

survfit(survival4)                           R Documentation

_C_o_m_p_u_t_e _a _s_u_r_v_i_v_a_l _C_u_r_v_e _f_o_r _C_e_n_s_o_r_e_d _D_a_t_a

_D_e_s_c_r_i_p_t_i_o_n_:

     Actually, the estimates used are the Kalbfleisch-Pren-
     tice (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 wt input by the user.
     There is also an extra term in the variance of the
     curve, due to the variance of coef 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 wt for all individu-
     als 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 Bres-
     low 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 inter-
     vals.  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.

_U_s_a_g_e_:

     survfit( object, data=sys.parent(), weights, subset, na.action,
               newdata, individual=F, conf.int=.95, se.fit=T,
               type=c("kaplan-meier","flemington-harrington", "fh2"),
               error=c("greenwood","tsiatis"),
               conf.type=c("log","log-log","plain","none"),
               conf.lower=c("usual", "peto", "modified")

_A_r_g_u_m_e_n_t_s_:

  object: 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.  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 indi-
          cate 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 `new-
          data'.

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: either "kaplan-meier" , "fleming-harrington" or
          "fh2",  (only the   first  two characters  are
          necessary).   The  default  is "fleming-harring-
          ton" 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 effec-
          tive n argument as the modified limit, but also
          replaces the usual Greenwood variance term with a
          simple approximation.  It is known to be conserva-
          tive.

_V_a_l_u_e_:

     a survfit object. Methods defined for survfit objects
     are print, plot, lines, and points.

_R_e_f_e_r_e_n_c_e_s_:

     Terry Therneau, author of local function.

     Dorey, F.J. and Korn, E.L. (1987).  Effective sample
     sizes for confidence intervals for survival probabili-
     ties.  Statistics in Medicine 6, 679-87.

     Fleming, T. H. and Harrington, D.P. (1984).  Nonpara-
     metric estimation of the survival distribution in cen-
     sored data.  Comm. in Statistics 13, 2469-86.

     Kablfleisch, 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 sur-
     vival function using Cox's proportional hazards model
     with covariates.  Biometrics 40, 601-610.

     Tsiatis, A. (1981). A large sample study of the esti-
     mate for the integrated hazard function in Cox's
     regression model for survival data. Annals of Statis-
     tics 9, 93-108.

_S_e_e _A_l_s_o_:

     `print', `plot', `lines', `coxph', `Surv', `strata'.

_E_x_a_m_p_l_e_s_:

     data(ovarian)
     #fit a Kaplan-Meier and plot it
     fit <- coxph( Surv(futime,fustat) ~ rx, ovarian)
     plot(fit)

     #fit a cox proportional hazards model and plot the
     #predicted survival curve
     fit <- coxph( Surv(futime,fustat) ~ rx, ovarian)
     plot( survfit( fit))

