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"))
    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.

`fit` | a `coxph` object
`centered` | Compute the baseline hazard at the covariate mean rather than at zero?

### 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.

### 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`, `coxph`, `Surv`, `strata`.

### Examples

    #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[2])

    #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))

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