R: Compute a Survival Curve from a Cox model

survfit.coxph {survival} | R Documentation

## Compute a Survival Curve from a Cox model

### Description

Computes the predicted survivor function for a Cox proportional hazards model.

### Usage

    ## S3 method for class 'coxph'
    survfit(formula, newdata,
            se.fit=TRUE, conf.int=.95,
            individual=FALSE,
            type,vartype,
            conf.type=c("log","log-log","plain","none"), censor=TRUE, id,
            na.action=na.pass, ...)

### Arguments

`formula` | A `coxph` object.
`newdata` | a data frame with the same variable names as those that appear in the `coxph` formula. It is also valid to use a vector, if the data frame would consist of a single row. The curve(s) produced will be representative of a cohort whose covariates correspond to the values in `newdata`. Default is the mean of the covariates used in the `coxph` fit.
`individual` | This argument has been superseded by the `id` argument and is present only for backwards compatability. A logical value indicating whether each row of `newdata` represents a distinct individual (FALSE, the default), or if each row of the data frame represents different time epochs for only one individual (TRUE). In the former case the result will have one curve for each row in `newdata`, in the latter only a single curve will be produced.
`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,vartype` | a character string specifying the type of survival curve. Possible values are `"aalen"`, `"efron"`, or `"kalbfleish-prentice"` (only the first two characters are necessary). The default is to match the computation used in the Cox model. The Nelson-Aalen-Breslow estimate for `ties='breslow'`, the Efron estimate for `ties='efron'` and the Kalbfleisch-Prentice estimate for a discrete time model `ties='exact'`. Variance estimates are the Aalen-Link-Tsiatis, Efron, and Greenwood. The default will be the Efron estimate for `ties='efron'` and the Aalen estimate 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)).
`censor` | if FALSE time points at which there are no events (only censoring) are not included in the result.
`id` | optional variable name of subject identifiers. If this is present, then each group of rows with the same subject id represents the covariate path through time of a single subject, and the result will contain one curve per subject. If the `coxph` fit had strata then that must also be specified in `newdata`. If missing, then each individual row of `newdata` is presumed to represent a distinct subject and there will be `nrow(newdata)` times the number of strata curves in the result (one for each strata/subject combination). result.
`na.action` | the na.action to be used on the newdata argument
`...` | for future methods

### Details

Serious thought has been given to removing the ‘default’ for `newdata`, which is to use a single "psuedo" subject with covariate values equal to the means of the data set. The resulting curve(s) almost never make sense. It remains due to the unwarranted attachment to the option shown by some users and by other packages. Two particularly egregious examples are factor variables and interactions. Suppose one were studying interspecies transmission of a virus, and the data set has a factor variable with levels ("pig", "chicken") and about equal numbers of observations for each. The “mean” covariate level will be 1/2 – is this a flying pig? As to interactions assume data with sex coded as 0/1, ages ranging from 50 to 80, and a model with age*sex. The “mean” value for the age:sex interaction term will be about 30, a value that does not occur in the data. Users are strongly advised to use the newdata argument.

When the original model contains time-dependent covariates, then the path of that covariate through time needs to be specified in order to obtain a predicted curve. This requires `newdata` to contain multiple lines for each hypothetical subject which gives the covariate values, time interval, and strata for each line (a subject can change strata), along with an `id` variable which demarks which rows belong to each subject. The time interval must have the same (start, stop, status) variables as the original model: although the status variable is not used and thus can be set to a dummy value of 0 or 1, it is necessary for the variables to be recognized as a `Surv` object. Last, although predictions with a time-dependent covariate path can be useful, it is very easy to create a prediction that is senseless. Users are encouraged to seek out a text that discusses the issue in detail.

When a model contains strata but no time-dependent covariates the user of this routine has a choice. If newdata argument does not contain strata variables then the returned object will be a matrix of survival curves with one row for each strata in the model and one column for each row in newdata. (This is the historical behavior of the routine.) If newdata does contain strata variables, then the result will contain one curve per row of newdata, based on the appropriate stratum of the original model. In the rare case of a model with strata by covariate interactions the strata variable must be included in newdata. (The model Surv(time, status) ~ age*strata(sex) expands internally to strata(sex) + age:sex; the sex variable is needed for the second term of the model.)

When all the coefficients are zero, the Kalbfleisch-Prentice estimator reduces to the Kaplan-Meier, the Aalen estimate to the exponential of Nelson's cumulative hazard estimate, and the Efron estimate to the Fleming-Harrington estimate of survival. The variances of the curves from a Cox model are larger than these non-parametrec estimates, however, due to the variance of the coefficients.

See `survfit` for more details about the counts (number of events, number at risk, etc.)

The censor argument was fixed at FALSE in earlier versions of the code and not made available to the user. The default argument is sensible in most instances — and causes the familiar + sign to appear on plots — it is not sensible for time dependent covariates since it may lead to a large number of spurious marks.

### Value

an object of class `"survfit"`. See `survfit.object` for details. Methods defined for survfit objects are `print`, `plot`, `lines`, and `points`.

### References

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

Kablfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. New York:Wiley.

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

Therneau T and Grambsch P (2000), Modeling Survival Data: Extending the Cox Model, Springer-Verlag.

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

### Examples

    #fit a Kaplan-Meier and plot it
    fit <- survfit(Surv(time, status) ~ x, data = aml)
    plot(fit, lty = 2:3)
    legend(100, .8, c("Maintained", "Nonmaintained"), lty = 2:3)

    #fit a Cox proportional hazards model and plot the
    #predicted survival for a 60 year old
    fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian)
    plot(survfit(fit, newdata=data.frame(age=60)),
         xscale=365.25, xlab = "Years", ylab="Survival")

    # Here is the data set from Turnbull
    #  There are no interval censored subjects, only left-censored (status=3),
    #  right-censored (status 0) and observed events (status 1)
    #
    #                             Time
    #                         1    2   3   4
    # Type of observation
    #           death        12    6   2   3
    #          losses         3    2   0   3
    #      late entry         2    4   2   5
    #
    tdata <- data.frame(time  =c(1,1,1,2,2,2,3,3,3,4,4,4),
                        status=rep(c(1,0,2),4),
                        n     =c(12,3,2,6,2,4,2,0,2,3,3,5))
    fit  <- survfit(Surv(time, time, status, type='interval') ~1,
                  data=tdata, weight=n)

    #
    # Time to progression/death for patients with monoclonal gammopathy
    #  Competing risk curves (cumulative incidence)
    fit1 <- survfit(Surv(stop, event=='progression') ~1, data=mgus1,
                        subset=(start==0))
    fit2 <- survfit(Surv(stop, status) ~1, data=mgus1,
                        subset=(start==0), etype=event) #competing risks
    # CI curves are always plotted from 0 upwards, rather than 1 down
    plot(fit2, fun='event', xscale=365.25, xmax=7300, mark.time=FALSE,
                col=2:3, xlab="Years post diagnosis of MGUS")
    lines(fit1, fun='event', xscale=365.25, xmax=7300, mark.time=FALSE,
                conf.int=FALSE)
    text(10, .4, "Competing Risk: death", col=3)
    text(16, .15,"Competing Risk: progression", col=2)
    text(15, .30,"KM:prog")

[Package survival version 2.37-7 Index]