Compute a Survival Curve for Censored Data
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.
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")) basehaz(fit,centered=TRUE)
- A formula object or a
coxphobject. If a formula object is supplied it must have a
Survobject as the response on the left of the
~operator and, if desired, terms separated by + operators on the right. One of the
- a data frame in which to interpret the variables named in the formula,
or in the
- 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
- expression saying that only a subset of the rows of the data should be used in the fit.
- a missing-data filter function, applied to the model frame, after any
subsetargument has been used. Default is
- a data frame with the same variable names as those that appear
coxphformula. Only applicable when
coxphobject. The curve(s) produced will be representative of a cohort who's covariates correspo
- 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 wi
- the level for a two-sided confidence interval on the survival curve(s). Default is 0.95.
- a logical value indicating whether standard errors should be
computed. Default is
- a character string specifying the type of survival curve.
Possible values are
"fh2"if a formula is given and
"kaplan-meier"if the first a
- either the string
"greenwood"for the Greenwood formula or
"tsiatis"for the Tsiatis formula, (only the first character is necessary). The default is
coxphobject is given, and it is
- One of
"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 c
- 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
- Compute the baseline hazard at the covariate mean rather than at zero?
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.
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.
survfitobject; see the help on
survfit.objectfor details. Methods defined for
survfitobjects are provided for
basehaz, a dataframe with the baseline hazard, times, and strata.
survfit(formula, data, weights, subset, na.action, ...)
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.
#fit a Kaplan-Meier and plot it data(aml) fit <- survfit(Surv(time, status) ~ x, data=aml) plot(fit) # plot only 1 of the 2 curves from above plot(fit) #fit a cox proportional hazards model and plot the #predicted survival curve data(ovarian) fit <- coxph( Surv(futime,fustat)~resid.ds+rx+ecog.ps,data=ovarian) plot( survfit( fit))