
     fit <- coxph( Surv(futime,fustat)~resid.ds+rx+ecog.ps,data=ovarian)
     plot( survfit( fit))

