survfit {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[2])

#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))

[Package survival version 2.17 Index]