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, stype=2, ctype,
            conf.type=c("log","log-log","plain","none", "logit", "arcsin"),
            censor=TRUE, start.time, id, influence=FALSE,
            na.action=na.pass, type, ...)

### 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.
`se.fit` | a logical value indicating whether standard errors should be computed. Default is `TRUE`.
`conf.int` | the level for a two-sided confidence interval on the survival curve(s). Default is 0.95.
`individual` | depricated argument, replaced by the general `id`
`stype` | computation of the survival curve, 1=direct, 2= exponenial of the cumulative hazard.
`ctype` | whether the cumulative hazard computation should have a correction for ties, 1=no, 2=yes.
`conf.type` | One of `"none"`, `"plain"`, `"log"` (the default), `"log-log"` or `"logit"`. 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 log-log option uses the log hazard or log(-log(survival)), and the logit log(survival/(1-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, it will be search for in the `newdata` data frame. Each group of rows in `newdata` 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 `newid` is not present, then each individual row of `newdata` is presumed to represent a distinct subject.
`start.time` | optional starting time, a single numeric value. If present the returned curve contains survival after `start.time` conditional on surviving to `start.time`.
`influence` | option to return the influence values
`na.action` | the na.action to be used on the newdata argument
`type` | older argument that encompassed `stype` and `ctype`, now depricated
`...` | for future methods

### Details

This routine produces survival curves based on a `coxph` model fit. The `ctype` option found in `survfit.formula` is not present, it instead follows from the choice of the `ties` option in the `coxph` call. Likewise the choice between a model based and robust variance estimate for the curve will mirror the choice made in the `coxph` call. The `cluster` and `influence` options are only relevant for the robust variance. A `id` statment in the original call causes subjects that have multiple lines in the original data to be correctly identified. (This calculation needs both the original data and the new data.)

If the `newdata` argument is missing, then a curve is produced for a single "pseudo" subject with covariate values equal to the means of the data set. The resulting curve(s) almost never make sense, but The default remains due to an 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 0.5 – 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 response 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 indicated 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 routine does not allow it to be omitted (predictions become too confusing). (Note that 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.)

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

### Value

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

### Notes

If the following pair of lines is used inside of another function then the `model=TRUE` argument must be added to the coxph call: `fit <- coxph(...); survfit(fit)`. This is a consequence of the non-standard evaluation process used by the `model.frame` function when a formula is involved.

### References

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. 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`.

[Package survival version 3.2-7 Index]