survfit.coxph: Compute a Survival Curve from a Cox model

Description

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

Usage

# S3 method for 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, time0=FALSE, ...)
# S3 method for coxphms
survfit(formula, newdata, 
        se.fit=FALSE, 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, p0=NULL, time0= FALSE, ...)

Value

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

Arguments

formula: A coxph object.
newdata: a data frame with the same variable names as those that appear in the coxph formula. One curve is produced per row. The curve(s) produced will be representative of a cohort whose covariates correspond to the values in newdata.
se.fit: a logical value indicating whether standard errors should be computed. Default is TRUE for standard models, FALSE for multi-state (code not yet present for that case.)
conf.int: the level for a two-sided confidence interval on the survival curve(s). Default is 0.95.
individual: deprecated 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 deprecated
p0: optional, a vector of probabilities. The returned curve will be for a cohort with this mixture of starting states. Most often a single state is chosen
time0: include the starting time for the curve in the output
...: for future methods

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.

Let \(\log[S(t; z)]\) be the log of the survival curve for a fixed covariate vector \(z\), then \(\log[S(t; x)]= e^{(x-z)\beta}\log[S(t; z)]\) is the log of the curve for any new covariate vector \(x\). There is an unfortunate tendency to refer to the reference curve with \(z=0\) as `THE' baseline hazard. However, any \(z\) can be used as the reference point, and more importantly, if \(x-z\) is large the compuation can suffer severe roundoff error. It is always safest to provide the desired \(x\) values directly via newdata.

Details

This routine produces Pr(state) curves based on a coxph model fit. For single state models it produces the single curve for S(t) = Pr(remain in initial state at time t), known as the survival curve; for multi-state models a matrix giving probabilities for all states. The stype argument states the type of estimate, and defaults to the exponential of the cumulative hazard, better known as the Breslow estimate. For a multi-state Cox model this involves the exponential of a matrix. The argument stype=1 uses a non-exponential or `direct' estimate. For a single endpoint coxph model the code evaluates the Kalbfleich-Prentice estimate, and for a multi-state model it uses an analog of the Aalen-Johansen estimator. The latter approach is the default in the mstate package.

The ctype option affects the estimated cumulative hazard, and if stype=2 the estimated P(state) curves as well. If not present it is chosen so as to be concordant with the ties option in the coxph call. (For multistate coxphms objects, only ctype=1 is currently implemented.) Likewise the choice between a model based and robust variance estimate for the curve will mirror the choice made in the coxph call, any clustering is also inherited from the parent model.

If the newdata argument is missing, then a curve is produced for a single "pseudo" subject with covariate values equal to the means component of the fit. The resulting curve(s) rarely make scientific sense, but the default remains due to an unwarranted belief by many that it represents an "average" curve, and it's use as a default in other packages. For coxph, the means component will contain the value 0 for any 0/1 or TRUE/FALSE variables, and the mean value in the data for others. Its primary reason for this default is to increase numerical accuracy in internal computations of the routine via recentering the X matrix; there is no reason to assume this represents an `interesting' hypothetical subject for prediction of their survival curve. Users are strongly advised to use the newdata argument; predictions from a multistate coxph model require the newdata argument.

If the coxph model contained an offset term, then the data set in the newdata argument should also contain that variable.

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.)

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.